Henrywood and Agarwal, Equation (13)

Percentage Accurate: 25.5% → 55.2%

Time: 19.4s

Alternatives: 7

Speedup: 156.0×

• could not determine a ground truth

  1. c0 = 8.107113344642593e+265
  2. w = 2.6123107854032394e-279
  3. h = -1.0423989909424802e-255
  4. D = 5.6995035449241726e-297
  5. d = -1.6865203657020572e+233
  6. M = 1.7112161360666946e-305

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: 25.5% 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: 55.2% accurate, 0.7× speedup

Math

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

FPCore

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

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

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = (((c0 * d) / w) * ((c0 * d) / h)) / (w * (D * D))
	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(w * h) * Float64(D * D)))
	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(Float64(Float64(Float64(c0 * d) / w) * Float64(Float64(c0 * d) / h)) / Float64(w * Float64(D * D)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = (((c0 * d) / w) * ((c0 * d) / h)) / (w * (D * D));
	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[(w * h), $MachinePrecision] * N[(D * D), $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[(N[(N[(N[(c0 * d), $MachinePrecision] / w), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / h), $MachinePrecision]), $MachinePrecision] / N[(w * N[(D * D), $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 66.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   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. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 57.5

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

   5. Simplified 57.5%

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

      1. div-inv N/A

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

      2. unswap-sqr N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 62.1

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

   7. Applied egg-rr 62.1%

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

      1. associate-*r/ N/A

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

      2. frac-times N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{c0 \cdot d}{w}}{w} \cdot \color{blue}{\frac{\frac{c0 \cdot d}{h}}{D \cdot D}} \]

      5. frac-times N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 75.4

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

   9. Applied egg-rr 75.4%

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

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 41.8

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

   5. Simplified 41.8%

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

4. Final simplification 54.1%

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

Alternative 2: 42.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0 \cdot d}{w} \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(h \cdot D\right)\right)}\\ \mathbf{if}\;h \leq -3.6 \cdot 10^{-237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;h \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (* (/ (* c0 d) w) (/ (* c0 d) (* D (* w (* h D)))))))
   (if (<= h -3.6e-237) t_0 (if (<= h 2.9e-130) 0.0 t_0))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = ((c0 * d) / w) * ((c0 * d) / (D * (w * (h * D))));
	double tmp;
	if (h <= -3.6e-237) {
		tmp = t_0;
	} else if (h <= 2.9e-130) {
		tmp = 0.0;
	} else {
		tmp = 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 = ((c0 * d_1) / w) * ((c0 * d_1) / (d * (w * (h * d))))
    if (h <= (-3.6d-237)) then
        tmp = t_0
    else if (h <= 2.9d-130) then
        tmp = 0.0d0
    else
        tmp = 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 = ((c0 * d) / w) * ((c0 * d) / (D * (w * (h * D))));
	double tmp;
	if (h <= -3.6e-237) {
		tmp = t_0;
	} else if (h <= 2.9e-130) {
		tmp = 0.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = ((c0 * d) / w) * ((c0 * d) / (D * (w * (h * D))))
	tmp = 0
	if h <= -3.6e-237:
		tmp = t_0
	elif h <= 2.9e-130:
		tmp = 0.0
	else:
		tmp = t_0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(Float64(c0 * d) / w) * Float64(Float64(c0 * d) / Float64(D * Float64(w * Float64(h * D)))))
	tmp = 0.0
	if (h <= -3.6e-237)
		tmp = t_0;
	elseif (h <= 2.9e-130)
		tmp = 0.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = ((c0 * d) / w) * ((c0 * d) / (D * (w * (h * D))));
	tmp = 0.0;
	if (h <= -3.6e-237)
		tmp = t_0;
	elseif (h <= 2.9e-130)
		tmp = 0.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(N[(c0 * d), $MachinePrecision] / w), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * N[(h * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[h, -3.6e-237], t$95$0, If[LessEqual[h, 2.9e-130], 0.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if h < -3.59999999999999997e-237 or 2.9e-130 < h

   1. Initial program 28.8%

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

   3. Taylor expanded in c0 around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 28.5

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

   5. Simplified 28.5%

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

      1. div-inv N/A

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

      2. unswap-sqr N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 34.7

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

   7. Applied egg-rr 34.7%

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

      1. associate-*r/ N/A

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

      2. associate-*l* N/A

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

      3. times-frac N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

      17. *-lowering-*.f64 46.5

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

   9. Applied egg-rr 46.5%

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

   if -3.59999999999999997e-237 < h < 2.9e-130

   1. Initial program 13.1%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 48.0

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

   5. Simplified 48.0%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;h \leq -3.6 \cdot 10^{-237}:\\ \;\;\;\;\frac{c0 \cdot d}{w} \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(h \cdot D\right)\right)}\\ \mathbf{elif}\;h \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot d}{w} \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(h \cdot D\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;h \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(w \cdot \left(h \cdot D\right)\right)\right)}\\ \mathbf{elif}\;h \leq 5.2 \cdot 10^{-130}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \left(c0 \cdot d\right)}{D} \cdot \frac{d}{\left(h \cdot D\right) \cdot \left(w \cdot w\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= h -3.5e-237)
   (* (* c0 d) (/ (* c0 d) (* D (* w (* w (* h D))))))
   (if (<= h 5.2e-130)
     0.0
     (* (/ (* c0 (* c0 d)) D) (/ d (* (* h D) (* w w)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (h <= -3.5e-237) {
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))));
	} else if (h <= 5.2e-130) {
		tmp = 0.0;
	} else {
		tmp = ((c0 * (c0 * d)) / D) * (d / ((h * D) * (w * 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 (h <= (-3.5d-237)) then
        tmp = (c0 * d_1) * ((c0 * d_1) / (d * (w * (w * (h * d)))))
    else if (h <= 5.2d-130) then
        tmp = 0.0d0
    else
        tmp = ((c0 * (c0 * d_1)) / d) * (d_1 / ((h * d) * (w * 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 (h <= -3.5e-237) {
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))));
	} else if (h <= 5.2e-130) {
		tmp = 0.0;
	} else {
		tmp = ((c0 * (c0 * d)) / D) * (d / ((h * D) * (w * w)));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if h <= -3.5e-237:
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))))
	elif h <= 5.2e-130:
		tmp = 0.0
	else:
		tmp = ((c0 * (c0 * d)) / D) * (d / ((h * D) * (w * w)))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (h <= -3.5e-237)
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(D * Float64(w * Float64(w * Float64(h * D))))));
	elseif (h <= 5.2e-130)
		tmp = 0.0;
	else
		tmp = Float64(Float64(Float64(c0 * Float64(c0 * d)) / D) * Float64(d / Float64(Float64(h * D) * Float64(w * w))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (h <= -3.5e-237)
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))));
	elseif (h <= 5.2e-130)
		tmp = 0.0;
	else
		tmp = ((c0 * (c0 * d)) / D) * (d / ((h * D) * (w * w)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[h, -3.5e-237], N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * N[(w * N[(h * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[h, 5.2e-130], 0.0, N[(N[(N[(c0 * N[(c0 * d), $MachinePrecision]), $MachinePrecision] / D), $MachinePrecision] * N[(d / N[(N[(h * D), $MachinePrecision] * N[(w * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if h < -3.49999999999999983e-237

   1. Initial program 27.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   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. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 27.3

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

   5. Simplified 27.3%

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

      1. div-inv N/A

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

      2. unswap-sqr N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 29.6

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

   7. Applied egg-rr 29.6%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 40.9

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

   9. Applied egg-rr 40.9%

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

   if -3.49999999999999983e-237 < h < 5.2000000000000001e-130

   1. Initial program 13.1%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 48.0

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

   5. Simplified 48.0%

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

   if 5.2000000000000001e-130 < h

   1. Initial program 29.9%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
   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. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 29.9

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

   5. Simplified 29.9%

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

      1. associate-*r* N/A

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

      2. associate-*l* N/A

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

      3. times-frac N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. associate-*r* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 48.4

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

   7. Applied egg-rr 48.4%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;h \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(w \cdot \left(h \cdot D\right)\right)\right)}\\ \mathbf{elif}\;h \leq 5.2 \cdot 10^{-130}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \left(c0 \cdot d\right)}{D} \cdot \frac{d}{\left(h \cdot D\right) \cdot \left(w \cdot w\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(w \cdot \left(h \cdot D\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 6.2e-59) 0.0 (* (* c0 d) (/ (* c0 d) (* D (* w (* w (* h D))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 6.2e-59) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))));
	}
	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 <= 6.2d-59) then
        tmp = 0.0d0
    else
        tmp = (c0 * d_1) * ((c0 * d_1) / (d * (w * (w * (h * d)))))
    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 <= 6.2e-59) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 6.2e-59:
		tmp = 0.0
	else:
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 6.2e-59)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(D * Float64(w * Float64(w * Float64(h * D))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 6.2e-59)
		tmp = 0.0;
	else
		tmp = (c0 * d) * ((c0 * d) / (D * (w * (w * (h * D)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 6.2e-59], 0.0, N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * N[(w * N[(h * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 6.19999999999999998e-59

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 34.4

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

   5. Simplified 34.4%

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

   if 6.19999999999999998e-59 < M

   1. Initial program 20.2%

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

   3. Taylor expanded in c0 around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 27.9

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

   5. Simplified 27.9%

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

      1. div-inv N/A

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

      2. unswap-sqr N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 34.8

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

   7. Applied egg-rr 34.8%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 43.8

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

   9. Applied egg-rr 43.8%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{D \cdot \left(w \cdot \left(w \cdot \left(h \cdot D\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{\left(D \cdot D\right) \cdot \left(w \cdot \left(w \cdot h\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 6.2e-59) 0.0 (* (* c0 d) (/ (* c0 d) (* (* D D) (* w (* w h)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 6.2e-59) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / ((D * D) * (w * (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 <= 6.2d-59) then
        tmp = 0.0d0
    else
        tmp = (c0 * d_1) * ((c0 * d_1) / ((d * d) * (w * (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 <= 6.2e-59) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / ((D * D) * (w * (w * h))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 6.2e-59:
		tmp = 0.0
	else:
		tmp = (c0 * d) * ((c0 * d) / ((D * D) * (w * (w * h))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 6.2e-59)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(Float64(D * D) * Float64(w * Float64(w * h)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 6.2e-59)
		tmp = 0.0;
	else
		tmp = (c0 * d) * ((c0 * d) / ((D * D) * (w * (w * h))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 6.2e-59], 0.0, N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(N[(D * D), $MachinePrecision] * N[(w * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 6.19999999999999998e-59

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 34.4

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

   5. Simplified 34.4%

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

   if 6.19999999999999998e-59 < M

   1. Initial program 20.2%

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

   3. Taylor expanded in c0 around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 27.9

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

   5. Simplified 27.9%

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

      1. div-inv N/A

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

      2. unswap-sqr N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 34.8

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

   7. Applied egg-rr 34.8%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 37.1

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

   9. Applied egg-rr 37.1%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{\left(D \cdot D\right) \cdot \left(w \cdot \left(w \cdot h\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 7 \cdot 10^{-59}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot d\right) \cdot \frac{c0 \cdot d}{\left(w \cdot w\right) \cdot \left(h \cdot \left(D \cdot D\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= M 7e-59) 0.0 (* (* c0 d) (/ (* c0 d) (* (* w w) (* h (* D D)))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (M <= 7e-59) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / ((w * w) * (h * (D * D))));
	}
	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 <= 7d-59) then
        tmp = 0.0d0
    else
        tmp = (c0 * d_1) * ((c0 * d_1) / ((w * w) * (h * (d * d))))
    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 <= 7e-59) {
		tmp = 0.0;
	} else {
		tmp = (c0 * d) * ((c0 * d) / ((w * w) * (h * (D * D))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if M <= 7e-59:
		tmp = 0.0
	else:
		tmp = (c0 * d) * ((c0 * d) / ((w * w) * (h * (D * D))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (M <= 7e-59)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(Float64(w * w) * Float64(h * Float64(D * D)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (M <= 7e-59)
		tmp = 0.0;
	else
		tmp = (c0 * d) * ((c0 * d) / ((w * w) * (h * (D * D))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[M, 7e-59], 0.0, N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(N[(w * w), $MachinePrecision] * N[(h * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 7.0000000000000002e-59

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 34.4

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

   5. Simplified 34.4%

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

   if 7.0000000000000002e-59 < M

   1. Initial program 20.2%

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

   3. Taylor expanded in c0 around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.f64 27.9

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

   5. Simplified 27.9%

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

      1. div-inv N/A

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

      2. unswap-sqr N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 34.8

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

   7. Applied egg-rr 34.8%

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

Alternative 7: 33.2% 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 24.5%

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

3. Taylor expanded in 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. associate-/l* N/A

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

   2. distribute-lft1-in N/A

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

   3. metadata-eval N/A

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

   4. mul0-lft N/A

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

   5. div0 N/A

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

   6. mul0-rgt N/A

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

   7. metadata-eval 31.5

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

5. Simplified 31.5%

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

Reproduce

herbie shell --seed 2024196 
(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))))))