Henrywood and Agarwal, Equation (13)

Percentage Accurate: 25.0% → 69.2%

Time: 9.2s

Alternatives: 8

Speedup: N/A×

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: 25.0% 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: 69.2% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := {\left(D \cdot M\right)}^{1}\\ t_2 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_0 \cdot \left(t\_2 + \sqrt{t\_2 \cdot t\_2 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;t\_0 \cdot \frac{\frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{h \cdot w}}{D}}{D}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(t\_1 \cdot t\_1\right) \cdot h}{d}}{d} \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w)))
        (t_1 (pow (* D M) 1.0))
        (t_2 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_2 (sqrt (- (* t_2 t_2) (* M M))))) INFINITY)
     (* t_0 (/ (/ (/ (* (* (* d d) c0) 2.0) (* h w)) D) D))
     (* (/ (/ (* (* t_1 t_1) h) d) d) 0.25))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = pow((D * M), 1.0);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_2 + sqrt(((t_2 * t_2) - (M * M))))) <= ((double) INFINITY)) {
		tmp = t_0 * ((((((d * d) * c0) * 2.0) / (h * w)) / D) / D);
	} else {
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = Math.pow((D * M), 1.0);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_2 + Math.sqrt(((t_2 * t_2) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = t_0 * ((((((d * d) * c0) * 2.0) / (h * w)) / D) / D);
	} else {
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = c0 / (2.0 * w)
	t_1 = math.pow((D * M), 1.0)
	t_2 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_2 + math.sqrt(((t_2 * t_2) - (M * M))))) <= math.inf:
		tmp = t_0 * ((((((d * d) * c0) * 2.0) / (h * w)) / D) / D)
	else:
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(c0 / Float64(2.0 * w))
	t_1 = Float64(D * M) ^ 1.0
	t_2 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(t_0 * Float64(t_2 + sqrt(Float64(Float64(t_2 * t_2) - Float64(M * M))))) <= Inf)
		tmp = Float64(t_0 * Float64(Float64(Float64(Float64(Float64(Float64(d * d) * c0) * 2.0) / Float64(h * w)) / D) / D));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(t_1 * t_1) * h) / d) / d) * 0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (D * M) ^ 1.0;
	t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_2 + sqrt(((t_2 * t_2) - (M * M))))) <= Inf)
		tmp = t_0 * ((((((d * d) * c0) * 2.0) / (h * w)) / D) / D);
	else
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(D * M), $MachinePrecision], 1.0], $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$0 * N[(t$95$2 + N[Sqrt[N[(N[(t$95$2 * t$95$2), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(N[(N[(N[(d * d), $MachinePrecision] * c0), $MachinePrecision] * 2.0), $MachinePrecision] / N[(h * w), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision] / D), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t$95$1 * t$95$1), $MachinePrecision] * h), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] * 0.25), $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 80.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. pow2 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{{D}^{2} \cdot \left(h \cdot w\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{{D}^{2} \cdot \left(h \cdot w\right)} \]

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. pow2 N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      15. lower-*.f64 83.5

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

   5. Applied rewrites 83.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      10. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left({d}^{2} \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(c0 \cdot {d}^{2}\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(c0 \cdot {d}^{2}\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(c0 \cdot {d}^{2}\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(c0 \cdot {d}^{2}\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      15. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left({d}^{2} \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      16. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      19. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      20. lift-*.f64 85.7

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

   7. Applied rewrites 85.7%

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

      1. lift-/.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      7. associate-/r* N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{h \cdot w}}{D}}{D} \]

      8. *-commutative N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{h \cdot w}}{D}}{D} \]

      9. pow2 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\frac{2 \cdot \left({d}^{2} \cdot c0\right)}{h \cdot w}}{D}}{D} \]

      10. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\frac{2 \cdot \left(c0 \cdot {d}^{2}\right)}{h \cdot w}}{D}}{D} \]

      11. associate-*r/ N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \frac{c0 \cdot {d}^{2}}{h \cdot w}}{D}}{D} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \frac{c0 \cdot {d}^{2}}{h \cdot w}}{D}}{D} \]

   9. Applied rewrites 85.8%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{h \cdot w}}{D}}{D} \]

   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 0.0%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   5. Applied rewrites 0.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

   6. Taylor expanded in c0 around 0

      \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      6. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. pow2 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      12. lift-*.f64 39.9

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

   8. Applied rewrites 39.9%

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

   10. Applied rewrites 49.1%

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot 0.25 \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       4. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       5. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       6. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       7. associate-*r* N/A

          \[\leadsto \frac{\frac{\left({M}^{2} \cdot {D}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       8. *-commutative N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       10. pow-prod-down N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{2} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       11. metadata-eval N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{\left(1 + 1\right)} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       12. unpow-prod-up N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       13. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       14. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       16. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       17. lower-*.f64 62.6

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]

   12. Applied rewrites 62.6%

       \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 68.7% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := {\left(D \cdot M\right)}^{1}\\ t_2 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_0 \cdot \left(t\_2 + \sqrt{t\_2 \cdot t\_2 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;t\_0 \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(t\_1 \cdot t\_1\right) \cdot h}{d}}{d} \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w)))
        (t_1 (pow (* D M) 1.0))
        (t_2 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_2 (sqrt (- (* t_2 t_2) (* M M))))) INFINITY)
     (* t_0 (/ (/ (* (* (* d d) c0) 2.0) (* (* h w) D)) D))
     (* (/ (/ (* (* t_1 t_1) h) d) d) 0.25))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = pow((D * M), 1.0);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_2 + sqrt(((t_2 * t_2) - (M * M))))) <= ((double) INFINITY)) {
		tmp = t_0 * (((((d * d) * c0) * 2.0) / ((h * w) * D)) / D);
	} else {
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = Math.pow((D * M), 1.0);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_2 + Math.sqrt(((t_2 * t_2) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = t_0 * (((((d * d) * c0) * 2.0) / ((h * w) * D)) / D);
	} else {
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = c0 / (2.0 * w)
	t_1 = math.pow((D * M), 1.0)
	t_2 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_2 + math.sqrt(((t_2 * t_2) - (M * M))))) <= math.inf:
		tmp = t_0 * (((((d * d) * c0) * 2.0) / ((h * w) * D)) / D)
	else:
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(c0 / Float64(2.0 * w))
	t_1 = Float64(D * M) ^ 1.0
	t_2 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(t_0 * Float64(t_2 + sqrt(Float64(Float64(t_2 * t_2) - Float64(M * M))))) <= Inf)
		tmp = Float64(t_0 * Float64(Float64(Float64(Float64(Float64(d * d) * c0) * 2.0) / Float64(Float64(h * w) * D)) / D));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(t_1 * t_1) * h) / d) / d) * 0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (D * M) ^ 1.0;
	t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_2 + sqrt(((t_2 * t_2) - (M * M))))) <= Inf)
		tmp = t_0 * (((((d * d) * c0) * 2.0) / ((h * w) * D)) / D);
	else
		tmp = ((((t_1 * t_1) * h) / d) / d) * 0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(D * M), $MachinePrecision], 1.0], $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$0 * N[(t$95$2 + N[Sqrt[N[(N[(t$95$2 * t$95$2), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(N[(N[(d * d), $MachinePrecision] * c0), $MachinePrecision] * 2.0), $MachinePrecision] / N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t$95$1 * t$95$1), $MachinePrecision] * h), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] * 0.25), $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 80.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. pow2 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{{D}^{2} \cdot \left(h \cdot w\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{{D}^{2} \cdot \left(h \cdot w\right)} \]

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. pow2 N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      15. lower-*.f64 83.5

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

   5. Applied rewrites 83.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D} \]

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(\left(d \cdot d\right) \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      10. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left({d}^{2} \cdot c0\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      11. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(c0 \cdot {d}^{2}\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      12. lower-/.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{2 \cdot \left(c0 \cdot {d}^{2}\right)}{\left(h \cdot w\right) \cdot D}}{D} \]

      13. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(c0 \cdot {d}^{2}\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(c0 \cdot {d}^{2}\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      15. *-commutative N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left({d}^{2} \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      16. pow2 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      18. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      19. lift-*.f64 N/A

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

      20. lift-*.f64 85.7

          \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\frac{\left(\left(d \cdot d\right) \cdot c0\right) \cdot 2}{\left(h \cdot w\right) \cdot D}}{D} \]

   7. Applied rewrites 85.7%

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

   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 0.0%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   5. Applied rewrites 0.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

   6. Taylor expanded in c0 around 0

      \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      6. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. pow2 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      12. lift-*.f64 39.9

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

   8. Applied rewrites 39.9%

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

   10. Applied rewrites 49.1%

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot 0.25 \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       4. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       5. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       6. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       7. associate-*r* N/A

          \[\leadsto \frac{\frac{\left({M}^{2} \cdot {D}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       8. *-commutative N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       10. pow-prod-down N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{2} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       11. metadata-eval N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{\left(1 + 1\right)} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       12. unpow-prod-up N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       13. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       14. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       16. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       17. lower-*.f64 62.6

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]

   12. Applied rewrites 62.6%

       \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 68.3% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(D \cdot M\right)}^{1}\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;\left(d \cdot c0\right) \cdot \frac{d \cdot c0}{\left(\left(\left(h \cdot w\right) \cdot D\right) \cdot D\right) \cdot w}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(t\_0 \cdot t\_0\right) \cdot h}{d}}{d} \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (pow (* D M) 1.0)) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_1 (sqrt (- (* t_1 t_1) (* M M)))))
        INFINITY)
     (* (* d c0) (/ (* d c0) (* (* (* (* h w) D) D) w)))
     (* (/ (/ (* (* t_0 t_0) h) d) d) 0.25))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = pow((D * M), 1.0);
	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))))) <= ((double) INFINITY)) {
		tmp = (d * c0) * ((d * c0) / ((((h * w) * D) * D) * w));
	} else {
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = Math.pow((D * M), 1.0);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_1 + Math.sqrt(((t_1 * t_1) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = (d * c0) * ((d * c0) / ((((h * w) * D) * D) * w));
	} else {
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = math.pow((D * M), 1.0)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_1 + math.sqrt(((t_1 * t_1) - (M * M))))) <= math.inf:
		tmp = (d * c0) * ((d * c0) / ((((h * w) * D) * D) * w))
	else:
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(D * M) ^ 1.0
	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))))) <= Inf)
		tmp = Float64(Float64(d * c0) * Float64(Float64(d * c0) / Float64(Float64(Float64(Float64(h * w) * D) * D) * w)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(t_0 * t_0) * h) / d) / d) * 0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = (D * M) ^ 1.0;
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = (d * c0) * ((d * c0) / ((((h * w) * D) * D) * w));
	else
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[Power[N[(D * M), $MachinePrecision], 1.0], $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 * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(d * c0), $MachinePrecision] * N[(N[(d * c0), $MachinePrecision] / N[(N[(N[(N[(h * w), $MachinePrecision] * D), $MachinePrecision] * D), $MachinePrecision] * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] * h), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] * 0.25), $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 80.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. pow2 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. pow2 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot {w}^{2}} \]

      12. lift-*.f64 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot {w}^{2}} \]

      13. unpow2 N/A

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

      14. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. pow2 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. pow2 N/A

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

      7. associate-*r/ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

         \[\leadsto \frac{{c0}^{2} \cdot {d}^{2}}{\left(\left(D \cdot D\right) \cdot h\right) \cdot \left(w \cdot w\right)} \]

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. pow2 N/A

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

      13. pow2 N/A

          \[\leadsto \frac{{c0}^{2} \cdot {d}^{2}}{\left({D}^{2} \cdot h\right) \cdot {w}^{2}} \]

      14. associate-*r* N/A

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

      15. lower-/.f64 N/A

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

   7. Applied rewrites 67.1%

      \[\leadsto \frac{{\left(c0 \cdot d\right)}^{1} \cdot {\left(c0 \cdot d\right)}^{1}}{\color{blue}{\left(\left(D \cdot D\right) \cdot h\right) \cdot \left(w \cdot w\right)}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. pow2 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow1 N/A

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

      7. pow2 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 74.2

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-*r* N/A

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

      18. lift-*.f64 N/A

          \[\leadsto \left(d \cdot c0\right) \cdot \frac{d \cdot c0}{\left(\left(\left(D \cdot D\right) \cdot h\right) \cdot w\right) \cdot w} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(d \cdot c0\right) \cdot \frac{d \cdot c0}{\left(\left(\left(D \cdot D\right) \cdot h\right) \cdot w\right) \cdot w} \]

      20. pow2 N/A

          \[\leadsto \left(d \cdot c0\right) \cdot \frac{d \cdot c0}{\left(\left({D}^{2} \cdot h\right) \cdot w\right) \cdot w} \]

      21. associate-*r* N/A

          \[\leadsto \left(d \cdot c0\right) \cdot \frac{d \cdot c0}{\left({D}^{2} \cdot \left(h \cdot w\right)\right) \cdot w} \]

      22. lower-*.f64 N/A

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

   9. Applied rewrites 84.8%

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

   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 0.0%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   5. Applied rewrites 0.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

   6. Taylor expanded in c0 around 0

      \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      6. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. pow2 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      12. lift-*.f64 39.9

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

   8. Applied rewrites 39.9%

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

   10. Applied rewrites 49.1%

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot 0.25 \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       4. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       5. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       6. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       7. associate-*r* N/A

          \[\leadsto \frac{\frac{\left({M}^{2} \cdot {D}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       8. *-commutative N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       10. pow-prod-down N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{2} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       11. metadata-eval N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{\left(1 + 1\right)} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       12. unpow-prod-up N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       13. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       14. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       16. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       17. lower-*.f64 62.6

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]

   12. Applied rewrites 62.6%

       \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 61.7% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(D \cdot M\right)}^{1}\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;\left(c0 \cdot c0\right) \cdot \left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot \left(w \cdot w\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(t\_0 \cdot t\_0\right) \cdot h}{d}}{d} \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (pow (* D M) 1.0)) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_1 (sqrt (- (* t_1 t_1) (* M M)))))
        INFINITY)
     (* (* c0 c0) (* d (/ d (* (* (* D D) h) (* w w)))))
     (* (/ (/ (* (* t_0 t_0) h) d) d) 0.25))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = pow((D * M), 1.0);
	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))))) <= ((double) INFINITY)) {
		tmp = (c0 * c0) * (d * (d / (((D * D) * h) * (w * w))));
	} else {
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = Math.pow((D * M), 1.0);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_1 + Math.sqrt(((t_1 * t_1) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = (c0 * c0) * (d * (d / (((D * D) * h) * (w * w))));
	} else {
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = math.pow((D * M), 1.0)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_1 + math.sqrt(((t_1 * t_1) - (M * M))))) <= math.inf:
		tmp = (c0 * c0) * (d * (d / (((D * D) * h) * (w * w))))
	else:
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(D * M) ^ 1.0
	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))))) <= Inf)
		tmp = Float64(Float64(c0 * c0) * Float64(d * Float64(d / Float64(Float64(Float64(D * D) * h) * Float64(w * w)))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(t_0 * t_0) * h) / d) / d) * 0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = (D * M) ^ 1.0;
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = (c0 * c0) * (d * (d / (((D * D) * h) * (w * w))));
	else
		tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[Power[N[(D * M), $MachinePrecision], 1.0], $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 * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(c0 * c0), $MachinePrecision] * N[(d * N[(d / N[(N[(N[(D * D), $MachinePrecision] * h), $MachinePrecision] * N[(w * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] * h), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] * 0.25), $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 80.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. pow2 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. pow2 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot {w}^{2}} \]

      12. lift-*.f64 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \frac{d \cdot d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot {w}^{2}} \]

      13. unpow2 N/A

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

      14. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

         \[\leadsto \left(c0 \cdot c0\right) \cdot \left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot \left(w \cdot w\right)}\right) \]

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. pow2 N/A

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

      10. pow2 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \left(d \cdot \frac{d}{\left({D}^{2} \cdot h\right) \cdot {w}^{2}}\right) \]

      11. associate-*r* N/A

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

      12. lower-/.f64 N/A

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

      13. associate-*r* N/A

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

      14. pow2 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot {w}^{2}}\right) \]

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

          \[\leadsto \left(c0 \cdot c0\right) \cdot \left(d \cdot \frac{d}{\left(\left(D \cdot D\right) \cdot h\right) \cdot {w}^{2}}\right) \]

      17. pow2 N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 61.3

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

   7. Applied rewrites 61.3%

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

   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 0.0%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   5. Applied rewrites 0.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

   6. Taylor expanded in c0 around 0

      \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      6. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. pow2 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      12. lift-*.f64 39.9

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

   8. Applied rewrites 39.9%

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

   10. Applied rewrites 49.1%

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot 0.25 \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       4. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       5. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       6. pow2 N/A

          \[\leadsto \frac{\frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       7. associate-*r* N/A

          \[\leadsto \frac{\frac{\left({M}^{2} \cdot {D}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       8. *-commutative N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       10. pow-prod-down N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{2} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       11. metadata-eval N/A

           \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{\left(1 + 1\right)} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       12. unpow-prod-up N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       13. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       14. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       15. lower-*.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       16. lower-pow.f64 N/A

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

       17. lower-*.f64 62.6

           \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]

   12. Applied rewrites 62.6%

       \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 48.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(D \cdot M\right)}^{1}\\ \frac{\frac{\left(t\_0 \cdot t\_0\right) \cdot h}{d}}{d} \cdot 0.25 \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (pow (* D M) 1.0))) (* (/ (/ (* (* t_0 t_0) h) d) d) 0.25)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = pow((D * M), 1.0);
	return ((((t_0 * t_0) * h) / d) / d) * 0.25;
}

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 = (d * m) ** 1.0d0
    code = ((((t_0 * t_0) * h) / d_1) / d_1) * 0.25d0
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = Math.pow((D * M), 1.0);
	return ((((t_0 * t_0) * h) / d) / d) * 0.25;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = math.pow((D * M), 1.0)
	return ((((t_0 * t_0) * h) / d) / d) * 0.25

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(D * M) ^ 1.0
	return Float64(Float64(Float64(Float64(Float64(t_0 * t_0) * h) / d) / d) * 0.25)
end

MATLAB

function tmp = code(c0, w, h, D, d, M)
	t_0 = (D * M) ^ 1.0;
	tmp = ((((t_0 * t_0) * h) / d) / d) * 0.25;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[Power[N[(D * M), $MachinePrecision], 1.0], $MachinePrecision]}, N[(N[(N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] * h), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] * 0.25), $MachinePrecision]]

Derivation

1. Initial program 26.8%

   \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
2. Add Preprocessing

3. Taylor expanded in c0 around -inf

   \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

5. Applied rewrites 4.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

6. Taylor expanded in c0 around 0

   \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   4. *-commutative N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   6. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   8. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   9. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   11. pow2 N/A

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   12. lift-*.f64 32.1

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

8. Applied rewrites 32.1%

   \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   3. associate-/r* N/A

      \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

10. Applied rewrites 38.8%

    \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot 0.25 \]
11. Step-by-step derivation

    1. lift-*.f64 N/A

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

    2. lift-*.f64 N/A

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

    3. lift-*.f64 N/A

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

    4. lift-*.f64 N/A

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

    5. pow2 N/A

       \[\leadsto \frac{\frac{{M}^{2} \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

    6. pow2 N/A

       \[\leadsto \frac{\frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

    7. associate-*r* N/A

       \[\leadsto \frac{\frac{\left({M}^{2} \cdot {D}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    8. *-commutative N/A

       \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    9. lower-*.f64 N/A

       \[\leadsto \frac{\frac{\left({D}^{2} \cdot {M}^{2}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    10. pow-prod-down N/A

        \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{2} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    11. metadata-eval N/A

        \[\leadsto \frac{\frac{{\left(D \cdot M\right)}^{\left(1 + 1\right)} \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    12. unpow-prod-up N/A

        \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    13. lower-*.f64 N/A

        \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    14. lower-pow.f64 N/A

        \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    15. lower-*.f64 N/A

        \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    16. lower-pow.f64 N/A

        \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot \frac{1}{4} \]

    17. lower-*.f64 48.6

        \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]

12. Applied rewrites 48.6%

    \[\leadsto \frac{\frac{\left({\left(D \cdot M\right)}^{1} \cdot {\left(D \cdot M\right)}^{1}\right) \cdot h}{d}}{d} \cdot 0.25 \]
13. Add Preprocessing

Alternative 6: 45.2% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -2.8 \cdot 10^{-283}:\\ \;\;\;\;\frac{\frac{M \cdot \left(M \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{d}}{d} \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= w -2.8e-283)
   (* (/ (/ (* M (* M (* (* D D) h))) d) d) 0.25)
   (* (* D (* D (* (* (/ (/ h d) d) M) M))) 0.25)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (w <= -2.8e-283) {
		tmp = (((M * (M * ((D * D) * h))) / d) / d) * 0.25;
	} else {
		tmp = (D * (D * ((((h / d) / d) * M) * M))) * 0.25;
	}
	return tmp;
}

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) :: tmp
    if (w <= (-2.8d-283)) then
        tmp = (((m * (m * ((d * d) * h))) / d_1) / d_1) * 0.25d0
    else
        tmp = (d * (d * ((((h / d_1) / d_1) * m) * m))) * 0.25d0
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (w <= -2.8e-283) {
		tmp = (((M * (M * ((D * D) * h))) / d) / d) * 0.25;
	} else {
		tmp = (D * (D * ((((h / d) / d) * M) * M))) * 0.25;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if w <= -2.8e-283:
		tmp = (((M * (M * ((D * D) * h))) / d) / d) * 0.25
	else:
		tmp = (D * (D * ((((h / d) / d) * M) * M))) * 0.25
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (w <= -2.8e-283)
		tmp = Float64(Float64(Float64(Float64(M * Float64(M * Float64(Float64(D * D) * h))) / d) / d) * 0.25);
	else
		tmp = Float64(Float64(D * Float64(D * Float64(Float64(Float64(Float64(h / d) / d) * M) * M))) * 0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (w <= -2.8e-283)
		tmp = (((M * (M * ((D * D) * h))) / d) / d) * 0.25;
	else
		tmp = (D * (D * ((((h / d) / d) * M) * M))) * 0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[w, -2.8e-283], N[(N[(N[(N[(M * N[(M * N[(N[(D * D), $MachinePrecision] * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] * 0.25), $MachinePrecision], N[(N[(D * N[(D * N[(N[(N[(N[(h / d), $MachinePrecision] / d), $MachinePrecision] * M), $MachinePrecision] * M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if w < -2.7999999999999998e-283

   1. Initial program 26.3%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   5. Applied rewrites 4.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

   6. Taylor expanded in c0 around 0

      \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      6. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. pow2 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      12. lift-*.f64 30.9

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

   8. Applied rewrites 30.9%

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d}}{d} \cdot \frac{1}{4} \]

   10. Applied rewrites 39.3%

       \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot 0.25 \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d} \cdot \frac{1}{4} \]

       3. associate-*l* N/A

          \[\leadsto \frac{\frac{M \cdot \left(M \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{d}}{d} \cdot \frac{1}{4} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\frac{M \cdot \left(M \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{d}}{d} \cdot \frac{1}{4} \]

       5. lower-*.f64 46.5

          \[\leadsto \frac{\frac{M \cdot \left(M \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{d}}{d} \cdot 0.25 \]

   12. Applied rewrites 46.5%

       \[\leadsto \frac{\frac{M \cdot \left(M \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{d}}{d} \cdot 0.25 \]

   if -2.7999999999999998e-283 < w

   1. Initial program 27.2%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   5. Applied rewrites 4.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

   6. Taylor expanded in c0 around 0

      \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      6. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. pow2 N/A

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      12. lift-*.f64 33.1

          \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

   8. Applied rewrites 33.1%

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

      3. pow2 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      8. pow2 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      9. pow2 N/A

         \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

      10. *-commutative N/A

          \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

      11. associate-/l* N/A

          \[\leadsto \left({D}^{2} \cdot \frac{{M}^{2} \cdot h}{{d}^{2}}\right) \cdot \frac{1}{4} \]

      12. associate-*r/ N/A

          \[\leadsto \left({D}^{2} \cdot \left({M}^{2} \cdot \frac{h}{{d}^{2}}\right)\right) \cdot \frac{1}{4} \]

      13. pow2 N/A

          \[\leadsto \left({D}^{2} \cdot \left({M}^{2} \cdot \frac{h}{d \cdot d}\right)\right) \cdot \frac{1}{4} \]

      14. pow2 N/A

          \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot \frac{1}{4} \]

      15. associate-/r* N/A

          \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

      16. lower-*.f64 N/A

          \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

      17. pow2 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

      18. lift-*.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

      19. pow2 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

      20. *-commutative N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right) \cdot \frac{1}{4} \]

      21. lower-*.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right) \cdot \frac{1}{4} \]

   10. Applied rewrites 38.1%

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot 0.25 \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       2. lift-*.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       3. lift-*.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       4. lift-/.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       5. lift-/.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       6. lift-*.f64 N/A

          \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       7. associate-*l* N/A

          \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right)\right) \cdot \frac{1}{4} \]

       8. lower-*.f64 N/A

          \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right)\right) \cdot \frac{1}{4} \]

       9. pow2 N/A

          \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right)\right) \cdot \frac{1}{4} \]

       10. *-commutative N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right)\right) \cdot \frac{1}{4} \]

       11. pow2 N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right)\right) \cdot \frac{1}{4} \]

       12. associate-/r* N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right)\right) \cdot \frac{1}{4} \]

       13. lower-*.f64 N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right)\right) \cdot \frac{1}{4} \]

       14. pow2 N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left({M}^{2} \cdot \frac{h}{d \cdot d}\right)\right)\right) \cdot \frac{1}{4} \]

       15. associate-/r* N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right)\right) \cdot \frac{1}{4} \]

       16. *-commutative N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right)\right) \cdot \frac{1}{4} \]

       17. pow2 N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right)\right) \cdot \frac{1}{4} \]

       18. associate-*r* N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

       19. lower-*.f64 N/A

           \[\leadsto \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

   12. Applied rewrites 47.0%

       \[\leadsto \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot 0.25 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 44.4% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot 0.25 \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (* (* D (* D (* (* (/ (/ h d) d) M) M))) 0.25))

C

double code(double c0, double w, double h, double D, double d, double M) {
	return (D * (D * ((((h / d) / d) * M) * M))) * 0.25;
}

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
    code = (d * (d * ((((h / d_1) / d_1) * m) * m))) * 0.25d0
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	return (D * (D * ((((h / d) / d) * M) * M))) * 0.25;
}

Python

def code(c0, w, h, D, d, M):
	return (D * (D * ((((h / d) / d) * M) * M))) * 0.25

Julia

function code(c0, w, h, D, d, M)
	return Float64(Float64(D * Float64(D * Float64(Float64(Float64(Float64(h / d) / d) * M) * M))) * 0.25)
end

MATLAB

function tmp = code(c0, w, h, D, d, M)
	tmp = (D * (D * ((((h / d) / d) * M) * M))) * 0.25;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := N[(N[(D * N[(D * N[(N[(N[(N[(h / d), $MachinePrecision] / d), $MachinePrecision] * M), $MachinePrecision] * M), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision]

Derivation

1. Initial program 26.8%

   \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
2. Add Preprocessing

3. Taylor expanded in c0 around -inf

   \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

5. Applied rewrites 4.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

6. Taylor expanded in c0 around 0

   \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   4. *-commutative N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   6. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   8. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   9. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   11. pow2 N/A

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   12. lift-*.f64 32.1

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

8. Applied rewrites 32.1%

   \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   3. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   6. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   8. pow2 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   9. pow2 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   10. *-commutative N/A

       \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   11. associate-/l* N/A

       \[\leadsto \left({D}^{2} \cdot \frac{{M}^{2} \cdot h}{{d}^{2}}\right) \cdot \frac{1}{4} \]

   12. associate-*r/ N/A

       \[\leadsto \left({D}^{2} \cdot \left({M}^{2} \cdot \frac{h}{{d}^{2}}\right)\right) \cdot \frac{1}{4} \]

   13. pow2 N/A

       \[\leadsto \left({D}^{2} \cdot \left({M}^{2} \cdot \frac{h}{d \cdot d}\right)\right) \cdot \frac{1}{4} \]

   14. pow2 N/A

       \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot \frac{1}{4} \]

   15. associate-/r* N/A

       \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   16. lower-*.f64 N/A

       \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   17. pow2 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   18. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   19. pow2 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   20. *-commutative N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right) \cdot \frac{1}{4} \]

   21. lower-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right) \cdot \frac{1}{4} \]

10. Applied rewrites 34.6%

    \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot 0.25 \]
11. Step-by-step derivation

    1. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    2. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    3. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    4. lift-/.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    5. lift-/.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    6. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    7. associate-*l* N/A

       \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right)\right) \cdot \frac{1}{4} \]

    8. lower-*.f64 N/A

       \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right)\right) \cdot \frac{1}{4} \]

    9. pow2 N/A

       \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right)\right) \cdot \frac{1}{4} \]

    10. *-commutative N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right)\right) \cdot \frac{1}{4} \]

    11. pow2 N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right)\right) \cdot \frac{1}{4} \]

    12. associate-/r* N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right)\right) \cdot \frac{1}{4} \]

    13. lower-*.f64 N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right)\right) \cdot \frac{1}{4} \]

    14. pow2 N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left({M}^{2} \cdot \frac{h}{d \cdot d}\right)\right)\right) \cdot \frac{1}{4} \]

    15. associate-/r* N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right)\right) \cdot \frac{1}{4} \]

    16. *-commutative N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right)\right) \cdot \frac{1}{4} \]

    17. pow2 N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right)\right) \cdot \frac{1}{4} \]

    18. associate-*r* N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    19. lower-*.f64 N/A

        \[\leadsto \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

12. Applied rewrites 43.5%

    \[\leadsto \left(D \cdot \left(D \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right)\right)\right) \cdot 0.25 \]
13. Add Preprocessing

Alternative 8: 38.3% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \left(D \cdot D\right) \cdot \left(\left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right) \cdot 0.25\right) \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (* (* D D) (* (* (* (/ (/ h d) d) M) M) 0.25)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	return (D * D) * (((((h / d) / d) * M) * M) * 0.25);
}

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
    code = (d * d) * (((((h / d_1) / d_1) * m) * m) * 0.25d0)
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	return (D * D) * (((((h / d) / d) * M) * M) * 0.25);
}

Python

def code(c0, w, h, D, d, M):
	return (D * D) * (((((h / d) / d) * M) * M) * 0.25)

Julia

function code(c0, w, h, D, d, M)
	return Float64(Float64(D * D) * Float64(Float64(Float64(Float64(Float64(h / d) / d) * M) * M) * 0.25))
end

MATLAB

function tmp = code(c0, w, h, D, d, M)
	tmp = (D * D) * (((((h / d) / d) * M) * M) * 0.25);
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := N[(N[(D * D), $MachinePrecision] * N[(N[(N[(N[(N[(h / d), $MachinePrecision] / d), $MachinePrecision] * M), $MachinePrecision] * M), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 26.8%

   \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
2. Add Preprocessing

3. Taylor expanded in c0 around -inf

   \[\leadsto \color{blue}{{c0}^{2} \cdot \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\frac{-1}{2} \cdot \frac{-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}}{w} + \frac{1}{4} \cdot \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{c0}^{2} \cdot {d}^{2}}\right) \cdot \color{blue}{{c0}^{2}} \]

5. Applied rewrites 4.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 \cdot \frac{d \cdot d}{\left(\left(h \cdot w\right) \cdot D\right) \cdot D}}{w}, -0.5, \left(\frac{D \cdot D}{c0 \cdot c0} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot 0.25\right) \cdot \left(c0 \cdot c0\right)} \]

6. Taylor expanded in c0 around 0

   \[\leadsto \frac{1}{4} \cdot \color{blue}{\frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}}} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   4. *-commutative N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   6. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   8. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   9. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   11. pow2 N/A

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   12. lift-*.f64 32.1

       \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot 0.25 \]

8. Applied rewrites 32.1%

   \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \color{blue}{0.25} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d} \cdot \frac{1}{4} \]

   3. pow2 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   6. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(M \cdot M\right) \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   8. pow2 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot \left(D \cdot D\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   9. pow2 N/A

      \[\leadsto \frac{\left({M}^{2} \cdot h\right) \cdot {D}^{2}}{{d}^{2}} \cdot \frac{1}{4} \]

   10. *-commutative N/A

       \[\leadsto \frac{{D}^{2} \cdot \left({M}^{2} \cdot h\right)}{{d}^{2}} \cdot \frac{1}{4} \]

   11. associate-/l* N/A

       \[\leadsto \left({D}^{2} \cdot \frac{{M}^{2} \cdot h}{{d}^{2}}\right) \cdot \frac{1}{4} \]

   12. associate-*r/ N/A

       \[\leadsto \left({D}^{2} \cdot \left({M}^{2} \cdot \frac{h}{{d}^{2}}\right)\right) \cdot \frac{1}{4} \]

   13. pow2 N/A

       \[\leadsto \left({D}^{2} \cdot \left({M}^{2} \cdot \frac{h}{d \cdot d}\right)\right) \cdot \frac{1}{4} \]

   14. pow2 N/A

       \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right)\right) \cdot \frac{1}{4} \]

   15. associate-/r* N/A

       \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   16. lower-*.f64 N/A

       \[\leadsto \left({D}^{2} \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   17. pow2 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   18. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   19. pow2 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right)\right) \cdot \frac{1}{4} \]

   20. *-commutative N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right) \cdot \frac{1}{4} \]

   21. lower-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right)\right) \cdot \frac{1}{4} \]

10. Applied rewrites 34.6%

    \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot 0.25 \]
11. Step-by-step derivation

    1. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    2. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    3. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    4. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    5. lift-/.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    6. lift-/.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    7. lift-*.f64 N/A

       \[\leadsto \left(\left(D \cdot D\right) \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    8. pow2 N/A

       \[\leadsto \left({D}^{2} \cdot \left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right)\right) \cdot \frac{1}{4} \]

    9. associate-*l* N/A

       \[\leadsto {D}^{2} \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot \left(M \cdot M\right)\right) \cdot \color{blue}{\frac{1}{4}}\right) \]

    10. pow2 N/A

        \[\leadsto {D}^{2} \cdot \left(\left(\frac{\frac{h}{d}}{d} \cdot {M}^{2}\right) \cdot \frac{1}{4}\right) \]

    11. *-commutative N/A

        \[\leadsto {D}^{2} \cdot \left(\left({M}^{2} \cdot \frac{\frac{h}{d}}{d}\right) \cdot \frac{1}{4}\right) \]

    12. pow2 N/A

        \[\leadsto {D}^{2} \cdot \left(\left(\left(M \cdot M\right) \cdot \frac{\frac{h}{d}}{d}\right) \cdot \frac{1}{4}\right) \]

    13. associate-/r* N/A

        \[\leadsto {D}^{2} \cdot \left(\left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right) \cdot \frac{1}{4}\right) \]

    14. lower-*.f64 N/A

        \[\leadsto {D}^{2} \cdot \left(\left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right) \cdot \color{blue}{\frac{1}{4}}\right) \]

    15. pow2 N/A

        \[\leadsto \left(D \cdot D\right) \cdot \left(\left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right) \cdot \frac{1}{4}\right) \]

    16. lift-*.f64 N/A

        \[\leadsto \left(D \cdot D\right) \cdot \left(\left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right) \cdot \frac{1}{4}\right) \]

    17. lower-*.f64 N/A

        \[\leadsto \left(D \cdot D\right) \cdot \left(\left(\left(M \cdot M\right) \cdot \frac{h}{d \cdot d}\right) \cdot \frac{1}{4}\right) \]

12. Applied rewrites 38.4%

    \[\leadsto \left(D \cdot D\right) \cdot \left(\left(\left(\frac{\frac{h}{d}}{d} \cdot M\right) \cdot M\right) \cdot \color{blue}{0.25}\right) \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2025066 
(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))))))