Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.5% → 56.4%

Time: 18.8s

Alternatives: 10

Speedup: 156.0×

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: 24.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 56.4% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* (/ (/ (* c0 d) D) (* w D)) (/ (* c0 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = (((c0 * d) / D) / (w * D)) * ((c0 * 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = (((c0 * d) / D) / (w * D)) * ((c0 * d) / (w * h));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = (((c0 * d) / D) / (w * D)) * ((c0 * 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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(Float64(Float64(c0 * d) / D) / Float64(w * D)) * Float64(Float64(c0 * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = (((c0 * d) / D) / (w * D)) * ((c0 * 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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(c0 * d), $MachinePrecision] / D), $MachinePrecision] / N[(w * D), $MachinePrecision]), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(w * h), $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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 62.6%

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

   11. Applied rewrites 85.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 2: 56.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* (/ (* c0 d) D) (* (/ d (* w D)) (/ c0 (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = ((c0 * d) / D) * ((d / (w * D)) * (c0 / (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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = ((c0 * d) / D) * ((d / (w * D)) * (c0 / (w * h)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = ((c0 * d) / D) * ((d / (w * D)) * (c0 / (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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(Float64(c0 * d) / D) * Float64(Float64(d / Float64(w * D)) * Float64(c0 / 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = ((c0 * d) / D) * ((d / (w * D)) * (c0 / (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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(c0 * d), $MachinePrecision] / D), $MachinePrecision] * N[(N[(d / N[(w * D), $MachinePrecision]), $MachinePrecision] * N[(c0 / N[(w * h), $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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 72.1%

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

   11. Applied rewrites 77.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 3: 53.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* (/ (* c0 d) (* w (* w h))) (/ (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = ((c0 * d) / (w * (w * h))) * ((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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = ((c0 * d) / (w * (w * h))) * ((c0 * d) / (D * D));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = ((c0 * d) / (w * (w * h))) * ((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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(Float64(c0 * d) / Float64(w * Float64(w * h))) * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = ((c0 * d) / (w * (w * h))) * ((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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(c0 * d), $MachinePrecision] / N[(w * N[(w * h), $MachinePrecision]), $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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 77.1%

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

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 4: 55.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(c0 * d), $MachinePrecision] / D), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(w * N[(w * N[(h * D), $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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 72.1%

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

   11. Applied rewrites 72.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

4. Final simplification 51.0%

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

Alternative 5: 54.9% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* (/ (* c0 d) D) (/ (* c0 d) (* D (* w (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = ((c0 * d) / D) * ((c0 * d) / (D * (w * (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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = ((c0 * d) / D) * ((c0 * d) / (D * (w * (w * h))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = ((c0 * d) / D) * ((c0 * d) / (D * (w * (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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(Float64(c0 * d) / D) * Float64(Float64(c0 * d) / Float64(D * Float64(w * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = ((c0 * d) / D) * ((c0 * d) / (D * (w * (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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(c0 * d), $MachinePrecision] / D), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(w * N[(w * h), $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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 72.1%

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

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 6: 54.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* (* c0 d) (/ (* c0 d) (* D (* D (* w (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = (c0 * d) * ((c0 * d) / (D * (D * (w * (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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = (c0 * d) * ((c0 * d) / (D * (D * (w * (w * h)))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = (c0 * d) * ((c0 * d) / (D * (D * (w * (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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(c0 * d) * Float64(Float64(c0 * d) / Float64(D * Float64(D * Float64(w * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = (c0 * d) * ((c0 * d) / (D * (D * (w * (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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(c0 * d), $MachinePrecision] * N[(N[(c0 * d), $MachinePrecision] / N[(D * N[(D * N[(w * 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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 72.1%

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

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 7: 53.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* d (* (* c0 d) (/ c0 (* D (* D (* w (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = d * ((c0 * d) * (c0 / (D * (D * (w * (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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = d * ((c0 * d) * (c0 / (D * (D * (w * (w * h))))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = d * ((c0 * d) * (c0 / (D * (D * (w * (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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(d * Float64(Float64(c0 * d) * Float64(c0 / Float64(D * Float64(D * Float64(w * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = d * ((c0 * d) * (c0 / (D * (D * (w * (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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(d * N[(N[(c0 * d), $MachinePrecision] * N[(c0 / N[(D * N[(D * N[(w * N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 62.6%

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

   11. Applied rewrites 70.1%

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

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 8: 53.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (* d (* c0 (* d (/ c0 (* D (* D (* w (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = d * (c0 * (d * (c0 / (D * (D * (w * (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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = d * (c0 * (d * (c0 / (D * (D * (w * (w * h)))))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = d * (c0 * (d * (c0 / (D * (D * (w * (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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(d * Float64(c0 * Float64(d * Float64(c0 / Float64(D * Float64(D * Float64(w * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = d * (c0 * (d * (c0 / (D * (D * (w * (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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(d * N[(c0 * N[(d * N[(c0 / N[(D * N[(D * N[(w * N[(w * h), $MachinePrecision]), $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 77.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 61.2

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

   7. Applied rewrites 61.2%

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

   9. Applied rewrites 62.6%

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

   11. Applied rewrites 70.1%

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

   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. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

4. Final simplification 50.1%

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

Alternative 9: 49.2% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<=
        (* (/ c0 (* 2.0 w)) (+ t_0 (sqrt (- (* t_0 t_0) (* M M)))))
        INFINITY)
     (/ (* (* d d) (* c0 c0)) (* (* D D) (* h (* 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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= ((double) INFINITY)) {
		tmp = ((d * d) * (c0 * c0)) / ((D * D) * (h * (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)) / ((w * h) * (D * D));
	double tmp;
	if (((c0 / (2.0 * w)) * (t_0 + Math.sqrt(((t_0 * t_0) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = ((d * d) * (c0 * c0)) / ((D * D) * (h * (w * w)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if ((c0 / (2.0 * w)) * (t_0 + math.sqrt(((t_0 * t_0) - (M * M))))) <= math.inf:
		tmp = ((d * d) * (c0 * c0)) / ((D * D) * (h * (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(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(Float64(d * d) * Float64(c0 * c0)) / Float64(Float64(D * D) * Float64(h * 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)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = ((d * d) * (c0 * c0)) / ((D * D) * (h * (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[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(d * d), $MachinePrecision] * N[(c0 * c0), $MachinePrecision]), $MachinePrecision] / N[(N[(D * D), $MachinePrecision] * N[(h * N[(w * w), $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 77.6%

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

   3. Taylor expanded in c0 around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 61.2

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

   5. Applied rewrites 61.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 39.2

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

   5. Applied rewrites 39.2%

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

4. Final simplification 47.0%

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

Alternative 10: 33.9% 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 27.6%

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

3. Taylor expanded in c0 around -inf

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

   1. associate-/l* N/A

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

   2. distribute-lft1-in N/A

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

   3. metadata-eval N/A

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

   4. mul0-lft N/A

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

   5. div0 N/A

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

   6. mul0-rgt N/A

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

   7. metadata-eval 29.5

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

5. Applied rewrites 29.5%

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

Reproduce

herbie shell --seed 2024214 
(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))))))