Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.6% → 54.7%

Time: 18.2s

Alternatives: 7

Speedup: 156.0×

• could not determine a ground truth

  1. c0 = -1.2105958706817529e+158
  2. w = -1.0727596418515984e-32
  3. h = -7.865681325564472e-261
  4. D = -9.686642653069686e-255
  5. d = 3.441350631221837e+225
  6. M = -2.068174693358511e-93

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: 24.6% 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: 54.7% accurate, 0.7× speedup

Math

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

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)
     (* (* (/ d (* w h)) (/ c0 w)) (/ (* c0 d) (* 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)) / ((D * D) * (w * h));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = ((d / (w * h)) * (c0 / w)) * ((c0 * d) / (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)) / ((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 = ((d / (w * h)) * (c0 / w)) * ((c0 * d) / (D * D));
	} 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 = ((d / (w * h)) * (c0 / w)) * ((c0 * d) / (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(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(Float64(Float64(d / Float64(w * h)) * Float64(c0 / w)) * Float64(Float64(c0 * d) / 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)) / ((D * D) * (w * h));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = ((d / (w * h)) * (c0 / w)) * ((c0 * d) / (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[(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[(N[(N[(d / N[(w * h), $MachinePrecision]), $MachinePrecision] * N[(c0 / w), $MachinePrecision]), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / 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 73.4%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \color{blue}{\frac{{c0}^{2} \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot {w}^{2}\right)}} \]
   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 50.9

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

   5. Simplified 50.9%

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

      1. unswap-sqr N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      11. *-lowering-*.f64 70.0

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

   7. Applied egg-rr 70.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

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

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

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

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

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

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

      7. /-lowering-/.f64 80.6

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

   9. Applied egg-rr 80.6%

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

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 #s(literal 2 binary64) w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft1-in N/A

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

      9. associate-*l/ N/A

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

   5. Simplified 34.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul0-rgt N/A

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

      3. metadata-eval N/A

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

      4. div0 53.9

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

   7. Applied egg-rr 53.9%

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

4. Final simplification 62.8%

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

Alternative 2: 55.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* D D) (* w h)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* (/ (* c0 d) (* w h)) (/ (* c0 d) (* D (* w D))))
     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 * d) / (w * h)) * ((c0 * d) / (D * (w * 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)) / ((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 * d) / (w * h)) * ((c0 * d) / (D * (w * D)));
	} 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 * d) / (w * h)) * ((c0 * d) / (D * (w * 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(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(Float64(Float64(c0 * d) / Float64(w * h)) * Float64(Float64(c0 * d) / Float64(D * Float64(w * 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)) / ((D * D) * (w * h));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = ((c0 * d) / (w * h)) * ((c0 * d) / (D * (w * 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[(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[(N[(N[(c0 * d), $MachinePrecision] / N[(w * h), $MachinePrecision]), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * D), $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 73.4%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \color{blue}{\frac{{c0}^{2} \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot {w}^{2}\right)}} \]
   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 50.9

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

   5. Simplified 50.9%

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

      1. unswap-sqr N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. associate-*l* N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

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

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

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

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

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

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

      15. *-lowering-*.f64 66.4

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

   7. Applied egg-rr 66.4%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-/l/ N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r* N/A

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

      10. times-frac N/A

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

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

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

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

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

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

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

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

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

      15. associate-/l/ N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. /-lowering-/.f64 N/A

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

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

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

      20. *-commutative N/A

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

   9. Applied egg-rr 77.3%

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

   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

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft1-in N/A

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

      9. associate-*l/ N/A

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

   5. Simplified 34.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul0-rgt N/A

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

      3. metadata-eval N/A

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

      4. div0 53.9

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

   7. Applied egg-rr 53.9%

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

4. Final simplification 61.6%

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

Alternative 3: 55.3% accurate, 0.7× speedup

Math

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

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 d) (/ (* c0 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 * d) * ((c0 * 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 * d) * ((c0 * 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 * d) * ((c0 * 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(Float64(c0 * d) * Float64(Float64(c0 * 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 * d) * ((c0 * 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[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * N[(D * N[(w * h), $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 73.4%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \color{blue}{\frac{{c0}^{2} \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot {w}^{2}\right)}} \]
   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 50.9

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

   5. Simplified 50.9%

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

      1. unswap-sqr N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. associate-*l* N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

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

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

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

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

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

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

      15. *-lowering-*.f64 66.4

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

   7. Applied egg-rr 66.4%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

      7. *-lowering-*.f64 76.7

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

   9. Applied egg-rr 76.7%

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

   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. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft1-in N/A

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

      9. associate-*l/ N/A

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

   5. Simplified 34.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul0-rgt N/A

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

      3. metadata-eval N/A

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

      4. div0 53.9

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

   7. Applied egg-rr 53.9%

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

4. Final simplification 61.4%

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

Alternative 4: 53.5% accurate, 0.7× speedup

Math

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

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)
     (* (/ d (* D (* w (* D (* w h))))) (* c0 (* c0 d)))
     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 = (d / (D * (w * (D * (w * h))))) * (c0 * (c0 * 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)) / ((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 = (d / (D * (w * (D * (w * h))))) * (c0 * (c0 * d));
	} 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 = (d / (D * (w * (D * (w * h))))) * (c0 * (c0 * 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(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(Float64(d / Float64(D * Float64(w * Float64(D * Float64(w * h))))) * Float64(c0 * Float64(c0 * 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)) / ((D * D) * (w * h));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = (d / (D * (w * (D * (w * h))))) * (c0 * (c0 * 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[(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[(N[(d / N[(D * N[(w * N[(D * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c0 * N[(c0 * 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 73.4%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \color{blue}{\frac{{c0}^{2} \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot {w}^{2}\right)}} \]
   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 50.9

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

   5. Simplified 50.9%

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. associate-*l* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. associate-*l* N/A

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

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

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

      16. *-lowering-*.f64 59.5

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

   7. Applied egg-rr 59.5%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

      7. *-lowering-*.f64 67.7

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

   9. Applied egg-rr 67.7%

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

   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

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft1-in N/A

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

      9. associate-*l/ N/A

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

   5. Simplified 34.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul0-rgt N/A

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

      3. metadata-eval N/A

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

      4. div0 53.9

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

   7. Applied egg-rr 53.9%

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

4. Final simplification 58.5%

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

Alternative 5: 52.8% accurate, 0.7× speedup

Math

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

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 (* h (* w (* w D))))))
     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 * (h * (w * (w * 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)) / ((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 * (h * (w * (w * D)))));
	} 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 * (h * (w * (w * 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(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(Float64(c0 * Float64(c0 * d)) * Float64(d / Float64(D * Float64(h * Float64(w * Float64(w * 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)) / ((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 * (h * (w * (w * 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[(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[(N[(c0 * N[(c0 * d), $MachinePrecision]), $MachinePrecision] * N[(d / N[(D * N[(h * N[(w * N[(w * D), $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 73.4%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \color{blue}{\frac{{c0}^{2} \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot {w}^{2}\right)}} \]
   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 50.9

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

   5. Simplified 50.9%

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. associate-*l* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. associate-*l* N/A

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

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

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

      16. *-lowering-*.f64 59.5

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

   7. Applied egg-rr 59.5%

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

      1. associate-*r* N/A

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

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

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

      3. *-lowering-*.f64 65.5

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

   9. Applied egg-rr 65.5%

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

   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

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft1-in N/A

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

      9. associate-*l/ N/A

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

   5. Simplified 34.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul0-rgt N/A

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

      3. metadata-eval N/A

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

      4. div0 53.9

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

   7. Applied egg-rr 53.9%

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

4. Final simplification 57.7%

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

Alternative 6: 52.8% accurate, 0.7× speedup

Math

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

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 (* d (/ (* c0 d) (* D (* h (* D (* w w)))))))
     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 * (d * ((c0 * d) / (D * (h * (D * (w * w))))));
	} 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 * (d * ((c0 * d) / (D * (h * (D * (w * w))))));
	} 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 * (d * ((c0 * d) / (D * (h * (D * (w * w))))))
	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(d * Float64(Float64(c0 * d) / Float64(D * Float64(h * Float64(D * Float64(w * w)))))));
	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 * (d * ((c0 * d) / (D * (h * (D * (w * w))))));
	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[(d * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(h * N[(D * N[(w * w), $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 73.4%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \color{blue}{\frac{{c0}^{2} \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot {w}^{2}\right)}} \]
   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 50.9

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

   5. Simplified 50.9%

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

      1. unswap-sqr N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. associate-*l* N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

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

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

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

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

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

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

      15. *-lowering-*.f64 66.4

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

   7. Applied egg-rr 66.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      11. *-lowering-*.f64 64.7

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

   9. Applied egg-rr 64.7%

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

   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

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft1-in N/A

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

      9. associate-*l/ N/A

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

   5. Simplified 34.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul0-rgt N/A

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

      3. metadata-eval N/A

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

      4. div0 53.9

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

   7. Applied egg-rr 53.9%

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

4. Final simplification 57.5%

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

Alternative 7: 33.3% 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 24.4%

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

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

   2. distribute-lft1-in N/A

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

   3. metadata-eval N/A

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

   4. mul0-lft N/A

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

   5. metadata-eval N/A

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

   6. mul0-lft N/A

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

   7. metadata-eval N/A

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

   8. distribute-lft1-in N/A

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

   9. associate-*l/ N/A

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

5. Simplified 26.2%

   \[\leadsto \color{blue}{-0.5 \cdot \frac{\left(c0 \cdot c0\right) \cdot 0}{w}} \]
6. Step-by-step derivation

   1. associate-*r/ N/A

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

   2. mul0-rgt N/A

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

   3. metadata-eval N/A

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

   4. div0 39.0

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

7. Applied egg-rr 39.0%

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

Reproduce

herbie shell --seed 2024194 
(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))))))