Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.6% → 55.1%

Time: 30.4s

Alternatives: 9

Speedup: 151.0×

• could not determine a ground truth

  1. c0 = 5.458978610711113e+137
  2. w = 2.803421440676376e-286
  3. h = -1.7696618167058425e-279
  4. D = 2.0351496541524424e-307
  5. d = 3.2014096235700826e+249
  6. M = -2.038507417091274e-179

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 24.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 55.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(c0, w, h, D, d, M):
	t_0 = c0 / (2.0 * w)
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D))
	tmp = 0
	if (t_0 * (t_1 + math.sqrt(((t_1 * t_1) - (M * M))))) <= math.inf:
		tmp = t_0 * (2.0 * math.pow((math.sqrt(((c0 / w) / h)) / (D / d)), 2.0))
	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(2.0 * (Float64(sqrt(Float64(Float64(c0 / w) / h)) / Float64(D / d)) ^ 2.0)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = t_0 * (2.0 * ((sqrt(((c0 / w) / h)) / (D / d)) ^ 2.0));
	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[(2.0 * N[Power[N[(N[Sqrt[N[(N[(c0 / w), $MachinePrecision] / h), $MachinePrecision]], $MachinePrecision] / N[(D / d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 54.8% accurate, 0.4× speedup

Math

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

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 w) (pow (* (sqrt (/ c0 (* w h))) (/ d D)) 2.0))
     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 / w) * pow((sqrt((c0 / (w * h))) * (d / D)), 2.0);
	} 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 / w) * Math.pow((Math.sqrt((c0 / (w * h))) * (d / D)), 2.0);
	} 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 / w) * math.pow((math.sqrt((c0 / (w * h))) * (d / D)), 2.0)
	else:
		tmp = 0.0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(c0 / w) * (Float64(sqrt(Float64(c0 / Float64(w * h))) * Float64(d / D)) ^ 2.0));
	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 / w) * ((sqrt((c0 / (w * h))) * (d / D)) ^ 2.0);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 54.0% accurate, 0.6× speedup

Math

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

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 w) 2.0) (/ (/ (* 2.0 (/ c0 w)) h) (pow (/ D d) 2.0)))
     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 / w) / 2.0) * (((2.0 * (c0 / w)) / h) / pow((D / d), 2.0));
	} 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 / w) / 2.0) * (((2.0 * (c0 / w)) / h) / Math.pow((D / d), 2.0));
	} 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 / w) / 2.0) * (((2.0 * (c0 / w)) / h) / math.pow((D / d), 2.0))
	else:
		tmp = 0.0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	tmp = 0.0
	if (Float64(Float64(c0 / Float64(2.0 * w)) * Float64(t_0 + sqrt(Float64(Float64(t_0 * t_0) - Float64(M * M))))) <= Inf)
		tmp = Float64(Float64(Float64(c0 / w) / 2.0) * Float64(Float64(Float64(2.0 * Float64(c0 / w)) / h) / (Float64(D / d) ^ 2.0)));
	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 / w) / 2.0) * (((2.0 * (c0 / w)) / h) / ((D / d) ^ 2.0));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 45.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c0 \leq -4.8 \cdot 10^{-79}:\\ \;\;\;\;\frac{c0}{w} \cdot \frac{c0}{\left(w \cdot h\right) \cdot \left(\frac{D}{d} \cdot \frac{1}{\frac{d}{D}}\right)}\\ \mathbf{elif}\;c0 \leq 1.32 \cdot 10^{-18}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{w} \cdot \frac{c0}{w \cdot \left(h \cdot {\left(\frac{d}{D}\right)}^{-2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= c0 -4.8e-79)
   (* (/ c0 w) (/ c0 (* (* w h) (* (/ D d) (/ 1.0 (/ d D))))))
   (if (<= c0 1.32e-18)
     0.0
     (* (/ c0 w) (/ c0 (* w (* h (pow (/ d D) -2.0))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (c0 <= -4.8e-79) {
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))));
	} else if (c0 <= 1.32e-18) {
		tmp = 0.0;
	} else {
		tmp = (c0 / w) * (c0 / (w * (h * pow((d / D), -2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: tmp
    if (c0 <= (-4.8d-79)) then
        tmp = (c0 / w) * (c0 / ((w * h) * ((d / d_1) * (1.0d0 / (d_1 / d)))))
    else if (c0 <= 1.32d-18) then
        tmp = 0.0d0
    else
        tmp = (c0 / w) * (c0 / (w * (h * ((d_1 / d) ** (-2.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (c0 <= -4.8e-79) {
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))));
	} else if (c0 <= 1.32e-18) {
		tmp = 0.0;
	} else {
		tmp = (c0 / w) * (c0 / (w * (h * Math.pow((d / D), -2.0))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if c0 <= -4.8e-79:
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))))
	elif c0 <= 1.32e-18:
		tmp = 0.0
	else:
		tmp = (c0 / w) * (c0 / (w * (h * math.pow((d / D), -2.0))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (c0 <= -4.8e-79)
		tmp = Float64(Float64(c0 / w) * Float64(c0 / Float64(Float64(w * h) * Float64(Float64(D / d) * Float64(1.0 / Float64(d / D))))));
	elseif (c0 <= 1.32e-18)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 / w) * Float64(c0 / Float64(w * Float64(h * (Float64(d / D) ^ -2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (c0 <= -4.8e-79)
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))));
	elseif (c0 <= 1.32e-18)
		tmp = 0.0;
	else
		tmp = (c0 / w) * (c0 / (w * (h * ((d / D) ^ -2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[c0, -4.8e-79], N[(N[(c0 / w), $MachinePrecision] * N[(c0 / N[(N[(w * h), $MachinePrecision] * N[(N[(D / d), $MachinePrecision] * N[(1.0 / N[(d / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c0, 1.32e-18], 0.0, N[(N[(c0 / w), $MachinePrecision] * N[(c0 / N[(w * N[(h * N[Power[N[(d / D), $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 44.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\frac{d}{D}\right)}^{-2}\\ \mathbf{if}\;c0 \leq -2.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{c0}{w} \cdot \frac{c0}{\left(w \cdot h\right) \cdot t_0}\\ \mathbf{elif}\;c0 \leq 1.02 \cdot 10^{-13}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{w} \cdot \frac{c0}{w \cdot \left(h \cdot t_0\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (pow (/ d D) -2.0)))
   (if (<= c0 -2.8e-77)
     (* (/ c0 w) (/ c0 (* (* w h) t_0)))
     (if (<= c0 1.02e-13) 0.0 (* (/ c0 w) (/ c0 (* w (* h t_0))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = pow((d / D), -2.0);
	double tmp;
	if (c0 <= -2.8e-77) {
		tmp = (c0 / w) * (c0 / ((w * h) * t_0));
	} else if (c0 <= 1.02e-13) {
		tmp = 0.0;
	} else {
		tmp = (c0 / w) * (c0 / (w * (h * t_0)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (d_1 / d) ** (-2.0d0)
    if (c0 <= (-2.8d-77)) then
        tmp = (c0 / w) * (c0 / ((w * h) * t_0))
    else if (c0 <= 1.02d-13) then
        tmp = 0.0d0
    else
        tmp = (c0 / w) * (c0 / (w * (h * t_0)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = Math.pow((d / D), -2.0);
	double tmp;
	if (c0 <= -2.8e-77) {
		tmp = (c0 / w) * (c0 / ((w * h) * t_0));
	} else if (c0 <= 1.02e-13) {
		tmp = 0.0;
	} else {
		tmp = (c0 / w) * (c0 / (w * (h * t_0)));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	t_0 = math.pow((d / D), -2.0)
	tmp = 0
	if c0 <= -2.8e-77:
		tmp = (c0 / w) * (c0 / ((w * h) * t_0))
	elif c0 <= 1.02e-13:
		tmp = 0.0
	else:
		tmp = (c0 / w) * (c0 / (w * (h * t_0)))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(d / D) ^ -2.0
	tmp = 0.0
	if (c0 <= -2.8e-77)
		tmp = Float64(Float64(c0 / w) * Float64(c0 / Float64(Float64(w * h) * t_0)));
	elseif (c0 <= 1.02e-13)
		tmp = 0.0;
	else
		tmp = Float64(Float64(c0 / w) * Float64(c0 / Float64(w * Float64(h * t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = (d / D) ^ -2.0;
	tmp = 0.0;
	if (c0 <= -2.8e-77)
		tmp = (c0 / w) * (c0 / ((w * h) * t_0));
	elseif (c0 <= 1.02e-13)
		tmp = 0.0;
	else
		tmp = (c0 / w) * (c0 / (w * (h * t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[Power[N[(d / D), $MachinePrecision], -2.0], $MachinePrecision]}, If[LessEqual[c0, -2.8e-77], N[(N[(c0 / w), $MachinePrecision] * N[(c0 / N[(N[(w * h), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c0, 1.02e-13], 0.0, N[(N[(c0 / w), $MachinePrecision] * N[(c0 / N[(w * N[(h * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 45.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c0 \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{c0}{w} \cdot \frac{c0}{\left(w \cdot h\right) \cdot {\left(\frac{d}{D}\right)}^{-2}}\\ \mathbf{elif}\;c0 \leq 1.1 \cdot 10^{-19}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{w}{{\left(\frac{d}{D}\right)}^{2} \cdot \frac{c0}{w \cdot h}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= c0 -5.6e-79)
   (* (/ c0 w) (/ c0 (* (* w h) (pow (/ d D) -2.0))))
   (if (<= c0 1.1e-19) 0.0 (/ c0 (/ w (* (pow (/ d D) 2.0) (/ c0 (* w h))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (c0 <= -5.6e-79) {
		tmp = (c0 / w) * (c0 / ((w * h) * pow((d / D), -2.0)));
	} else if (c0 <= 1.1e-19) {
		tmp = 0.0;
	} else {
		tmp = c0 / (w / (pow((d / D), 2.0) * (c0 / (w * h))));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: tmp
    if (c0 <= (-5.6d-79)) then
        tmp = (c0 / w) * (c0 / ((w * h) * ((d_1 / d) ** (-2.0d0))))
    else if (c0 <= 1.1d-19) then
        tmp = 0.0d0
    else
        tmp = c0 / (w / (((d_1 / d) ** 2.0d0) * (c0 / (w * h))))
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (c0 <= -5.6e-79) {
		tmp = (c0 / w) * (c0 / ((w * h) * Math.pow((d / D), -2.0)));
	} else if (c0 <= 1.1e-19) {
		tmp = 0.0;
	} else {
		tmp = c0 / (w / (Math.pow((d / D), 2.0) * (c0 / (w * h))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if c0 <= -5.6e-79:
		tmp = (c0 / w) * (c0 / ((w * h) * math.pow((d / D), -2.0)))
	elif c0 <= 1.1e-19:
		tmp = 0.0
	else:
		tmp = c0 / (w / (math.pow((d / D), 2.0) * (c0 / (w * h))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (c0 <= -5.6e-79)
		tmp = Float64(Float64(c0 / w) * Float64(c0 / Float64(Float64(w * h) * (Float64(d / D) ^ -2.0))));
	elseif (c0 <= 1.1e-19)
		tmp = 0.0;
	else
		tmp = Float64(c0 / Float64(w / Float64((Float64(d / D) ^ 2.0) * Float64(c0 / Float64(w * h)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (c0 <= -5.6e-79)
		tmp = (c0 / w) * (c0 / ((w * h) * ((d / D) ^ -2.0)));
	elseif (c0 <= 1.1e-19)
		tmp = 0.0;
	else
		tmp = c0 / (w / (((d / D) ^ 2.0) * (c0 / (w * h))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[c0, -5.6e-79], N[(N[(c0 / w), $MachinePrecision] * N[(c0 / N[(N[(w * h), $MachinePrecision] * N[Power[N[(d / D), $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c0, 1.1e-19], 0.0, N[(c0 / N[(w / N[(N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision] * N[(c0 / N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 45.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c0 \leq -5.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{c0}{w} \cdot \left(c0 \cdot \frac{\frac{1}{h}}{w \cdot {\left(\frac{D}{d}\right)}^{2}}\right)\\ \mathbf{elif}\;c0 \leq 7.5 \cdot 10^{-20}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{w}{{\left(\frac{d}{D}\right)}^{2} \cdot \frac{c0}{w \cdot h}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= c0 -5.6e-78)
   (* (/ c0 w) (* c0 (/ (/ 1.0 h) (* w (pow (/ D d) 2.0)))))
   (if (<= c0 7.5e-20) 0.0 (/ c0 (/ w (* (pow (/ d D) 2.0) (/ c0 (* w h))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (c0 <= -5.6e-78) {
		tmp = (c0 / w) * (c0 * ((1.0 / h) / (w * pow((D / d), 2.0))));
	} else if (c0 <= 7.5e-20) {
		tmp = 0.0;
	} else {
		tmp = c0 / (w / (pow((d / D), 2.0) * (c0 / (w * h))));
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: tmp
    if (c0 <= (-5.6d-78)) then
        tmp = (c0 / w) * (c0 * ((1.0d0 / h) / (w * ((d / d_1) ** 2.0d0))))
    else if (c0 <= 7.5d-20) then
        tmp = 0.0d0
    else
        tmp = c0 / (w / (((d_1 / d) ** 2.0d0) * (c0 / (w * h))))
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if (c0 <= -5.6e-78) {
		tmp = (c0 / w) * (c0 * ((1.0 / h) / (w * Math.pow((D / d), 2.0))));
	} else if (c0 <= 7.5e-20) {
		tmp = 0.0;
	} else {
		tmp = c0 / (w / (Math.pow((d / D), 2.0) * (c0 / (w * h))));
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if c0 <= -5.6e-78:
		tmp = (c0 / w) * (c0 * ((1.0 / h) / (w * math.pow((D / d), 2.0))))
	elif c0 <= 7.5e-20:
		tmp = 0.0
	else:
		tmp = c0 / (w / (math.pow((d / D), 2.0) * (c0 / (w * h))))
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if (c0 <= -5.6e-78)
		tmp = Float64(Float64(c0 / w) * Float64(c0 * Float64(Float64(1.0 / h) / Float64(w * (Float64(D / d) ^ 2.0)))));
	elseif (c0 <= 7.5e-20)
		tmp = 0.0;
	else
		tmp = Float64(c0 / Float64(w / Float64((Float64(d / D) ^ 2.0) * Float64(c0 / Float64(w * h)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if (c0 <= -5.6e-78)
		tmp = (c0 / w) * (c0 * ((1.0 / h) / (w * ((D / d) ^ 2.0))));
	elseif (c0 <= 7.5e-20)
		tmp = 0.0;
	else
		tmp = c0 / (w / (((d / D) ^ 2.0) * (c0 / (w * h))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[LessEqual[c0, -5.6e-78], N[(N[(c0 / w), $MachinePrecision] * N[(c0 * N[(N[(1.0 / h), $MachinePrecision] / N[(w * N[Power[N[(D / d), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c0, 7.5e-20], 0.0, N[(c0 / N[(w / N[(N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision] * N[(c0 / N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 45.0% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c0 \leq -3.2 \cdot 10^{-79} \lor \neg \left(c0 \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{c0}{w} \cdot \frac{c0}{\left(w \cdot h\right) \cdot \left(\frac{D}{d} \cdot \frac{1}{\frac{d}{D}}\right)}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (or (<= c0 -3.2e-79) (not (<= c0 4.9e-27)))
   (* (/ c0 w) (/ c0 (* (* w h) (* (/ D d) (/ 1.0 (/ d D))))))
   0.0))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if ((c0 <= -3.2e-79) || !(c0 <= 4.9e-27)) {
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(c0, w, h, d, d_1, m)
    real(8), intent (in) :: c0
    real(8), intent (in) :: w
    real(8), intent (in) :: h
    real(8), intent (in) :: d
    real(8), intent (in) :: d_1
    real(8), intent (in) :: m
    real(8) :: tmp
    if ((c0 <= (-3.2d-79)) .or. (.not. (c0 <= 4.9d-27))) then
        tmp = (c0 / w) * (c0 / ((w * h) * ((d / d_1) * (1.0d0 / (d_1 / d)))))
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if ((c0 <= -3.2e-79) || !(c0 <= 4.9e-27)) {
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if (c0 <= -3.2e-79) or not (c0 <= 4.9e-27):
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))))
	else:
		tmp = 0.0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if ((c0 <= -3.2e-79) || !(c0 <= 4.9e-27))
		tmp = Float64(Float64(c0 / w) * Float64(c0 / Float64(Float64(w * h) * Float64(Float64(D / d) * Float64(1.0 / Float64(d / D))))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if ((c0 <= -3.2e-79) || ~((c0 <= 4.9e-27)))
		tmp = (c0 / w) * (c0 / ((w * h) * ((D / d) * (1.0 / (d / D)))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[Or[LessEqual[c0, -3.2e-79], N[Not[LessEqual[c0, 4.9e-27]], $MachinePrecision]], N[(N[(c0 / w), $MachinePrecision] * N[(c0 / N[(N[(w * h), $MachinePrecision] * N[(N[(D / d), $MachinePrecision] * N[(1.0 / N[(d / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 32.8% accurate, 151.0× 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023343 
(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))))))