Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.3% → 42.8%

Time: 11.2s

Alternatives: 16

Speedup: 1.0×

• could not determine a ground truth

  1. c0 = -1.2764565454880982e+249
  2. w = -2.9758103134427115e-234
  3. h = -9.742015768100109e-293
  4. D = -4.012685700259268e-307
  5. d = 3.4893550364843115e+256
  6. M = -2.4459097697287245e+20

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \frac{c0}{2 \cdot w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M \cdot M}\right) \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	return (c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(c0, w, h, d, d_1, m)
use fmin_fmax_functions
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: t_0
    t_0 = (c0 * (d_1 * d_1)) / ((w * h) * (d * d))
    code = (c0 / (2.0d0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (m * m))))
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	return (c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))));
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	return (c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	return Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M)))))
end

MATLAB

function tmp = code(c0, w, h, D, d, M)
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = (c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))));
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Initial Program: 24.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \frac{c0}{2 \cdot w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M \cdot M}\right) \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	return (c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(c0, w, h, d, d_1, m)
use fmin_fmax_functions
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: t_0
    t_0 = (c0 * (d_1 * d_1)) / ((w * h) * (d * d))
    code = (c0 / (2.0d0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (m * m))))
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	return (c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))));
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	return (c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	return Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M)))))
end

MATLAB

function tmp = code(c0, w, h, D, d, M)
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = (c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))));
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 42.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D}\\ t_1 := \frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}\\ \mathbf{if}\;M\_m \leq 126000:\\ \;\;\;\;\frac{c0}{w + w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(t\_1, d, M\_m\right)} \cdot \sqrt{t\_1 \cdot d - M\_m}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ (/ (* (* (/ d D) c0) d) (* h w)) D))
        (t_1 (/ (* d c0) (* (* D (* h w)) D))))
   (if (<= M_m 126000.0)
     (* (/ c0 (+ w w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M_m M_m)))))
     (*
      (/ c0 (* 2.0 w))
      (+
       (/ (* d (* (/ d (* (* h w) D)) c0)) D)
       (* (sqrt (fma t_1 d M_m)) (sqrt (- (* t_1 d) M_m))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = ((((d / D) * c0) * d) / (h * w)) / D;
	double t_1 = (d * c0) / ((D * (h * w)) * D);
	double tmp;
	if (M_m <= 126000.0) {
		tmp = (c0 / (w + w)) * (t_0 + sqrt(((t_0 * t_0) - (M_m * M_m))));
	} else {
		tmp = (c0 / (2.0 * w)) * (((d * ((d / ((h * w) * D)) * c0)) / D) + (sqrt(fma(t_1, d, M_m)) * sqrt(((t_1 * d) - M_m))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(Float64(Float64(Float64(d / D) * c0) * d) / Float64(h * w)) / D)
	t_1 = Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D))
	tmp = 0.0
	if (M_m <= 126000.0)
		tmp = Float64(Float64(c0 / Float64(w + w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D) + Float64(sqrt(fma(t_1, d, M_m)) * sqrt(Float64(Float64(t_1 * d) - M_m)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(N[(N[(N[(d / D), $MachinePrecision] * c0), $MachinePrecision] * d), $MachinePrecision] / N[(h * w), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision]}, Block[{t$95$1 = N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[M$95$m, 126000.0], N[(N[(c0 / N[(w + w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision] + N[(N[Sqrt[N[(t$95$1 * d + M$95$m), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(t$95$1 * d), $MachinePrecision] - M$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if M < 126000

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right) \cdot d}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(\color{blue}{\frac{d}{\left(h \cdot w\right) \cdot D}} \cdot c0\right) \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot c0}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot c0}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       8. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(\frac{d}{D} \cdot \frac{c0}{h \cdot w}\right)} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(\color{blue}{\frac{d}{D}} \cdot \frac{c0}{h \cdot w}\right) \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       10. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\frac{d}{D} \cdot c0}{h \cdot w}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       11. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\frac{d}{D} \cdot c0}}{h \cdot w} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       12. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       13. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \left(\color{blue}{\frac{d}{D}} \cdot c0\right)}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       16. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\frac{d \cdot c0}{D}}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       17. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot \frac{c0}{D}\right)}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \left(d \cdot \color{blue}{\frac{c0}{D}}\right)}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot \frac{c0}{D}}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot \frac{c0}{D}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       21. lower-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot d\right) \cdot \frac{c0}{D}}{h \cdot w}}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   15. Applied rewrites 32.8%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]
   16. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right) \cdot d}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\left(\color{blue}{\frac{d}{\left(h \cdot w\right) \cdot D}} \cdot c0\right) \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot c0}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot c0}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       8. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\left(\frac{d}{D} \cdot \frac{c0}{h \cdot w}\right)} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\left(\color{blue}{\frac{d}{D}} \cdot \frac{c0}{h \cdot w}\right) \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       10. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\frac{d}{D} \cdot c0}{h \cdot w}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       11. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{\frac{d}{D} \cdot c0}}{h \cdot w} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       12. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       13. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \left(\color{blue}{\frac{d}{D}} \cdot c0\right)}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       16. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\frac{d \cdot c0}{D}}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       17. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot \frac{c0}{D}\right)}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \left(d \cdot \color{blue}{\frac{c0}{D}}\right)}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot \frac{c0}{D}}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot \frac{c0}{D}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       21. lower-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot d\right) \cdot \frac{c0}{D}}{h \cdot w}}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   17. Applied rewrites 33.2%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]
   18. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right) \cdot d}}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)} \cdot d}{D} - M \cdot M}\right) \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\left(\color{blue}{\frac{d}{\left(h \cdot w\right) \cdot D}} \cdot c0\right) \cdot d}{D} - M \cdot M}\right) \]

       5. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} - M \cdot M}\right) \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot c0}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot c0}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       8. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\left(\frac{d}{D} \cdot \frac{c0}{h \cdot w}\right)} \cdot d}{D} - M \cdot M}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\left(\color{blue}{\frac{d}{D}} \cdot \frac{c0}{h \cdot w}\right) \cdot d}{D} - M \cdot M}\right) \]

       10. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\frac{d}{D} \cdot c0}{h \cdot w}} \cdot d}{D} - M \cdot M}\right) \]

       11. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{\frac{d}{D} \cdot c0}}{h \cdot w} \cdot d}{D} - M \cdot M}\right) \]

       12. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} - M \cdot M}\right) \]

       13. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} - M \cdot M}\right) \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} - M \cdot M}\right) \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \left(\color{blue}{\frac{d}{D}} \cdot c0\right)}{h \cdot w}}{D} - M \cdot M}\right) \]

       16. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \color{blue}{\frac{d \cdot c0}{D}}}{h \cdot w}}{D} - M \cdot M}\right) \]

       17. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot \frac{c0}{D}\right)}}{h \cdot w}}{D} - M \cdot M}\right) \]

       18. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \left(d \cdot \color{blue}{\frac{c0}{D}}\right)}{h \cdot w}}{D} - M \cdot M}\right) \]

       19. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot \frac{c0}{D}}}{h \cdot w}}{D} - M \cdot M}\right) \]

       20. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot \frac{c0}{D}}{h \cdot w}}{D} - M \cdot M}\right) \]

       21. lower-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot d\right) \cdot \frac{c0}{D}}{h \cdot w}}}{D} - M \cdot M}\right) \]

   19. Applied rewrites 34.6%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} - M \cdot M}\right) \]
   20. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{\color{blue}{2 \cdot w}} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} - M \cdot M}\right) \]

       2. count-2-rev N/A

          \[\leadsto \frac{c0}{\color{blue}{w + w}} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} - M \cdot M}\right) \]

       3. lift-+.f64 34.6

          \[\leadsto \frac{c0}{\color{blue}{w + w}} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} - M \cdot M}\right) \]

   21. Applied rewrites 34.6%

       \[\leadsto \frac{c0}{\color{blue}{w + w}} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} - M \cdot M}\right) \]

   if 126000 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 35.7%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \color{blue}{\sqrt{\mathsf{fma}\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}, d, M\right)} \cdot \sqrt{\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d - M}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 42.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\\ t_1 := \frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}\\ \mathbf{if}\;M\_m \leq 1020000000000:\\ \;\;\;\;\frac{c0}{w + w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(t\_0 + \sqrt{\mathsf{fma}\left(t\_1, d, M\_m\right)} \cdot \sqrt{t\_1 \cdot d - M\_m}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ (* d (* (/ d (* (* h w) D)) c0)) D))
        (t_1 (/ (* d c0) (* (* D (* h w)) D))))
   (if (<= M_m 1020000000000.0)
     (* (/ c0 (+ w w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M_m M_m)))))
     (*
      (/ c0 (* 2.0 w))
      (+ t_0 (* (sqrt (fma t_1 d M_m)) (sqrt (- (* t_1 d) M_m))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (d * ((d / ((h * w) * D)) * c0)) / D;
	double t_1 = (d * c0) / ((D * (h * w)) * D);
	double tmp;
	if (M_m <= 1020000000000.0) {
		tmp = (c0 / (w + w)) * (t_0 + sqrt(((t_0 * t_0) - (M_m * M_m))));
	} else {
		tmp = (c0 / (2.0 * w)) * (t_0 + (sqrt(fma(t_1, d, M_m)) * sqrt(((t_1 * d) - M_m))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D)
	t_1 = Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D))
	tmp = 0.0
	if (M_m <= 1020000000000.0)
		tmp = Float64(Float64(c0 / Float64(w + w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + Float64(sqrt(fma(t_1, d, M_m)) * sqrt(Float64(Float64(t_1 * d) - M_m)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision]}, Block[{t$95$1 = N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[M$95$m, 1020000000000.0], N[(N[(c0 / N[(w + w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[(N[Sqrt[N[(t$95$1 * d + M$95$m), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(t$95$1 * d), $MachinePrecision] - M$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if M < 1.02e12

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. mult-flip N/A

          \[\leadsto \color{blue}{\left(c0 \cdot \frac{1}{2 \cdot w}\right)} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{2 \cdot w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. count-2-rev N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{w + w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. lift-+.f64 N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{w + w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. mult-flip N/A

          \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. lift-/.f64 36.0

          \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   15. Applied rewrites 36.0%

       \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   if 1.02e12 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 35.7%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \color{blue}{\sqrt{\mathsf{fma}\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}, d, M\right)} \cdot \sqrt{\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d - M}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 42.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\\ t_1 := \frac{d \cdot c0}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\\ \mathbf{if}\;M\_m \leq 10^{+21}:\\ \;\;\;\;\frac{c0}{w + w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\mathsf{fma}\left(t\_1, d, M\_m\right)} \cdot \sqrt{t\_1 \cdot d - M\_m}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ (* d (* (/ d (* (* h w) D)) c0)) D))
        (t_1 (/ (* d c0) (* (* (* D D) w) h))))
   (if (<= M_m 1e+21)
     (* (/ c0 (+ w w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M_m M_m)))))
     (*
      (/ c0 (* 2.0 w))
      (+
       (* (/ (* d c0) (* D (* h w))) (/ d D))
       (* (sqrt (fma t_1 d M_m)) (sqrt (- (* t_1 d) M_m))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (d * ((d / ((h * w) * D)) * c0)) / D;
	double t_1 = (d * c0) / (((D * D) * w) * h);
	double tmp;
	if (M_m <= 1e+21) {
		tmp = (c0 / (w + w)) * (t_0 + sqrt(((t_0 * t_0) - (M_m * M_m))));
	} else {
		tmp = (c0 / (2.0 * w)) * ((((d * c0) / (D * (h * w))) * (d / D)) + (sqrt(fma(t_1, d, M_m)) * sqrt(((t_1 * d) - M_m))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D)
	t_1 = Float64(Float64(d * c0) / Float64(Float64(Float64(D * D) * w) * h))
	tmp = 0.0
	if (M_m <= 1e+21)
		tmp = Float64(Float64(c0 / Float64(w + w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64(Float64(d * c0) / Float64(D * Float64(h * w))) * Float64(d / D)) + Float64(sqrt(fma(t_1, d, M_m)) * sqrt(Float64(Float64(t_1 * d) - M_m)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision]}, Block[{t$95$1 = N[(N[(d * c0), $MachinePrecision] / N[(N[(N[(D * D), $MachinePrecision] * w), $MachinePrecision] * h), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[M$95$m, 1e+21], N[(N[(c0 / N[(w + w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(d * c0), $MachinePrecision] / N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(d / D), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$1 * d + M$95$m), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(t$95$1 * d), $MachinePrecision] - M$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if M < 1e21

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. mult-flip N/A

          \[\leadsto \color{blue}{\left(c0 \cdot \frac{1}{2 \cdot w}\right)} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{2 \cdot w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. count-2-rev N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{w + w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. lift-+.f64 N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{w + w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. mult-flip N/A

          \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. lift-/.f64 36.0

          \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   15. Applied rewrites 36.0%

       \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   if 1e21 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

   9. Applied rewrites 32.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \color{blue}{\sqrt{\mathsf{fma}\left(\frac{d \cdot c0}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, d, M\right)} \cdot \sqrt{\frac{d \cdot c0}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d - M}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 41.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\\ \mathbf{if}\;M\_m \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{c0}{w + w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(t\_0 + \sqrt{\mathsf{fma}\left(-M\_m, M\_m, {\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ (* d (* (/ d (* (* h w) D)) c0)) D)))
   (if (<= M_m 4.5e+79)
     (* (/ c0 (+ w w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M_m M_m)))))
     (*
      (/ c0 (* 2.0 w))
      (+
       t_0
       (sqrt
        (fma
         (- M_m)
         M_m
         (pow (* (/ (* d c0) (* (* D (* h w)) D)) d) 2.0))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (d * ((d / ((h * w) * D)) * c0)) / D;
	double tmp;
	if (M_m <= 4.5e+79) {
		tmp = (c0 / (w + w)) * (t_0 + sqrt(((t_0 * t_0) - (M_m * M_m))));
	} else {
		tmp = (c0 / (2.0 * w)) * (t_0 + sqrt(fma(-M_m, M_m, pow((((d * c0) / ((D * (h * w)) * D)) * d), 2.0))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D)
	tmp = 0.0
	if (M_m <= 4.5e+79)
		tmp = Float64(Float64(c0 / Float64(w + w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(fma(Float64(-M_m), M_m, (Float64(Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D)) * d) ^ 2.0)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision]}, If[LessEqual[M$95$m, 4.5e+79], N[(N[(c0 / N[(w + w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[((-M$95$m) * M$95$m + N[Power[N[(N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if M < 4.49999999999999994e79

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. mult-flip N/A

          \[\leadsto \color{blue}{\left(c0 \cdot \frac{1}{2 \cdot w}\right)} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{2 \cdot w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. count-2-rev N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{w + w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. lift-+.f64 N/A

          \[\leadsto \left(c0 \cdot \frac{1}{\color{blue}{w + w}}\right) \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. mult-flip N/A

          \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. lift-/.f64 36.0

          \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   15. Applied rewrites 36.0%

       \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   if 4.49999999999999994e79 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}}\right) \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - \color{blue}{M \cdot M}}\right) \]

       3. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \left(\mathsf{neg}\left(M\right)\right) \cdot M}}\right) \]

       4. +-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\mathsf{neg}\left(M\right)\right) \cdot M + \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}}\right) \]

       5. lower-fma.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(M\right), M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}}\right) \]

       6. lower-neg.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(\color{blue}{-M}, M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}\right) \]

       7. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}\right)}\right) \]

       8. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

       9. lower-pow.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

   15. Applied rewrites 38.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(-M, M, {\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2}\right)}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 41.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := D \cdot \left(h \cdot w\right)\\ t_1 := \frac{d \cdot c0}{t\_0} \cdot \frac{d}{D}\\ \mathbf{if}\;M\_m \leq 2 \cdot 10^{+76}:\\ \;\;\;\;\frac{c0}{w + w} \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M\_m, M\_m, {\left(\frac{d \cdot c0}{t\_0 \cdot D} \cdot d\right)}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (* D (* h w))) (t_1 (* (/ (* d c0) t_0) (/ d D))))
   (if (<= M_m 2e+76)
     (* (/ c0 (+ w w)) (+ t_1 (sqrt (- (* t_1 t_1) (* M_m M_m)))))
     (*
      (/ c0 (* 2.0 w))
      (+
       (/ (* d (* (/ d (* (* h w) D)) c0)) D)
       (sqrt (fma (- M_m) M_m (pow (* (/ (* d c0) (* t_0 D)) d) 2.0))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = D * (h * w);
	double t_1 = ((d * c0) / t_0) * (d / D);
	double tmp;
	if (M_m <= 2e+76) {
		tmp = (c0 / (w + w)) * (t_1 + sqrt(((t_1 * t_1) - (M_m * M_m))));
	} else {
		tmp = (c0 / (2.0 * w)) * (((d * ((d / ((h * w) * D)) * c0)) / D) + sqrt(fma(-M_m, M_m, pow((((d * c0) / (t_0 * D)) * d), 2.0))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(D * Float64(h * w))
	t_1 = Float64(Float64(Float64(d * c0) / t_0) * Float64(d / D))
	tmp = 0.0
	if (M_m <= 2e+76)
		tmp = Float64(Float64(c0 / Float64(w + w)) * Float64(t_1 + sqrt(Float64(Float64(t_1 * t_1) - Float64(M_m * M_m)))));
	else
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D) + sqrt(fma(Float64(-M_m), M_m, (Float64(Float64(Float64(d * c0) / Float64(t_0 * D)) * d) ^ 2.0)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(d * c0), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(d / D), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[M$95$m, 2e+76], N[(N[(c0 / N[(w + w), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision] + N[Sqrt[N[((-M$95$m) * M$95$m + N[Power[N[(N[(N[(d * c0), $MachinePrecision] / N[(t$95$0 * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if M < 2.0000000000000001e76

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{\color{blue}{2 \cdot w}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. count-2-rev N/A

         \[\leadsto \frac{c0}{\color{blue}{w + w}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. lift-+.f64 35.0

         \[\leadsto \frac{c0}{\color{blue}{w + w}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 35.0%

      \[\leadsto \color{blue}{\frac{c0}{w + w}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   if 2.0000000000000001e76 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}}\right) \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - \color{blue}{M \cdot M}}\right) \]

       3. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \left(\mathsf{neg}\left(M\right)\right) \cdot M}}\right) \]

       4. +-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\mathsf{neg}\left(M\right)\right) \cdot M + \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}}\right) \]

       5. lower-fma.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(M\right), M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}}\right) \]

       6. lower-neg.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(\color{blue}{-M}, M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}\right) \]

       7. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}\right)}\right) \]

       8. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

       9. lower-pow.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

   15. Applied rewrites 38.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(-M, M, {\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2}\right)}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 41.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := D \cdot \left(h \cdot w\right)\\ t_1 := \frac{c0}{2 \cdot w}\\ t_2 := \frac{d \cdot c0}{t\_0 \cdot D} \cdot d\\ \mathbf{if}\;M\_m \leq 2.5 \cdot 10^{-239}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \mathbf{elif}\;M\_m \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;t\_1 \cdot \left(t\_2 + \sqrt{{t\_2}^{2} - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(\frac{d \cdot c0}{t\_0} \cdot \frac{d}{D} + \sqrt{\mathsf{fma}\left(-M\_m, M\_m, {\left(\frac{d \cdot c0}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (* D (* h w)))
        (t_1 (/ c0 (* 2.0 w)))
        (t_2 (* (/ (* d c0) (* t_0 D)) d)))
   (if (<= M_m 2.5e-239)
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w)))
     (if (<= M_m 1.5e+76)
       (* t_1 (+ t_2 (sqrt (- (pow t_2 2.0) (* M_m M_m)))))
       (*
        t_1
        (+
         (* (/ (* d c0) t_0) (/ d D))
         (sqrt
          (fma
           (- M_m)
           M_m
           (pow (* (/ (* d c0) (* (* (* D D) w) h)) d) 2.0)))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = D * (h * w);
	double t_1 = c0 / (2.0 * w);
	double t_2 = ((d * c0) / (t_0 * D)) * d;
	double tmp;
	if (M_m <= 2.5e-239) {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	} else if (M_m <= 1.5e+76) {
		tmp = t_1 * (t_2 + sqrt((pow(t_2, 2.0) - (M_m * M_m))));
	} else {
		tmp = t_1 * ((((d * c0) / t_0) * (d / D)) + sqrt(fma(-M_m, M_m, pow((((d * c0) / (((D * D) * w) * h)) * d), 2.0))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(D * Float64(h * w))
	t_1 = Float64(c0 / Float64(2.0 * w))
	t_2 = Float64(Float64(Float64(d * c0) / Float64(t_0 * D)) * d)
	tmp = 0.0
	if (M_m <= 2.5e-239)
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	elseif (M_m <= 1.5e+76)
		tmp = Float64(t_1 * Float64(t_2 + sqrt(Float64((t_2 ^ 2.0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(t_1 * Float64(Float64(Float64(Float64(d * c0) / t_0) * Float64(d / D)) + sqrt(fma(Float64(-M_m), M_m, (Float64(Float64(Float64(d * c0) / Float64(Float64(Float64(D * D) * w) * h)) * d) ^ 2.0)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(d * c0), $MachinePrecision] / N[(t$95$0 * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision]}, If[LessEqual[M$95$m, 2.5e-239], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[M$95$m, 1.5e+76], N[(t$95$1 * N[(t$95$2 + N[Sqrt[N[(N[Power[t$95$2, 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[(N[(N[(d * c0), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(d / D), $MachinePrecision]), $MachinePrecision] + N[Sqrt[N[((-M$95$m) * M$95$m + N[Power[N[(N[(N[(d * c0), $MachinePrecision] / N[(N[(N[(D * D), $MachinePrecision] * w), $MachinePrecision] * h), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if M < 2.5e-239

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]

   if 2.5e-239 < M < 1.4999999999999999e76

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 32.2%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d + \sqrt{{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2} - M \cdot M}\right)} \]

   if 1.4999999999999999e76 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

   9. Applied rewrites 33.9%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(-M, M, {\left(\frac{d \cdot c0}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)}^{2}\right)}}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\\ t_2 := D \cdot \left(h \cdot w\right)\\ \mathbf{if}\;M\_m \cdot M\_m \leq 5 \cdot 10^{+152}:\\ \;\;\;\;t\_0 \cdot \left(t\_1 + \sqrt{{\left(\frac{\left(d \cdot c0\right) \cdot \frac{d}{t\_2}}{\left|D\right|}\right)}^{2} - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(t\_1 + \sqrt{\mathsf{fma}\left(-M\_m, M\_m, {\left(\frac{d \cdot c0}{t\_2 \cdot D} \cdot d\right)}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w)))
        (t_1 (/ (* d (* (/ d (* (* h w) D)) c0)) D))
        (t_2 (* D (* h w))))
   (if (<= (* M_m M_m) 5e+152)
     (*
      t_0
      (+
       t_1
       (sqrt (- (pow (/ (* (* d c0) (/ d t_2)) (fabs D)) 2.0) (* M_m M_m)))))
     (*
      t_0
      (+
       t_1
       (sqrt (fma (- M_m) M_m (pow (* (/ (* d c0) (* t_2 D)) d) 2.0))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = (d * ((d / ((h * w) * D)) * c0)) / D;
	double t_2 = D * (h * w);
	double tmp;
	if ((M_m * M_m) <= 5e+152) {
		tmp = t_0 * (t_1 + sqrt((pow((((d * c0) * (d / t_2)) / fabs(D)), 2.0) - (M_m * M_m))));
	} else {
		tmp = t_0 * (t_1 + sqrt(fma(-M_m, M_m, pow((((d * c0) / (t_2 * D)) * d), 2.0))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(c0 / Float64(2.0 * w))
	t_1 = Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D)
	t_2 = Float64(D * Float64(h * w))
	tmp = 0.0
	if (Float64(M_m * M_m) <= 5e+152)
		tmp = Float64(t_0 * Float64(t_1 + sqrt(Float64((Float64(Float64(Float64(d * c0) * Float64(d / t_2)) / abs(D)) ^ 2.0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(t_0 * Float64(t_1 + sqrt(fma(Float64(-M_m), M_m, (Float64(Float64(Float64(d * c0) / Float64(t_2 * D)) * d) ^ 2.0)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision]}, Block[{t$95$2 = N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(M$95$m * M$95$m), $MachinePrecision], 5e+152], N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[Power[N[(N[(N[(d * c0), $MachinePrecision] * N[(d / t$95$2), $MachinePrecision]), $MachinePrecision] / N[Abs[D], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[((-M$95$m) * M$95$m + N[Power[N[(N[(N[(d * c0), $MachinePrecision] / N[(t$95$2 * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 M M) < 5e152

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

       4. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\left(d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)\right) \cdot \left(d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)\right)}{D \cdot D}} - M \cdot M}\right) \]

       5. sqr-abs-rev N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\left(d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)\right) \cdot \left(d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)\right)}{\color{blue}{\left|D\right| \cdot \left|D\right|}} - M \cdot M}\right) \]

       6. times-frac N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{\left|D\right|} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{\left|D\right|}} - M \cdot M}\right) \]

       7. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{\left|D\right|}\right)}^{2}} - M \cdot M}\right) \]

       8. lower-pow.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{\left|D\right|}\right)}^{2}} - M \cdot M}\right) \]

   15. Applied rewrites 34.3%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{{\left(\frac{\left(d \cdot c0\right) \cdot \frac{d}{D \cdot \left(h \cdot w\right)}}{\left|D\right|}\right)}^{2}} - M \cdot M}\right) \]

   if 5e152 < (*.f64 M M)

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}}\right) \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - \color{blue}{M \cdot M}}\right) \]

       3. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \left(\mathsf{neg}\left(M\right)\right) \cdot M}}\right) \]

       4. +-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\mathsf{neg}\left(M\right)\right) \cdot M + \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}}\right) \]

       5. lower-fma.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(M\right), M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}}\right) \]

       6. lower-neg.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(\color{blue}{-M}, M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}\right) \]

       7. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}\right)}\right) \]

       8. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

       9. lower-pow.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

   15. Applied rewrites 38.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(-M, M, {\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2}\right)}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 39.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := \frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\\ \mathbf{if}\;M\_m \leq 2.5 \cdot 10^{-239}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \mathbf{elif}\;M\_m \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;t\_0 \cdot \left(t\_1 + \sqrt{{t\_1}^{2} - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\mathsf{fma}\left(-M\_m, M\_m, {\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w))) (t_1 (* (/ (* d c0) (* (* D (* h w)) D)) d)))
   (if (<= M_m 2.5e-239)
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w)))
     (if (<= M_m 1.5e+76)
       (* t_0 (+ t_1 (sqrt (- (pow t_1 2.0) (* M_m M_m)))))
       (*
        t_0
        (+
         (/ (* c0 (* d d)) (* (* w h) (* D D)))
         (sqrt
          (fma
           (- M_m)
           M_m
           (pow (* (/ (* d d) (* (* (* D D) w) h)) c0) 2.0)))))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = ((d * c0) / ((D * (h * w)) * D)) * d;
	double tmp;
	if (M_m <= 2.5e-239) {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	} else if (M_m <= 1.5e+76) {
		tmp = t_0 * (t_1 + sqrt((pow(t_1, 2.0) - (M_m * M_m))));
	} else {
		tmp = t_0 * (((c0 * (d * d)) / ((w * h) * (D * D))) + sqrt(fma(-M_m, M_m, pow((((d * d) / (((D * D) * w) * h)) * c0), 2.0))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(c0 / Float64(2.0 * w))
	t_1 = Float64(Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D)) * d)
	tmp = 0.0
	if (M_m <= 2.5e-239)
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	elseif (M_m <= 1.5e+76)
		tmp = Float64(t_0 * Float64(t_1 + sqrt(Float64((t_1 ^ 2.0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(t_0 * Float64(Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D))) + sqrt(fma(Float64(-M_m), M_m, (Float64(Float64(Float64(d * d) / Float64(Float64(Float64(D * D) * w) * h)) * c0) ^ 2.0)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision]}, If[LessEqual[M$95$m, 2.5e-239], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[M$95$m, 1.5e+76], N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[Power[t$95$1, 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Sqrt[N[((-M$95$m) * M$95$m + N[Power[N[(N[(N[(d * d), $MachinePrecision] / N[(N[(N[(D * D), $MachinePrecision] * w), $MachinePrecision] * h), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if M < 2.5e-239

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]

   if 2.5e-239 < M < 1.4999999999999999e76

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 32.2%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d + \sqrt{{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2} - M \cdot M}\right)} \]

   if 1.4999999999999999e76 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \color{blue}{M \cdot M}}\right) \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \left(\mathsf{neg}\left(M\right)\right) \cdot M}}\right) \]

      4. +-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\color{blue}{\left(\mathsf{neg}\left(M\right)\right) \cdot M + \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}}}\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(M\right), M, \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\right)}}\right) \]

      6. lower-neg.f64 30.5

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\mathsf{fma}\left(\color{blue}{-M}, M, \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\right)}\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}}\right)}\right) \]

      8. pow2 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\right)}^{2}}\right)}\right) \]

      9. lower-pow.f64 30.5

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\right)}^{2}}\right)}\right) \]

   3. Applied rewrites 29.2%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\color{blue}{\mathsf{fma}\left(-M, M, {\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2}\right)}}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 39.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} \mathbf{if}\;M\_m \leq 2.5 \cdot 10^{-239}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M\_m, M\_m, {\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (if (<= M_m 2.5e-239)
   (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w)))
   (*
    (/ c0 (* 2.0 w))
    (+
     (/ (* d (* (/ d (* (* h w) D)) c0)) D)
     (sqrt
      (fma (- M_m) M_m (pow (* (/ (* d c0) (* (* D (* h w)) D)) d) 2.0)))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double tmp;
	if (M_m <= 2.5e-239) {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	} else {
		tmp = (c0 / (2.0 * w)) * (((d * ((d / ((h * w) * D)) * c0)) / D) + sqrt(fma(-M_m, M_m, pow((((d * c0) / ((D * (h * w)) * D)) * d), 2.0))));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	tmp = 0.0
	if (M_m <= 2.5e-239)
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	else
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64(d * Float64(Float64(d / Float64(Float64(h * w) * D)) * c0)) / D) + sqrt(fma(Float64(-M_m), M_m, (Float64(Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D)) * d) ^ 2.0)))));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := If[LessEqual[M$95$m, 2.5e-239], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(d * N[(N[(d / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * c0), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision] + N[Sqrt[N[((-M$95$m) * M$95$m + N[Power[N[(N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 2.5e-239

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]

   if 2.5e-239 < M

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}}\right) \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - \color{blue}{M \cdot M}}\right) \]

       3. fp-cancel-sub-sign-inv N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \left(\mathsf{neg}\left(M\right)\right) \cdot M}}\right) \]

       4. +-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\mathsf{neg}\left(M\right)\right) \cdot M + \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}}\right) \]

       5. lower-fma.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(M\right), M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}}\right) \]

       6. lower-neg.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(\color{blue}{-M}, M, \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}\right) \]

       7. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}}\right)}\right) \]

       8. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

       9. lower-pow.f64 43.1

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\mathsf{fma}\left(-M, M, \color{blue}{{\left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}\right)}^{2}}\right)}\right) \]

   15. Applied rewrites 38.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\mathsf{fma}\left(-M, M, {\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2}\right)}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 37.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\\ t_1 := \frac{c0}{2 \cdot w}\\ t_2 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_1 \cdot \left(t\_2 + \sqrt{t\_2 \cdot t\_2 - M\_m \cdot M\_m}\right) \leq \infty:\\ \;\;\;\;t\_1 \cdot \left(t\_0 + \sqrt{{t\_0}^{2} - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (* (/ (* d c0) (* (* D (* h w)) D)) d))
        (t_1 (/ c0 (* 2.0 w)))
        (t_2 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_1 (+ t_2 (sqrt (- (* t_2 t_2) (* M_m M_m))))) INFINITY)
     (* t_1 (+ t_0 (sqrt (- (pow t_0 2.0) (* M_m M_m)))))
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = ((d * c0) / ((D * (h * w)) * D)) * d;
	double t_1 = c0 / (2.0 * w);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_1 * (t_2 + sqrt(((t_2 * t_2) - (M_m * M_m))))) <= ((double) INFINITY)) {
		tmp = t_1 * (t_0 + sqrt((pow(t_0, 2.0) - (M_m * M_m))));
	} else {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Java

M_m = Math.abs(M);
public static double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = ((d * c0) / ((D * (h * w)) * D)) * d;
	double t_1 = c0 / (2.0 * w);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_1 * (t_2 + Math.sqrt(((t_2 * t_2) - (M_m * M_m))))) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 * (t_0 + Math.sqrt((Math.pow(t_0, 2.0) - (M_m * M_m))));
	} else {
		tmp = c0 * (0.5 * (Math.sqrt(-Math.pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
def code(c0, w, h, D, d, M_m):
	t_0 = ((d * c0) / ((D * (h * w)) * D)) * d
	t_1 = c0 / (2.0 * w)
	t_2 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_1 * (t_2 + math.sqrt(((t_2 * t_2) - (M_m * M_m))))) <= math.inf:
		tmp = t_1 * (t_0 + math.sqrt((math.pow(t_0, 2.0) - (M_m * M_m))))
	else:
		tmp = c0 * (0.5 * (math.sqrt(-math.pow(M_m, 2.0)) / w))
	return tmp

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D)) * d)
	t_1 = Float64(c0 / Float64(2.0 * w))
	t_2 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(t_1 * Float64(t_2 + sqrt(Float64(Float64(t_2 * t_2) - Float64(M_m * M_m))))) <= Inf)
		tmp = Float64(t_1 * Float64(t_0 + sqrt(Float64((t_0 ^ 2.0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
function tmp_2 = code(c0, w, h, D, d, M_m)
	t_0 = ((d * c0) / ((D * (h * w)) * D)) * d;
	t_1 = c0 / (2.0 * w);
	t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_1 * (t_2 + sqrt(((t_2 * t_2) - (M_m * M_m))))) <= Inf)
		tmp = t_1 * (t_0 + sqrt(((t_0 ^ 2.0) - (M_m * M_m))));
	else
		tmp = c0 * (0.5 * (sqrt(-(M_m ^ 2.0)) / w));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision]}, Block[{t$95$1 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(t$95$2 + N[Sqrt[N[(N[(t$95$2 * t$95$2), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 * N[(t$95$0 + N[Sqrt[N[(N[Power[t$95$0, 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < +inf.0

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 32.2%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d + \sqrt{{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2} - M \cdot M}\right)} \]

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 36.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}\\ t_1 := \frac{c0}{2 \cdot w}\\ t_2 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_1 \cdot \left(t\_2 + \sqrt{t\_2 \cdot t\_2 - M\_m \cdot M\_m}\right) \leq \infty:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(t\_0, d, \sqrt{{\left(t\_0 \cdot d\right)}^{2} - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ (* d c0) (* (* D (* h w)) D)))
        (t_1 (/ c0 (* 2.0 w)))
        (t_2 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_1 (+ t_2 (sqrt (- (* t_2 t_2) (* M_m M_m))))) INFINITY)
     (* t_1 (fma t_0 d (sqrt (- (pow (* t_0 d) 2.0) (* M_m M_m)))))
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (d * c0) / ((D * (h * w)) * D);
	double t_1 = c0 / (2.0 * w);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_1 * (t_2 + sqrt(((t_2 * t_2) - (M_m * M_m))))) <= ((double) INFINITY)) {
		tmp = t_1 * fma(t_0, d, sqrt((pow((t_0 * d), 2.0) - (M_m * M_m))));
	} else {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(d * c0) / Float64(Float64(D * Float64(h * w)) * D))
	t_1 = Float64(c0 / Float64(2.0 * w))
	t_2 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(t_1 * Float64(t_2 + sqrt(Float64(Float64(t_2 * t_2) - Float64(M_m * M_m))))) <= Inf)
		tmp = Float64(t_1 * fma(t_0, d, sqrt(Float64((Float64(t_0 * d) ^ 2.0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(d * c0), $MachinePrecision] / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(t$95$2 + N[Sqrt[N[(N[(t$95$2 * t$95$2), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 * N[(t$95$0 * d + N[Sqrt[N[(N[Power[N[(t$95$0 * d), $MachinePrecision], 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < +inf.0

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 30.7%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}, d, \sqrt{{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2} - M \cdot M}\right)} \]

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 36.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \left(D \cdot \left(h \cdot w\right)\right) \cdot D\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M\_m \cdot M\_m}\right) \leq \infty:\\ \;\;\;\;\frac{c0}{w + w} \cdot \mathsf{fma}\left(c0 \cdot \frac{d}{t\_0}, d, \sqrt{{\left(\frac{d \cdot c0}{t\_0} \cdot d\right)}^{2} - M\_m \cdot M\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (* (* D (* h w)) D)) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_1 (sqrt (- (* t_1 t_1) (* M_m M_m)))))
        INFINITY)
     (*
      (/ c0 (+ w w))
      (fma
       (* c0 (/ d t_0))
       d
       (sqrt (- (pow (* (/ (* d c0) t_0) d) 2.0) (* M_m M_m)))))
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (D * (h * w)) * D;
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_1 + sqrt(((t_1 * t_1) - (M_m * M_m))))) <= ((double) INFINITY)) {
		tmp = (c0 / (w + w)) * fma((c0 * (d / t_0)), d, sqrt((pow((((d * c0) / t_0) * d), 2.0) - (M_m * M_m))));
	} else {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(D * Float64(h * w)) * D)
	t_1 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_1 + sqrt(Float64(Float64(t_1 * t_1) - Float64(M_m * M_m))))) <= Inf)
		tmp = Float64(Float64(c0 / Float64(w + w)) * fma(Float64(c0 * Float64(d / t_0)), d, sqrt(Float64((Float64(Float64(Float64(d * c0) / t_0) * d) ^ 2.0) - Float64(M_m * M_m)))));
	else
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(c0 / N[(w + w), $MachinePrecision]), $MachinePrecision] * N[(N[(c0 * N[(d / t$95$0), $MachinePrecision]), $MachinePrecision] * d + N[Sqrt[N[(N[Power[N[(N[(N[(d * c0), $MachinePrecision] / t$95$0), $MachinePrecision] * d), $MachinePrecision], 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < +inf.0

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]

   15. Applied rewrites 30.5%

       \[\leadsto \color{blue}{\frac{c0}{w + w} \cdot \mathsf{fma}\left(c0 \cdot \frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}, d, \sqrt{{\left(\frac{d \cdot c0}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\right)}^{2} - M \cdot M}\right)} \]

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 36.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M\_m \cdot M\_m}\right) \leq \infty:\\ \;\;\;\;c0 \cdot \frac{\mathsf{fma}\left(t\_0, c0, \sqrt{{\left(t\_0 \cdot c0\right)}^{2} - M\_m \cdot M\_m}\right)}{w + w}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (* (/ d (* (* D (* h w)) D)) d))
        (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_1 (sqrt (- (* t_1 t_1) (* M_m M_m)))))
        INFINITY)
     (*
      c0
      (/ (fma t_0 c0 (sqrt (- (pow (* t_0 c0) 2.0) (* M_m M_m)))) (+ w w)))
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (d / ((D * (h * w)) * D)) * d;
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_1 + sqrt(((t_1 * t_1) - (M_m * M_m))))) <= ((double) INFINITY)) {
		tmp = c0 * (fma(t_0, c0, sqrt((pow((t_0 * c0), 2.0) - (M_m * M_m)))) / (w + w));
	} else {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(d / Float64(Float64(D * Float64(h * w)) * D)) * d)
	t_1 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_1 + sqrt(Float64(Float64(t_1 * t_1) - Float64(M_m * M_m))))) <= Inf)
		tmp = Float64(c0 * Float64(fma(t_0, c0, sqrt(Float64((Float64(t_0 * c0) ^ 2.0) - Float64(M_m * M_m)))) / Float64(w + w)));
	else
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(d / N[(N[(D * N[(h * w), $MachinePrecision]), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(c0 * N[(N[(t$95$0 * c0 + N[Sqrt[N[(N[Power[N[(t$95$0 * c0), $MachinePrecision], 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(w + w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < +inf.0

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right)} \cdot h} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot D\right)} \cdot \left(w \cdot h\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot D\right) \cdot \color{blue}{\left(h \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot D\right) \cdot \color{blue}{\left(h \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{D \cdot \left(D \cdot \left(h \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{D \cdot \color{blue}{\left(D \cdot \left(h \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 28.5

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.5%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right)} \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot D\right)} \cdot \left(w \cdot h\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot D\right) \cdot \color{blue}{\left(h \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot D\right) \cdot \color{blue}{\left(h \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{D \cdot \left(D \cdot \left(h \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{D \cdot \color{blue}{\left(D \cdot \left(h \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 31.0

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.0%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot \left(h \cdot w\right)\right) \cdot D}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 36.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M\_m \cdot M\_m}\right) \leq \infty:\\ \;\;\;\;c0 \cdot \frac{\mathsf{fma}\left(t\_0, c0, \sqrt{{\left(t\_0 \cdot c0\right)}^{2} - M\_m \cdot M\_m}\right)}{w + w}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (* (/ d (* (* D h) (* D w))) d))
        (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_1 (sqrt (- (* t_1 t_1) (* M_m M_m)))))
        INFINITY)
     (*
      c0
      (/ (fma t_0 c0 (sqrt (- (pow (* t_0 c0) 2.0) (* M_m M_m)))) (+ w w)))
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = (d / ((D * h) * (D * w))) * d;
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_1 + sqrt(((t_1 * t_1) - (M_m * M_m))))) <= ((double) INFINITY)) {
		tmp = c0 * (fma(t_0, c0, sqrt((pow((t_0 * c0), 2.0) - (M_m * M_m)))) / (w + w));
	} else {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(Float64(d / Float64(Float64(D * h) * Float64(D * w))) * d)
	t_1 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_1 + sqrt(Float64(Float64(t_1 * t_1) - Float64(M_m * M_m))))) <= Inf)
		tmp = Float64(c0 * Float64(fma(t_0, c0, sqrt(Float64((Float64(t_0 * c0) ^ 2.0) - Float64(M_m * M_m)))) / Float64(w + w)));
	else
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	end
	return tmp
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(N[(d / N[(N[(D * h), $MachinePrecision] * N[(D * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * d), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(c0 * N[(N[(t$95$0 * c0 + N[Sqrt[N[(N[Power[N[(t$95$0 * c0), $MachinePrecision], 2.0], $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(w + w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < +inf.0

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 17.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_0 \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M\_m \cdot M\_m}\right) \leq -\infty:\\ \;\;\;\;t\_0 \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{-1 \cdot {M\_m}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w))) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_1 (sqrt (- (* t_1 t_1) (* M_m M_m))))) (- INFINITY))
     (*
      t_0
      (+ (/ (/ (* (* (/ d D) c0) d) (* h w)) D) (sqrt (* -1.0 (pow M_m 2.0)))))
     (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M_m * M_m))))) <= -((double) INFINITY)) {
		tmp = t_0 * ((((((d / D) * c0) * d) / (h * w)) / D) + sqrt((-1.0 * pow(M_m, 2.0))));
	} else {
		tmp = c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Java

M_m = Math.abs(M);
public static double code(double c0, double w, double h, double D, double d, double M_m) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + Math.sqrt(((t_1 * t_1) - (M_m * M_m))))) <= -Double.POSITIVE_INFINITY) {
		tmp = t_0 * ((((((d / D) * c0) * d) / (h * w)) / D) + Math.sqrt((-1.0 * Math.pow(M_m, 2.0))));
	} else {
		tmp = c0 * (0.5 * (Math.sqrt(-Math.pow(M_m, 2.0)) / w));
	}
	return tmp;
}

Python

M_m = math.fabs(M)
def code(c0, w, h, D, d, M_m):
	t_0 = c0 / (2.0 * w)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_1 + math.sqrt(((t_1 * t_1) - (M_m * M_m))))) <= -math.inf:
		tmp = t_0 * ((((((d / D) * c0) * d) / (h * w)) / D) + math.sqrt((-1.0 * math.pow(M_m, 2.0))))
	else:
		tmp = c0 * (0.5 * (math.sqrt(-math.pow(M_m, 2.0)) / w))
	return tmp

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	t_0 = Float64(c0 / Float64(2.0 * w))
	t_1 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(t_0 * Float64(t_1 + sqrt(Float64(Float64(t_1 * t_1) - Float64(M_m * M_m))))) <= Float64(-Inf))
		tmp = Float64(t_0 * Float64(Float64(Float64(Float64(Float64(Float64(d / D) * c0) * d) / Float64(h * w)) / D) + sqrt(Float64(-1.0 * (M_m ^ 2.0)))));
	else
		tmp = Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)));
	end
	return tmp
end

MATLAB

M_m = abs(M);
function tmp_2 = code(c0, w, h, D, d, M_m)
	t_0 = c0 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M_m * M_m))))) <= -Inf)
		tmp = t_0 * ((((((d / D) * c0) * d) / (h * w)) / D) + sqrt((-1.0 * (M_m ^ 2.0))));
	else
		tmp = c0 * (0.5 * (sqrt(-(M_m ^ 2.0)) / w));
	end
	tmp_2 = tmp;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M$95$m * M$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(t$95$0 * N[(N[(N[(N[(N[(N[(d / D), $MachinePrecision] * c0), $MachinePrecision] * d), $MachinePrecision] / N[(h * w), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision] + N[Sqrt[N[(-1.0 * N[Power[M$95$m, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < -inf.0

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 23.8

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. Applied rewrites 23.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      18. lower-/.f64 24.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   5. Applied rewrites 24.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{c0 \cdot \color{blue}{\left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\color{blue}{\left(c0 \cdot d\right) \cdot d}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M \cdot M}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\left(w \cdot h\right) \cdot \color{blue}{\left(D \cdot D\right)}} - M \cdot M}\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \frac{\left(c0 \cdot d\right) \cdot d}{\color{blue}{\left(\left(w \cdot h\right) \cdot D\right) \cdot D}} - M \cdot M}\right) \]

      8. times-frac N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\color{blue}{\frac{c0 \cdot d}{\left(w \cdot h\right) \cdot D}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{\color{blue}{d \cdot c0}}{\left(w \cdot h\right) \cdot D} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{\color{blue}{D \cdot \left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(w \cdot h\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \color{blue}{\left(h \cdot w\right)}} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lower-/.f64 35.0

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      6. associate-*l/ N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      7. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      9. associate-*l* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      13. associate-/l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      14. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      17. lower-/.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

      20. lower-*.f64 33.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   9. Applied rewrites 33.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       17. lower-/.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

       20. lower-*.f64 33.9

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]

   11. Applied rewrites 33.9%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right) - M \cdot M}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \frac{d}{D}\right)} - M \cdot M}\right) \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \left(\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot \color{blue}{\frac{d}{D}}\right) - M \cdot M}\right) \]

       3. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)} \cdot d}{D}} - M \cdot M}\right) \]

       5. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       6. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot c0\right) \cdot d}{D \cdot \left(h \cdot w\right)}}}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot c0\right)}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       9. associate-*l* N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot c0}}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       10. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot c0}{D \cdot \left(h \cdot w\right)}}{D} - M \cdot M}\right) \]

       11. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\frac{d \cdot d}{D \cdot \left(h \cdot w\right)} \cdot c0}}{D} - M \cdot M}\right) \]

       12. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\frac{\color{blue}{d \cdot d}}{D \cdot \left(h \cdot w\right)} \cdot c0}{D} - M \cdot M}\right) \]

       13. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{\left(d \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right)} \cdot c0}{D} - M \cdot M}\right) \]

       14. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \color{blue}{\left(\frac{d}{D \cdot \left(h \cdot w\right)} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       17. lower-/.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\color{blue}{\frac{d}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lower-*.f64 36.0

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot c0\right)}{D} - M \cdot M}\right) \]

   13. Applied rewrites 36.0%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \color{blue}{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D}} - M \cdot M}\right) \]
   14. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right) \cdot d}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(\color{blue}{\frac{d}{\left(h \cdot w\right) \cdot D}} \cdot c0\right) \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{d \cdot c0}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot c0}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot c0}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       8. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\left(\frac{d}{D} \cdot \frac{c0}{h \cdot w}\right)} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\left(\color{blue}{\frac{d}{D}} \cdot \frac{c0}{h \cdot w}\right) \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       10. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\frac{d}{D} \cdot c0}{h \cdot w}} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       11. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\frac{d}{D} \cdot c0}}{h \cdot w} \cdot d}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       12. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       13. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{d \cdot \left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \left(\color{blue}{\frac{d}{D}} \cdot c0\right)}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       16. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\frac{d \cdot c0}{D}}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       17. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \color{blue}{\left(d \cdot \frac{c0}{D}\right)}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{d \cdot \left(d \cdot \color{blue}{\frac{c0}{D}}\right)}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot \frac{c0}{D}}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot \frac{c0}{D}}{h \cdot w}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       21. lower-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(d \cdot d\right) \cdot \frac{c0}{D}}{h \cdot w}}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   15. Applied rewrites 32.8%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} + \sqrt{\frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]
   16. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right) \cdot d}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\left(\color{blue}{\frac{d}{\left(h \cdot w\right) \cdot D}} \cdot c0\right) \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       5. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{d \cdot c0}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot c0}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot c0}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       8. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\left(\frac{d}{D} \cdot \frac{c0}{h \cdot w}\right)} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\left(\color{blue}{\frac{d}{D}} \cdot \frac{c0}{h \cdot w}\right) \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       10. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\frac{d}{D} \cdot c0}{h \cdot w}} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       11. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{\frac{d}{D} \cdot c0}}{h \cdot w} \cdot d}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       12. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       13. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{d \cdot \left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \left(\color{blue}{\frac{d}{D}} \cdot c0\right)}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       16. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\frac{d \cdot c0}{D}}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       17. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \color{blue}{\left(d \cdot \frac{c0}{D}\right)}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       18. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{d \cdot \left(d \cdot \color{blue}{\frac{c0}{D}}\right)}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       19. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot \frac{c0}{D}}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       20. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot \frac{c0}{D}}{h \cdot w}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

       21. lower-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\left(d \cdot d\right) \cdot \frac{c0}{D}}{h \cdot w}}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]

   17. Applied rewrites 33.2%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} \cdot \frac{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}{D} - M \cdot M}\right) \]
   18. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{d \cdot \left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)}}{D} - M \cdot M}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right) \cdot d}}{D} - M \cdot M}\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\left(\frac{d}{\left(h \cdot w\right) \cdot D} \cdot c0\right)} \cdot d}{D} - M \cdot M}\right) \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\left(\color{blue}{\frac{d}{\left(h \cdot w\right) \cdot D}} \cdot c0\right) \cdot d}{D} - M \cdot M}\right) \]

       5. associate-*l/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{d \cdot c0}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} - M \cdot M}\right) \]

       6. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot c0}{\color{blue}{\left(h \cdot w\right) \cdot D}} \cdot d}{D} - M \cdot M}\right) \]

       7. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot c0}{\color{blue}{D \cdot \left(h \cdot w\right)}} \cdot d}{D} - M \cdot M}\right) \]

       8. frac-times N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\left(\frac{d}{D} \cdot \frac{c0}{h \cdot w}\right)} \cdot d}{D} - M \cdot M}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\left(\color{blue}{\frac{d}{D}} \cdot \frac{c0}{h \cdot w}\right) \cdot d}{D} - M \cdot M}\right) \]

       10. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\frac{d}{D} \cdot c0}{h \cdot w}} \cdot d}{D} - M \cdot M}\right) \]

       11. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{\frac{d}{D} \cdot c0}}{h \cdot w} \cdot d}{D} - M \cdot M}\right) \]

       12. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} - M \cdot M}\right) \]

       13. *-commutative N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{d \cdot \left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} - M \cdot M}\right) \]

       14. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(\frac{d}{D} \cdot c0\right)}}{h \cdot w}}{D} - M \cdot M}\right) \]

       15. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \left(\color{blue}{\frac{d}{D}} \cdot c0\right)}{h \cdot w}}{D} - M \cdot M}\right) \]

       16. associate-*l/ N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \color{blue}{\frac{d \cdot c0}{D}}}{h \cdot w}}{D} - M \cdot M}\right) \]

       17. associate-/l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \color{blue}{\left(d \cdot \frac{c0}{D}\right)}}{h \cdot w}}{D} - M \cdot M}\right) \]

       18. lift-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{d \cdot \left(d \cdot \color{blue}{\frac{c0}{D}}\right)}{h \cdot w}}{D} - M \cdot M}\right) \]

       19. associate-*l* N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right) \cdot \frac{c0}{D}}}{h \cdot w}}{D} - M \cdot M}\right) \]

       20. lift-*.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\frac{\color{blue}{\left(d \cdot d\right)} \cdot \frac{c0}{D}}{h \cdot w}}{D} - M \cdot M}\right) \]

       21. lower-/.f64 N/A

           \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\left(d \cdot d\right) \cdot \frac{c0}{D}}{h \cdot w}}}{D} - M \cdot M}\right) \]

   19. Applied rewrites 34.6%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} \cdot \frac{\color{blue}{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}}{D} - M \cdot M}\right) \]

   20. Taylor expanded in c0 around 0

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\color{blue}{-1 \cdot {M}^{2}}}\right) \]
   21. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{-1 \cdot \color{blue}{{M}^{2}}}\right) \]

       2. lower-pow.f64 10.6

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{-1 \cdot {M}^{\color{blue}{2}}}\right) \]

   22. Applied rewrites 10.6%

       \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left(\frac{d}{D} \cdot c0\right) \cdot d}{h \cdot w}}{D} + \sqrt{\color{blue}{-1 \cdot {M}^{2}}}\right) \]

   if -inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 24.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   3. Applied rewrites 24.4%

      \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 24.4

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. Applied rewrites 24.4%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. associate-/l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-/.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. lower-*.f64 29.1

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. Applied rewrites 29.1%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      2. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      3. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      4. lift-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      5. associate-*l* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      6. associate-*r* N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      7. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      8. *-commutative N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      9. lower-*.f64 N/A

         \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      10. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      11. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

      12. lower-*.f64 28.7

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. Applied rewrites 28.7%

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       2. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       3. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       4. lift-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       5. associate-*l* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       6. associate-*r* N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       7. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       8. *-commutative N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       9. lower-*.f64 N/A

          \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       10. lower-*.f64 N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       11. *-commutative N/A

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

       12. lower-*.f64 31.4

           \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. Applied rewrites 31.4%

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. Taylor expanded in c0 around 0

       \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

       2. lower-/.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

       3. lower-sqrt.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

       5. lower-pow.f64 14.9

          \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

   14. Applied rewrites 14.9%

       \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 14.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M\_m}^{2}}}{w}\right) \end{array} \]

FPCore

M_m = (fabs.f64 M)
(FPCore (c0 w h D d M_m)
 :precision binary64
 (* c0 (* 0.5 (/ (sqrt (- (pow M_m 2.0))) w))))

C

M_m = fabs(M);
double code(double c0, double w, double h, double D, double d, double M_m) {
	return c0 * (0.5 * (sqrt(-pow(M_m, 2.0)) / w));
}

Fortran

M_m =     private
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(c0, w, h, d, d_1, m_m)
use fmin_fmax_functions
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m_m
    code = c0 * (0.5d0 * (sqrt(-(m_m ** 2.0d0)) / w))
end function

Java

M_m = Math.abs(M);
public static double code(double c0, double w, double h, double D, double d, double M_m) {
	return c0 * (0.5 * (Math.sqrt(-Math.pow(M_m, 2.0)) / w));
}

Python

M_m = math.fabs(M)
def code(c0, w, h, D, d, M_m):
	return c0 * (0.5 * (math.sqrt(-math.pow(M_m, 2.0)) / w))

Julia

M_m = abs(M)
function code(c0, w, h, D, d, M_m)
	return Float64(c0 * Float64(0.5 * Float64(sqrt(Float64(-(M_m ^ 2.0))) / w)))
end

MATLAB

M_m = abs(M);
function tmp = code(c0, w, h, D, d, M_m)
	tmp = c0 * (0.5 * (sqrt(-(M_m ^ 2.0)) / w));
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
code[c0_, w_, h_, D_, d_, M$95$m_] := N[(c0 * N[(0.5 * N[(N[Sqrt[(-N[Power[M$95$m, 2.0], $MachinePrecision])], $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 24.3%

   \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]

   2. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{c0}{2 \cdot w}} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{c0 \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}{2 \cdot w}} \]

   4. associate-/l* N/A

      \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{c0 \cdot \frac{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}{2 \cdot w}} \]

3. Applied rewrites 24.4%

   \[\leadsto \color{blue}{c0 \cdot \frac{\mathsf{fma}\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w}} \]
4. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   2. lift-*.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   3. associate-/l* N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   4. lift-/.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. *-commutative N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   6. lower-*.f64 24.4

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

5. Applied rewrites 24.4%

   \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d}, c0, \sqrt{{\left(\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   2. lift-*.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\frac{\color{blue}{d \cdot d}}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   3. associate-/l* N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   4. lift-/.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\left(d \cdot \color{blue}{\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}}\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. *-commutative N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   6. lower-*.f64 29.1

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

7. Applied rewrites 29.1%

   \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d, c0, \sqrt{{\left(\color{blue}{\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right)} \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   2. *-commutative N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   3. lift-*.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   4. lift-*.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   5. associate-*l* N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   6. associate-*r* N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   7. *-commutative N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   8. *-commutative N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   9. lower-*.f64 N/A

      \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   10. lower-*.f64 N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   11. *-commutative N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

   12. lower-*.f64 28.7

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

9. Applied rewrites 28.7%

   \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]
10. Step-by-step derivation

    1. lift-*.f64 N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(\left(D \cdot D\right) \cdot w\right) \cdot h}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    2. *-commutative N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{h \cdot \left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    3. lift-*.f64 N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(\left(D \cdot D\right) \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    4. lift-*.f64 N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    5. associate-*l* N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{h \cdot \color{blue}{\left(D \cdot \left(D \cdot w\right)\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    6. associate-*r* N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(h \cdot D\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    7. *-commutative N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(D \cdot w\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    8. *-commutative N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    9. lower-*.f64 N/A

       \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(w \cdot D\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    10. lower-*.f64 N/A

        \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right)} \cdot \left(w \cdot D\right)} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    11. *-commutative N/A

        \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

    12. lower-*.f64 31.4

        \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\left(D \cdot h\right) \cdot \color{blue}{\left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

11. Applied rewrites 31.4%

    \[\leadsto c0 \cdot \frac{\mathsf{fma}\left(\frac{d}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)} \cdot d, c0, \sqrt{{\left(\left(\frac{d}{\color{blue}{\left(D \cdot h\right) \cdot \left(D \cdot w\right)}} \cdot d\right) \cdot c0\right)}^{2} - M \cdot M}\right)}{w + w} \]

12. Taylor expanded in c0 around 0

    \[\leadsto c0 \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right)} \]
13. Step-by-step derivation

    1. lower-*.f64 N/A

       \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \color{blue}{\frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}}\right) \]

    2. lower-/.f64 N/A

       \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{\color{blue}{w}}\right) \]

    3. lower-sqrt.f64 N/A

       \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{\mathsf{neg}\left({M}^{2}\right)}}{w}\right) \]

    4. lower-neg.f64 N/A

       \[\leadsto c0 \cdot \left(\frac{1}{2} \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

    5. lower-pow.f64 14.9

       \[\leadsto c0 \cdot \left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right) \]

14. Applied rewrites 14.9%

    \[\leadsto c0 \cdot \color{blue}{\left(0.5 \cdot \frac{\sqrt{-{M}^{2}}}{w}\right)} \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2025164 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ c0 (* 2.0 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))