Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.5% → 56.1%

Time: 19.9s

Alternatives: 12

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: 56.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_0 \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;t\_0 \cdot \frac{\left(\frac{c0 \cdot d}{w} \cdot \frac{2}{h}\right) \cdot \frac{d}{D}}{D}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w))) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_1 (sqrt (- (* t_1 t_1) (* M M))))) INFINITY)
     (* t_0 (/ (* (* (/ (* c0 d) w) (/ 2.0 h)) (/ d D)) D))
     0.0)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= ((double) INFINITY)) {
		tmp = t_0 * (((((c0 * d) / w) * (2.0 / h)) * (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 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + Math.sqrt(((t_1 * t_1) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = t_0 * (((((c0 * d) / w) * (2.0 / h)) * (d / D)) / D);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = c0 / (2.0 * w)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_1 + math.sqrt(((t_1 * t_1) - (M * M))))) <= math.inf:
		tmp = t_0 * (((((c0 * d) / w) * (2.0 / h)) * (d / D)) / D)
	else:
		tmp = 0.0
	return tmp

Julia

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

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = t_0 * (((((c0 * d) / w) * (2.0 / h)) * (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[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(N[(N[(c0 * d), $MachinePrecision] / w), $MachinePrecision] * N[(2.0 / h), $MachinePrecision]), $MachinePrecision] * N[(d / D), $MachinePrecision]), $MachinePrecision] / D), $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

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.7

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

   5. Applied rewrites 77.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   7. Applied rewrites 78.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. clear-num N/A

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

      7. inv-pow N/A

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

   9. Applied rewrites 85.8%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-/.f64 N/A

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

       5. unpow-1 N/A

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

       6. lift-/.f64 N/A

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

       7. clear-num N/A

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

       8. lift-*.f64 N/A

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. times-frac N/A

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

       12. lower-*.f64 N/A

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

       13. lower-/.f64 N/A

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

       14. lower-/.f64 86.0

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

   11. Applied rewrites 86.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{{c0}^{2} \cdot \left(-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)}{w}} \]
   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: 55.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_0 \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;t\_0 \cdot \frac{\frac{d}{D} \cdot \frac{2 \cdot \left(c0 \cdot d\right)}{w \cdot h}}{D}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w))) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_1 (sqrt (- (* t_1 t_1) (* M M))))) INFINITY)
     (* t_0 (/ (* (/ d D) (/ (* 2.0 (* c0 d)) (* w h))) D))
     0.0)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= ((double) INFINITY)) {
		tmp = t_0 * (((d / D) * ((2.0 * (c0 * d)) / (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 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + Math.sqrt(((t_1 * t_1) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = t_0 * (((d / D) * ((2.0 * (c0 * d)) / (w * h))) / D);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = c0 / (2.0 * w)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_1 + math.sqrt(((t_1 * t_1) - (M * M))))) <= math.inf:
		tmp = t_0 * (((d / D) * ((2.0 * (c0 * d)) / (w * h))) / D)
	else:
		tmp = 0.0
	return tmp

Julia

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

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = t_0 * (((d / D) * ((2.0 * (c0 * d)) / (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[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(d / D), $MachinePrecision] * N[(N[(2.0 * N[(c0 * d), $MachinePrecision]), $MachinePrecision] / N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / D), $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

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.7

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

   5. Applied rewrites 77.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   7. Applied rewrites 78.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*r* N/A

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

      14. times-frac N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 N/A

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

      21. lower-/.f64 85.9

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

   9. Applied rewrites 85.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{{c0}^{2} \cdot \left(-1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)} + \frac{{d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)}{w}} \]
   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 55.8%

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

Alternative 3: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{if}\;t\_0 \cdot \left(t\_1 + \sqrt{t\_1 \cdot t\_1 - M \cdot M}\right) \leq \infty:\\ \;\;\;\;t\_0 \cdot \left(\frac{2 \cdot \left(c0 \cdot d\right)}{w \cdot h} \cdot \frac{d}{D \cdot D}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w))) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_1 (sqrt (- (* t_1 t_1) (* M M))))) INFINITY)
     (* t_0 (* (/ (* 2.0 (* c0 d)) (* w h)) (/ d (* D D))))
     0.0)))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= ((double) INFINITY)) {
		tmp = t_0 * (((2.0 * (c0 * d)) / (w * h)) * (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 / (2.0 * w);
	double t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	double tmp;
	if ((t_0 * (t_1 + Math.sqrt(((t_1 * t_1) - (M * M))))) <= Double.POSITIVE_INFINITY) {
		tmp = t_0 * (((2.0 * (c0 * d)) / (w * h)) * (d / (D * D)));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = c0 / (2.0 * w)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_1 + math.sqrt(((t_1 * t_1) - (M * M))))) <= math.inf:
		tmp = t_0 * (((2.0 * (c0 * d)) / (w * h)) * (d / (D * D)))
	else:
		tmp = 0.0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(c0 / Float64(2.0 * w))
	t_1 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(t_0 * Float64(t_1 + sqrt(Float64(Float64(t_1 * t_1) - Float64(M * M))))) <= Inf)
		tmp = Float64(t_0 * Float64(Float64(Float64(2.0 * Float64(c0 * d)) / Float64(w * h)) * Float64(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 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = t_0 * (((2.0 * (c0 * d)) / (w * h)) * (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[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(2.0 * N[(c0 * d), $MachinePrecision]), $MachinePrecision] / N[(w * h), $MachinePrecision]), $MachinePrecision] * N[(d / N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.7

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

   5. Applied rewrites 77.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-*l* N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

      21. lower-/.f64 77.3

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

   7. Applied rewrites 77.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-times N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*r* N/A

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

      17. lift-*.f64 N/A

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

      18. times-frac N/A

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

      19. lower-*.f64 N/A

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

   9. Applied rewrites 85.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 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: 55.0% accurate, 0.7× speedup

Math

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

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

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r* N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*r/ N/A

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

      10. lift-*.f64 N/A

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

      11. swap-sqr N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

   9. Applied rewrites 84.8%

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

   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 5: 54.3% accurate, 0.7× speedup

Math

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

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

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r* N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

   9. Applied rewrites 82.4%

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

   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 6: 55.2% accurate, 0.7× speedup

Math

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

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)
     (/ (* d (* c0 (/ (* c0 d) w))) (* D (* 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 = (d * (c0 * ((c0 * d) / w))) / (D * (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 = (d * (c0 * ((c0 * d) / w))) / (D * (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 = (d * (c0 * ((c0 * d) / w))) / (D * (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(d * Float64(c0 * Float64(Float64(c0 * d) / w))) / Float64(D * 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 = (d * (c0 * ((c0 * d) / w))) / (D * (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[(d * N[(c0 * N[(N[(c0 * d), $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(D * N[(w * N[(h * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

   9. Applied rewrites 79.1%

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

   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 53.4%

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

Alternative 7: 53.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(c0 * N[(c0 * d), $MachinePrecision]), $MachinePrecision] / N[(w * h), $MachinePrecision]), $MachinePrecision] * N[(d / N[(w * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r* N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

   9. Applied rewrites 76.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. associate-/l* N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. div0 N/A

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

      6. mul0-rgt N/A

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

      7. metadata-eval 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: 54.2% accurate, 0.7× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. lift-/.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 72.1

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. associate-*l* N/A

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

      18. *-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-*.f64 76.3

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

   9. Applied rewrites 72.6%

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

   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 9: 54.2% accurate, 0.7× speedup

Math

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

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)
     (* c0 (* d (* c0 (/ d (* w (* D (* 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 * (c0 * (d / (w * (D * (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 * (c0 * (d / (w * (D * (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 * (c0 * (d / (w * (D * (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(c0 * Float64(d * Float64(c0 * Float64(d / Float64(w * Float64(D * 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 * (c0 * (d / (w * (D * (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[(c0 * N[(d * N[(c0 * N[(d / N[(w * N[(D * N[(w * N[(h * D), $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. 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%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. associate-*l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

   9. Applied rewrites 72.6%

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

   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 51.0%

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

Alternative 10: 52.4% accurate, 0.7× speedup

Math

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

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 (* c0 (/ (* d 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 * (c0 * ((d * 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 * (c0 * ((d * 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 * (c0 * ((d * 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(c0 * Float64(c0 * Float64(Float64(d * d) / Float64(Float64(D * 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 * (c0 * ((d * 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[(c0 * N[(c0 * N[(N[(d * d), $MachinePrecision] / N[(N[(D * D), $MachinePrecision] * 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. 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%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 69.2

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

   9. Applied rewrites 69.2%

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

   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 49.9%

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

Alternative 11: 52.7% accurate, 0.7× speedup

Math

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

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)
     (* c0 (* c0 (/ (* d 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 * (c0 * ((d * 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 * (c0 * ((d * 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 * (c0 * ((d * 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(c0 * Float64(c0 * Float64(Float64(d * 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 * (c0 * ((d * 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[(c0 * N[(c0 * N[(N[(d * d), $MachinePrecision] / 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. 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%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 67.1

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 66.1

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

   7. Applied rewrites 68.2%

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

   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 12: 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))))))