Henrywood and Agarwal, Equation (13)

Percentage Accurate: 25.1% → 56.8%

Time: 16.9s

Alternatives: 8

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: 25.1% 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: 56.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 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 (* (/ 2.0 D) (* 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 * ((2.0 / D) * (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 * ((2.0 / D) * (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 * ((2.0 / D) * (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(d * Float64(Float64(2.0 / D) * Float64(c0 * Float64(d / Float64(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 * ((2.0 / D) * (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[(d * N[(N[(2.0 / D), $MachinePrecision] * N[(c0 * N[(d / N[(N[(w * h), $MachinePrecision] * 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 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

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

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. times-frac N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   7. Applied egg-rr 79.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. clear-num N/A

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

      6. frac-times N/A

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

      7. *-rgt-identity N/A

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

      8. associate-/l* N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/r* N/A

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

      12. associate-/r/ N/A

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

      13. lower-*.f64 N/A

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

   9. Applied egg-rr 82.3%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. times-frac N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. div-inv N/A

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

       8. clear-num N/A

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

       9. lift-*.f64 N/A

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

       10. associate-/l/ N/A

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

       11. lift-/.f64 N/A

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

       12. lower-*.f64 N/A

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

       13. lift-/.f64 N/A

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

       14. associate-/l/ N/A

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

       15. lift-*.f64 N/A

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

       16. lower-/.f64 85.2

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

   11. Applied egg-rr 85.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 59.0%

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

Alternative 2: 55.5% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 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 (* D (* (* w h) D))) (* 2.0 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 / (D * ((w * h) * D))) * (2.0 * 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 / (D * ((w * h) * D))) * (2.0 * 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 / (D * ((w * h) * D))) * (2.0 * 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(c0 * Float64(Float64(d / Float64(D * Float64(Float64(w * h) * D))) * Float64(2.0 * 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 / (D * ((w * h) * D))) * (2.0 * 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[(c0 * N[(N[(d / N[(D * N[(N[(w * h), $MachinePrecision] * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 * 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 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\frac{2 \cdot \left(c0 \cdot \left(d \cdot d\right)\right)}{\left(D \cdot D\right) \cdot \left(h \cdot w\right)}} \]
   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. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r/ N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*r/ N/A

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

      13. lift-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. lower-*.f64 N/A

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

   7. Applied egg-rr 78.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-*.f64 80.3

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

   9. Applied egg-rr 80.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 57.2%

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

Alternative 3: 55.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if (((c0 / (2.0 * w)) * (t_0 + sqrt(((t_0 * t_0) - (M * M))))) <= Inf)
		tmp = (d * (c0 * d)) / ((w * h) * ((D * (w * D)) / c0));
	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 * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(N[(D * N[(w * D), $MachinePrecision]), $MachinePrecision] / c0), $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 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

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

   6. Taylor expanded in c0 around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 60.0

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

   8. Simplified 60.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

   10. Applied egg-rr 74.3%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. lift-*.f64 N/A

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

       6. lift-/.f64 N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

       10. lift-*.f64 N/A

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

       11. lift-/.f64 N/A

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

       12. clear-num N/A

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

       13. un-div-inv N/A

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

       14. lower-/.f64 N/A

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

   12. Applied egg-rr 78.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 56.4%

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

Alternative 4: 54.8% accurate, 0.7× speedup

Math

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

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)
     (* (* d d) (* (/ c0 (* w (* (* w h) D))) (/ c0 D)))
     0.0)))

C

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

Java

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

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(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 * d) * Float64(Float64(c0 / Float64(w * Float64(Float64(w * h) * D))) * Float64(c0 / D)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

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

   6. Taylor expanded in c0 around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 60.0

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

   8. Simplified 60.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. times-frac N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lower-/.f64 78.2

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

   10. Applied egg-rr 78.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 56.4%

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

Alternative 5: 54.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

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

   6. Taylor expanded in c0 around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 60.0

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

   8. Simplified 60.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

   10. Applied egg-rr 74.3%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. lift-*.f64 N/A

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

       6. lift-/.f64 N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

       10. lift-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 75.1

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

   12. Applied egg-rr 75.9%

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

   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. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 55.6%

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

Alternative 6: 54.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(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 * d) * Float64(c0 * Float64(c0 / Float64(Float64(w * h) * Float64(D * Float64(w * D))))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

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

   6. Taylor expanded in c0 around 0

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 60.0

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

   8. Simplified 60.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

   10. Applied egg-rr 74.3%

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

       1. associate-*r* N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 75.2

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

   12. Applied egg-rr 75.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c0 around -inf

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

      1. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 55.3%

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

Alternative 7: 54.2% accurate, 0.7× speedup

Math

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

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 (* w (* D (* 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 * (w * (D * (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 * (w * (D * (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 * (w * (D * (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(w * Float64(D * 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 * (w * (D * (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[(w * N[(D * 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 77.7%

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

   3. Taylor expanded in c0 around inf

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{c0 \cdot {d}^{2}}{{D}^{2} \cdot \left(h \cdot w\right)}\right)} \]
   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 77.6

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

   5. Simplified 77.6%

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

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. times-frac N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   7. Applied egg-rr 79.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. clear-num N/A

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

      6. frac-times N/A

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

      7. *-rgt-identity N/A

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

      8. associate-/l* N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/r* N/A

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

      12. associate-/r/ N/A

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

      13. lower-*.f64 N/A

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

   9. Applied egg-rr 82.3%

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

   10. Taylor expanded in c0 around 0

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

       1. associate-/l* N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

       4. lower-*.f64 N/A

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

       5. associate-*r/ N/A

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

       6. unpow2 N/A

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-/l* N/A

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

       10. lower-*.f64 N/A

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

       11. associate-/l* N/A

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

       12. lower-*.f64 N/A

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

       13. lower-/.f64 N/A

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

       14. unpow2 N/A

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

       15. associate-*r* N/A

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

       16. associate-*r* N/A

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

       17. *-commutative N/A

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

       18. lower-*.f64 N/A

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

       19. associate-*r* N/A

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

       20. *-commutative N/A

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

       21. lower-*.f64 N/A

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

       22. unpow2 N/A

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

       23. associate-*l* N/A

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

   12. Simplified 74.9%

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

   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. *-commutative N/A

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

      2. distribute-lft1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. associate-/l* N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval 43.7

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

   5. Simplified 43.7%

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

4. Final simplification 55.2%

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

Alternative 8: 33.4% 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 28.5%

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

3. Taylor expanded in c0 around -inf

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

   1. *-commutative N/A

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

   2. distribute-lft1-in N/A

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

   3. metadata-eval N/A

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

   4. mul0-lft N/A

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

   5. associate-/l* N/A

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

   6. mul0-lft N/A

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

   7. metadata-eval 32.1

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

5. Simplified 32.1%

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

Reproduce

herbie shell --seed 2024221 
(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))))))