Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.8% → 46.7%

Time: 19.0s

Alternatives: 8

Speedup: 156.0×

• could not determine a ground truth

  1. c0 = 1.4865621803859512e+213
  2. w = -4.338262246573144e-284
  3. h = 2.397078459140097e-281
  4. D = 8.1657034875581315e-289
  5. d = -6.732752625590586e+271
  6. M = -5.912546069459659e+91

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 24.8% 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

real(8) function code(c0, w, h, d, d_1, m)
    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: 46.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := D \cdot \left(w \cdot h\right)\\ \mathbf{if}\;D \cdot D \leq 4 \cdot 10^{-273}:\\ \;\;\;\;\frac{\left(c0 \cdot \frac{d}{t\_0}\right) \cdot \left(c0 \cdot d\right)}{D \cdot w}\\ \mathbf{elif}\;D \cdot D \leq 10^{+63}:\\ \;\;\;\;\frac{\frac{c0 \cdot d}{w}}{w \cdot \frac{D \cdot \left(D \cdot h\right)}{c0 \cdot d}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot d}{D} \cdot \frac{c0 \cdot d}{w \cdot t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (* D (* w h))))
   (if (<= (* D D) 4e-273)
     (/ (* (* c0 (/ d t_0)) (* c0 d)) (* D w))
     (if (<= (* D D) 1e+63)
       (/ (/ (* c0 d) w) (* w (/ (* D (* D h)) (* c0 d))))
       (* (/ (* c0 d) D) (/ (* c0 d) (* w t_0)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = D * (w * h);
	double tmp;
	if ((D * D) <= 4e-273) {
		tmp = ((c0 * (d / t_0)) * (c0 * d)) / (D * w);
	} else if ((D * D) <= 1e+63) {
		tmp = ((c0 * d) / w) / (w * ((D * (D * h)) / (c0 * d)));
	} else {
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * t_0));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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
    real(8) :: tmp
    t_0 = d * (w * h)
    if ((d * d) <= 4d-273) then
        tmp = ((c0 * (d_1 / t_0)) * (c0 * d_1)) / (d * w)
    else if ((d * d) <= 1d+63) then
        tmp = ((c0 * d_1) / w) / (w * ((d * (d * h)) / (c0 * d_1)))
    else
        tmp = ((c0 * d_1) / d) * ((c0 * d_1) / (w * t_0))
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = D * (w * h);
	double tmp;
	if ((D * D) <= 4e-273) {
		tmp = ((c0 * (d / t_0)) * (c0 * d)) / (D * w);
	} else if ((D * D) <= 1e+63) {
		tmp = ((c0 * d) / w) / (w * ((D * (D * h)) / (c0 * d)));
	} else {
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * t_0));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = D * (w * h)
	tmp = 0
	if (D * D) <= 4e-273:
		tmp = ((c0 * (d / t_0)) * (c0 * d)) / (D * w)
	elif (D * D) <= 1e+63:
		tmp = ((c0 * d) / w) / (w * ((D * (D * h)) / (c0 * d)))
	else:
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * t_0))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(D * Float64(w * h))
	tmp = 0.0
	if (Float64(D * D) <= 4e-273)
		tmp = Float64(Float64(Float64(c0 * Float64(d / t_0)) * Float64(c0 * d)) / Float64(D * w));
	elseif (Float64(D * D) <= 1e+63)
		tmp = Float64(Float64(Float64(c0 * d) / w) / Float64(w * Float64(Float64(D * Float64(D * h)) / Float64(c0 * d))));
	else
		tmp = Float64(Float64(Float64(c0 * d) / D) * Float64(Float64(c0 * d) / Float64(w * t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = D * (w * h);
	tmp = 0.0;
	if ((D * D) <= 4e-273)
		tmp = ((c0 * (d / t_0)) * (c0 * d)) / (D * w);
	elseif ((D * D) <= 1e+63)
		tmp = ((c0 * d) / w) / (w * ((D * (D * h)) / (c0 * d)));
	else
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(D * D), $MachinePrecision], 4e-273], N[(N[(N[(c0 * N[(d / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(c0 * d), $MachinePrecision]), $MachinePrecision] / N[(D * w), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(D * D), $MachinePrecision], 1e+63], N[(N[(N[(c0 * d), $MachinePrecision] / w), $MachinePrecision] / N[(w * N[(N[(D * N[(D * h), $MachinePrecision]), $MachinePrecision] / N[(c0 * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c0 * d), $MachinePrecision] / D), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(w * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 D D) < 4e-273

   1. Initial program 30.2%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 27.1

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

   5. Applied rewrites 27.1%

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

   7. Applied rewrites 50.6%

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

   9. Applied rewrites 58.4%

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

   if 4e-273 < (*.f64 D D) < 1.00000000000000006e63

   1. Initial program 26.2%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 29.8

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

   5. Applied rewrites 29.8%

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

   7. Applied rewrites 50.9%

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

   9. Applied rewrites 60.9%

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

   if 1.00000000000000006e63 < (*.f64 D D)

   1. Initial program 15.5%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 13.9

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

   5. Applied rewrites 13.9%

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

   7. Applied rewrites 50.9%

      \[\leadsto \frac{c0 \cdot d}{D} \cdot \color{blue}{\frac{c0 \cdot d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot w}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;D \cdot D \leq 4 \cdot 10^{-273}:\\ \;\;\;\;\frac{\left(c0 \cdot \frac{d}{D \cdot \left(w \cdot h\right)}\right) \cdot \left(c0 \cdot d\right)}{D \cdot w}\\ \mathbf{elif}\;D \cdot D \leq 10^{+63}:\\ \;\;\;\;\frac{\frac{c0 \cdot d}{w}}{w \cdot \frac{D \cdot \left(D \cdot h\right)}{c0 \cdot d}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot d}{D} \cdot \frac{c0 \cdot d}{w \cdot \left(D \cdot \left(w \cdot h\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(t\_0 + \sqrt{t\_0 \cdot t\_0 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;c0 \cdot \left(c0 \cdot \frac{d \cdot d}{D \cdot \left(w \cdot \left(D \cdot \left(w \cdot h\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* D D) (* w h)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* c0 (* c0 (/ (* d d) (* D (* w (* D (* w h)))))))
     0.0)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (c0 * (d * d)) / ((D * D) * (w * h));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = c0 * (c0 * ((d * d) / (D * (w * (D * (w * h))))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (c0 * (d * d)) / ((D * D) * (w * h));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = c0 * (c0 * ((d * d) / (D * (w * (D * (w * h))))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((D * D) * (w * h))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = c0 * (c0 * ((d * d) / (D * (w * (D * (w * h))))))
	else:
		tmp = 0.0
	return tmp

Julia

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

MATLAB

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

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(D * D), $MachinePrecision] * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[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], Infinity], N[(c0 * N[(c0 * N[(N[(d * d), $MachinePrecision] / N[(D * N[(w * N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

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 73.1%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 48.9

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

   5. Applied rewrites 48.9%

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

   7. Applied rewrites 68.5%

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

   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

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

      5. mul0-lft N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

      6. mul0-rgt N/A

         \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{0}}{w} \]

      8. div0 36.9

         \[\leadsto \color{blue}{0} \]

   5. Applied rewrites 36.9%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \leq \infty:\\ \;\;\;\;c0 \cdot \left(c0 \cdot \frac{d \cdot d}{D \cdot \left(w \cdot \left(D \cdot \left(w \cdot h\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 1.28 \cdot 10^{-244}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(c0 \cdot \frac{d}{D \cdot \left(w \cdot h\right)}\right) \cdot \left(c0 \cdot d\right)}{D \cdot w}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 1.28e-244) 0.0 (/ (* (* c0 (/ d (* D (* w h)))) (* c0 d)) (* D w))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 1.28e-244) {
		tmp = 0.0;
	} else {
		tmp = ((c0 * (d / (D * (w * h)))) * (c0 * d)) / (D * w);
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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 (m <= 1.28d-244) then
        tmp = 0.0d0
    else
        tmp = ((c0 * (d_1 / (d * (w * h)))) * (c0 * d_1)) / (d * w)
    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 (M <= 1.28e-244) {
		tmp = 0.0;
	} else {
		tmp = ((c0 * (d / (D * (w * h)))) * (c0 * d)) / (D * w);
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 1.28e-244:
		tmp = 0.0
	else:
		tmp = ((c0 * (d / (D * (w * h)))) * (c0 * d)) / (D * w)
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 1.28e-244)
		tmp = 0.0;
	else
		tmp = Float64(Float64(Float64(c0 * Float64(d / Float64(D * Float64(w * h)))) * Float64(c0 * d)) / Float64(D * w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 1.28e-244)
		tmp = 0.0;
	else
		tmp = ((c0 * (d / (D * (w * h)))) * (c0 * d)) / (D * w);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 1.28e-244], 0.0, N[(N[(N[(c0 * N[(d / N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c0 * d), $MachinePrecision]), $MachinePrecision] / N[(D * w), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 1.27999999999999994e-244

   1. Initial program 22.1%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

      5. mul0-lft N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

      6. mul0-rgt N/A

         \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{0}}{w} \]

      8. div0 32.3

         \[\leadsto \color{blue}{0} \]

   5. Applied rewrites 32.3%

      \[\leadsto \color{blue}{0} \]

   if 1.27999999999999994e-244 < M

   1. Initial program 31.5%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 28.6

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

   5. Applied rewrites 28.6%

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

   7. Applied rewrites 57.9%

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

   9. Applied rewrites 61.3%

      \[\leadsto \frac{\left(c0 \cdot \frac{d}{D \cdot \left(h \cdot w\right)}\right) \cdot \left(c0 \cdot d\right)}{\color{blue}{w \cdot D}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 1.28 \cdot 10^{-244}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(c0 \cdot \frac{d}{D \cdot \left(w \cdot h\right)}\right) \cdot \left(c0 \cdot d\right)}{D \cdot w}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 40.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot d}{D} \cdot \frac{c0 \cdot d}{w \cdot \left(D \cdot \left(w \cdot h\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 2.7e-198) 0.0 (* (/ (* c0 d) D) (/ (* c0 d) (* w (* D (* w h)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 2.7e-198) {
		tmp = 0.0;
	} else {
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * (D * (w * h))));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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 (m <= 2.7d-198) then
        tmp = 0.0d0
    else
        tmp = ((c0 * d_1) / d) * ((c0 * d_1) / (w * (d * (w * h))))
    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 (M <= 2.7e-198) {
		tmp = 0.0;
	} else {
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * (D * (w * h))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 2.7e-198:
		tmp = 0.0
	else:
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * (D * (w * h))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 2.7e-198)
		tmp = 0.0;
	else
		tmp = Float64(Float64(Float64(c0 * d) / D) * Float64(Float64(c0 * d) / Float64(w * Float64(D * Float64(w * h)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 2.7e-198)
		tmp = 0.0;
	else
		tmp = ((c0 * d) / D) * ((c0 * d) / (w * (D * (w * h))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 2.7e-198], 0.0, N[(N[(N[(c0 * d), $MachinePrecision] / D), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(w * N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 2.7000000000000002e-198

   1. Initial program 24.6%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

      5. mul0-lft N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

      6. mul0-rgt N/A

         \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{0}}{w} \]

      8. div0 33.0

         \[\leadsto \color{blue}{0} \]

   5. Applied rewrites 33.0%

      \[\leadsto \color{blue}{0} \]

   if 2.7000000000000002e-198 < M

   1. Initial program 27.3%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.4

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

   5. Applied rewrites 30.4%

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

   7. Applied rewrites 59.0%

      \[\leadsto \frac{c0 \cdot d}{D} \cdot \color{blue}{\frac{c0 \cdot d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot w}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot d}{D} \cdot \frac{c0 \cdot d}{w \cdot \left(D \cdot \left(w \cdot h\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 2.3 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{\left(D \cdot \left(w \cdot h\right)\right) \cdot \left(D \cdot w\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 2.3e-198) 0.0 (* (* c0 d) (/ (* c0 d) (* (* D (* w h)) (* D w))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 2.3e-198) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / ((D * (w * h)) * (D * w)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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 (m <= 2.3d-198) then
        tmp = 0.0d0
    else
        tmp = (c0 * d_1) * ((c0 * d_1) / ((d * (w * h)) * (d * w)))
    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 (M <= 2.3e-198) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / ((D * (w * h)) * (D * w)));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 2.3e-198:
		tmp = 0.0
	else:
		tmp = (c0 * d) * ((c0 * d) / ((D * (w * h)) * (D * w)))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 2.3e-198)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(Float64(D * Float64(w * h)) * Float64(D * w))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 2.3e-198)
		tmp = 0.0;
	else
		tmp = (c0 * d) * ((c0 * d) / ((D * (w * h)) * (D * w)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 2.3e-198], 0.0, N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision] * N[(D * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 2.30000000000000013e-198

   1. Initial program 24.6%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

      5. mul0-lft N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

      6. mul0-rgt N/A

         \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{0}}{w} \]

      8. div0 33.0

         \[\leadsto \color{blue}{0} \]

   5. Applied rewrites 33.0%

      \[\leadsto \color{blue}{0} \]

   if 2.30000000000000013e-198 < M

   1. Initial program 27.3%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.4

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

   5. Applied rewrites 30.4%

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

   7. Applied rewrites 59.0%

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

   9. Applied rewrites 60.3%

      \[\leadsto \left(c0 \cdot d\right) \cdot \color{blue}{\frac{c0 \cdot d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot \left(w \cdot D\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 2.3 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{\left(D \cdot \left(w \cdot h\right)\right) \cdot \left(D \cdot w\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 2.3 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(D \cdot \left(w \cdot h\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 2.3e-198) 0.0 (* (* c0 d) (/ (* c0 d) (* D (* w (* D (* w h))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 2.3e-198) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (D * (w * h)))));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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 (m <= 2.3d-198) then
        tmp = 0.0d0
    else
        tmp = (c0 * d_1) * ((c0 * d_1) / (d * (w * (d * (w * h)))))
    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 (M <= 2.3e-198) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (D * (w * h)))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 2.3e-198:
		tmp = 0.0
	else:
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (D * (w * h)))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 2.3e-198)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(D * Float64(w * Float64(D * Float64(w * h))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 2.3e-198)
		tmp = 0.0;
	else
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (D * (w * h)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 2.3e-198], 0.0, N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 2.30000000000000013e-198

   1. Initial program 24.6%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

      5. mul0-lft N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

      6. mul0-rgt N/A

         \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{0}}{w} \]

      8. div0 33.0

         \[\leadsto \color{blue}{0} \]

   5. Applied rewrites 33.0%

      \[\leadsto \color{blue}{0} \]

   if 2.30000000000000013e-198 < M

   1. Initial program 27.3%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.4

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

   5. Applied rewrites 30.4%

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

   7. Applied rewrites 60.3%

      \[\leadsto \left(c0 \cdot d\right) \cdot \color{blue}{\frac{c0 \cdot d}{D \cdot \left(\left(D \cdot \left(h \cdot w\right)\right) \cdot w\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 2.3 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(D \cdot \left(w \cdot h\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 2.6 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(d \cdot \left(c0 \cdot \frac{d}{\left(D \cdot \left(w \cdot h\right)\right) \cdot \left(D \cdot w\right)}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 2.6e-198) 0.0 (* c0 (* d (* c0 (/ d (* (* D (* w h)) (* D w))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 2.6e-198) {
		tmp = 0.0;
	} else {
		tmp = c0 * (d * (c0 * (d / ((D * (w * h)) * (D * w)))));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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 (m <= 2.6d-198) then
        tmp = 0.0d0
    else
        tmp = c0 * (d_1 * (c0 * (d_1 / ((d * (w * h)) * (d * w)))))
    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 (M <= 2.6e-198) {
		tmp = 0.0;
	} else {
		tmp = c0 * (d * (c0 * (d / ((D * (w * h)) * (D * w)))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 2.6e-198:
		tmp = 0.0
	else:
		tmp = c0 * (d * (c0 * (d / ((D * (w * h)) * (D * w)))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 2.6e-198)
		tmp = 0.0;
	else
		tmp = Float64(c0 * Float64(d * Float64(c0 * Float64(d / Float64(Float64(D * Float64(w * h)) * Float64(D * w))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 2.6e-198)
		tmp = 0.0;
	else
		tmp = c0 * (d * (c0 * (d / ((D * (w * h)) * (D * w)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 2.6e-198], 0.0, N[(c0 * N[(d * N[(c0 * N[(d / N[(N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision] * N[(D * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 2.60000000000000007e-198

   1. Initial program 24.6%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

      5. mul0-lft N/A

         \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

      6. mul0-rgt N/A

         \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

      7. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{0}}{w} \]

      8. div0 33.0

         \[\leadsto \color{blue}{0} \]

   5. Applied rewrites 33.0%

      \[\leadsto \color{blue}{0} \]

   if 2.60000000000000007e-198 < M

   1. Initial program 27.3%

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

   3. Taylor expanded in w around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.4

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

   5. Applied rewrites 30.4%

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

   7. Applied rewrites 48.9%

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

   9. Applied rewrites 56.8%

      \[\leadsto c0 \cdot \left(d \cdot \color{blue}{\left(\frac{d}{\left(D \cdot \left(h \cdot w\right)\right) \cdot \left(w \cdot D\right)} \cdot c0\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 2.6 \cdot 10^{-198}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(d \cdot \left(c0 \cdot \frac{d}{\left(D \cdot \left(w \cdot h\right)\right) \cdot \left(D \cdot w\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.8% accurate, 156.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (c0 w h D d M) :precision binary64 0.0)

C

double code(double c0, double w, double h, double D, double d, double M) {
	return 0.0;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    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 = 0.0d0
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	return 0.0;
}

Python

def code(c0, w, h, D, d, M):
	return 0.0

Julia

function code(c0, w, h, D, d, M)
	return 0.0
end

MATLAB

function tmp = code(c0, w, h, D, d, M)
	tmp = 0.0;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := 0.0

Derivation

1. Initial program 25.4%

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

3. Taylor expanded in c0 around -inf

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

   3. distribute-lft1-in N/A

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

   4. metadata-eval N/A

      \[\leadsto \frac{\left({c0}^{2} \cdot \left(\color{blue}{0} \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)\right) \cdot \frac{-1}{2}}{w} \]

   5. mul0-lft N/A

      \[\leadsto \frac{\left({c0}^{2} \cdot \color{blue}{0}\right) \cdot \frac{-1}{2}}{w} \]

   6. mul0-rgt N/A

      \[\leadsto \frac{\color{blue}{0} \cdot \frac{-1}{2}}{w} \]

   7. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{0}}{w} \]

   8. div0 27.9

      \[\leadsto \color{blue}{0} \]

5. Applied rewrites 27.9%

   \[\leadsto \color{blue}{0} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024235 
(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))))))