Henrywood and Agarwal, Equation (13)

Percentage Accurate: 25.1% → 55.1%

Time: 25.6s

Alternatives: 6

Speedup: 151.0×

• could not determine a ground truth

  1. c0 = -2.405720809465237e+251
  2. w = 2.0888128563242268e-272
  3. h = 6.708255111974731e-254
  4. D = -3.1854722176076943e-283
  5. d = -7.597554123040921e+180
  6. M = -5.818078893750527e-40

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: 55.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{w}}{h}\right)\\ t_1 := \frac{c0}{2 \cdot w}\\ t_2 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ t_3 := t_1 \cdot \left(t_2 + \sqrt{t_2 \cdot t_2 - M \cdot M}\right)\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+237}:\\ \;\;\;\;t_1 \cdot \left(\frac{\frac{c0 \cdot {\left(\frac{d}{D}\right)}^{2}}{w}}{h} + t_0\right)\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_1 \cdot \mathsf{fma}\left(-1, c0 \cdot 0, 0.5 \cdot \left(\frac{{D}^{2}}{c0} \cdot \frac{{M}^{2}}{\frac{{d}^{2}}{w \cdot h}}\right)\right)\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_1 \cdot \left(t_0 + \frac{{\left(\frac{d}{D} \cdot \sqrt{\frac{c0}{w}}\right)}^{2}}{h}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (* (/ d D) (* (/ d D) (/ (/ c0 w) h))))
        (t_1 (/ c0 (* 2.0 w)))
        (t_2 (/ (* c0 (* d d)) (* (* w h) (* D D))))
        (t_3 (* t_1 (+ t_2 (sqrt (- (* t_2 t_2) (* M M)))))))
   (if (<= t_3 -5e+237)
     (* t_1 (+ (/ (/ (* c0 (pow (/ d D) 2.0)) w) h) t_0))
     (if (<= t_3 0.0)
       (*
        t_1
        (fma
         -1.0
         (* c0 0.0)
         (*
          0.5
          (* (/ (pow D 2.0) c0) (/ (pow M 2.0) (/ (pow d 2.0) (* w h)))))))
       (if (<= t_3 INFINITY)
         (* t_1 (+ t_0 (/ (pow (* (/ d D) (sqrt (/ c0 w))) 2.0) h)))
         0.0)))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = (d / D) * ((d / D) * ((c0 / w) / h));
	double t_1 = c0 / (2.0 * w);
	double t_2 = (c0 * (d * d)) / ((w * h) * (D * D));
	double t_3 = t_1 * (t_2 + sqrt(((t_2 * t_2) - (M * M))));
	double tmp;
	if (t_3 <= -5e+237) {
		tmp = t_1 * ((((c0 * pow((d / D), 2.0)) / w) / h) + t_0);
	} else if (t_3 <= 0.0) {
		tmp = t_1 * fma(-1.0, (c0 * 0.0), (0.5 * ((pow(D, 2.0) / c0) * (pow(M, 2.0) / (pow(d, 2.0) / (w * h))))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1 * (t_0 + (pow(((d / D) * sqrt((c0 / w))), 2.0) / h));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Julia

function code(c0, w, h, D, d, M)
	t_0 = Float64(Float64(d / D) * Float64(Float64(d / D) * Float64(Float64(c0 / w) / h)))
	t_1 = Float64(c0 / Float64(2.0 * w))
	t_2 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	t_3 = Float64(t_1 * Float64(t_2 + sqrt(Float64(Float64(t_2 * t_2) - Float64(M * M)))))
	tmp = 0.0
	if (t_3 <= -5e+237)
		tmp = Float64(t_1 * Float64(Float64(Float64(Float64(c0 * (Float64(d / D) ^ 2.0)) / w) / h) + t_0));
	elseif (t_3 <= 0.0)
		tmp = Float64(t_1 * fma(-1.0, Float64(c0 * 0.0), Float64(0.5 * Float64(Float64((D ^ 2.0) / c0) * Float64((M ^ 2.0) / Float64((d ^ 2.0) / Float64(w * h)))))));
	elseif (t_3 <= Inf)
		tmp = Float64(t_1 * Float64(t_0 + Float64((Float64(Float64(d / D) * sqrt(Float64(c0 / w))) ^ 2.0) / h)));
	else
		tmp = 0.0;
	end
	return tmp
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(N[(d / D), $MachinePrecision] * N[(N[(d / D), $MachinePrecision] * N[(N[(c0 / w), $MachinePrecision] / h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * N[(t$95$2 + N[Sqrt[N[(N[(t$95$2 * t$95$2), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+237], N[(t$95$1 * N[(N[(N[(N[(c0 * N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / w), $MachinePrecision] / h), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$1 * N[(-1.0 * N[(c0 * 0.0), $MachinePrecision] + N[(0.5 * N[(N[(N[Power[D, 2.0], $MachinePrecision] / c0), $MachinePrecision] * N[(N[Power[M, 2.0], $MachinePrecision] / N[(N[Power[d, 2.0], $MachinePrecision] / N[(w * h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$1 * N[(t$95$0 + N[(N[Power[N[(N[(d / D), $MachinePrecision] * N[Sqrt[N[(c0 / w), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]]]]]

Derivation

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

Alternative 2: 54.6% accurate, 0.4× speedup

Math

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

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
      (+
       (/ (* (pow (/ d D) 2.0) (/ c0 w)) h)
       (* (/ d D) (* (/ d D) (fabs (/ (/ c0 h) w))))))
     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 * (((pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * fabs(((c0 / h) / w)))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Java

public static double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (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 * (((Math.pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * Math.abs(((c0 / h) / w)))));
	} 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 * (((math.pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * math.fabs(((c0 / h) / w)))))
	else:
		tmp = 0.0
	return tmp

Julia

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

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = t_0 * (((((d / D) ^ 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * abs(((c0 / h) / w)))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision] * N[(c0 / w), $MachinePrecision]), $MachinePrecision] / h), $MachinePrecision] + N[(N[(d / D), $MachinePrecision] * N[(N[(d / D), $MachinePrecision] * N[Abs[N[(N[(c0 / h), $MachinePrecision] / w), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]

Derivation

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

Alternative 3: 54.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* 2.0 w))) (t_1 (/ (* c0 (* d d)) (* (* w h) (* D D)))))
   (if (<= (* t_0 (+ t_1 (sqrt (- (* t_1 t_1) (* M M))))) INFINITY)
     (*
      t_0
      (+
       (/ (* (pow (/ d D) 2.0) (/ c0 w)) h)
       (* (/ d D) (/ (* d (/ c0 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 * (((pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d * (c0 / 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 * (((Math.pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d * (c0 / 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 * (((math.pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d * (c0 / w)) / (h * D))))
	else:
		tmp = 0.0
	return tmp

Julia

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

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	t_0 = c0 / (2.0 * w);
	t_1 = (c0 * (d * d)) / ((w * h) * (D * D));
	tmp = 0.0;
	if ((t_0 * (t_1 + sqrt(((t_1 * t_1) - (M * M))))) <= Inf)
		tmp = t_0 * (((((d / D) ^ 2.0) * (c0 / w)) / h) + ((d / D) * ((d * (c0 / w)) / (h * D))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(t$95$1 + N[Sqrt[N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 * N[(N[(N[(N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision] * N[(c0 / w), $MachinePrecision]), $MachinePrecision] / h), $MachinePrecision] + N[(N[(d / D), $MachinePrecision] * N[(N[(d * N[(c0 / w), $MachinePrecision]), $MachinePrecision] / N[(h * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]

Derivation

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

Alternative 4: 45.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c0 \leq -4.5 \cdot 10^{-101} \lor \neg \left(c0 \leq 2 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{{\left(\frac{d}{D}\right)}^{2} \cdot \frac{c0}{w}}{h} + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (or (<= c0 -4.5e-101) (not (<= c0 2e-64)))
   (*
    (/ c0 (* 2.0 w))
    (+
     (/ (* (pow (/ d D) 2.0) (/ c0 w)) h)
     (* (/ d D) (* (/ d D) (/ (/ c0 h) w)))))
   0.0))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if ((c0 <= -4.5e-101) || !(c0 <= 2e-64)) {
		tmp = (c0 / (2.0 * w)) * (((pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * ((c0 / h) / w))));
	} 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 <= (-4.5d-101)) .or. (.not. (c0 <= 2d-64))) then
        tmp = (c0 / (2.0d0 * w)) * (((((d_1 / d) ** 2.0d0) * (c0 / w)) / h) + ((d_1 / d) * ((d_1 / d) * ((c0 / h) / w))))
    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 <= -4.5e-101) || !(c0 <= 2e-64)) {
		tmp = (c0 / (2.0 * w)) * (((Math.pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * ((c0 / h) / w))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if (c0 <= -4.5e-101) or not (c0 <= 2e-64):
		tmp = (c0 / (2.0 * w)) * (((math.pow((d / D), 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * ((c0 / h) / w))))
	else:
		tmp = 0.0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if ((c0 <= -4.5e-101) || !(c0 <= 2e-64))
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64((Float64(d / D) ^ 2.0) * Float64(c0 / w)) / h) + Float64(Float64(d / D) * Float64(Float64(d / D) * Float64(Float64(c0 / h) / w)))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if ((c0 <= -4.5e-101) || ~((c0 <= 2e-64)))
		tmp = (c0 / (2.0 * w)) * (((((d / D) ^ 2.0) * (c0 / w)) / h) + ((d / D) * ((d / D) * ((c0 / h) / w))));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[Or[LessEqual[c0, -4.5e-101], N[Not[LessEqual[c0, 2e-64]], $MachinePrecision]], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision] * N[(c0 / w), $MachinePrecision]), $MachinePrecision] / h), $MachinePrecision] + N[(N[(d / D), $MachinePrecision] * N[(N[(d / D), $MachinePrecision] * N[(N[(c0 / h), $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

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

Alternative 5: 45.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c0 \leq -5.2 \cdot 10^{-101} \lor \neg \left(c0 \leq 8.8 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{w}}{h}\right) + \frac{{\left(\frac{d}{D}\right)}^{2} \cdot \frac{c0}{w}}{h}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (if (or (<= c0 -5.2e-101) (not (<= c0 8.8e-66)))
   (*
    (/ c0 (* 2.0 w))
    (+
     (* (/ d D) (* (/ d D) (/ (/ c0 w) h)))
     (/ (* (pow (/ d D) 2.0) (/ c0 w)) h)))
   0.0))

C

double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if ((c0 <= -5.2e-101) || !(c0 <= 8.8e-66)) {
		tmp = (c0 / (2.0 * w)) * (((d / D) * ((d / D) * ((c0 / w) / h))) + ((pow((d / D), 2.0) * (c0 / w)) / h));
	} 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 <= (-5.2d-101)) .or. (.not. (c0 <= 8.8d-66))) then
        tmp = (c0 / (2.0d0 * w)) * (((d_1 / d) * ((d_1 / d) * ((c0 / w) / h))) + ((((d_1 / d) ** 2.0d0) * (c0 / w)) / h))
    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 <= -5.2e-101) || !(c0 <= 8.8e-66)) {
		tmp = (c0 / (2.0 * w)) * (((d / D) * ((d / D) * ((c0 / w) / h))) + ((Math.pow((d / D), 2.0) * (c0 / w)) / h));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(c0, w, h, D, d, M):
	tmp = 0
	if (c0 <= -5.2e-101) or not (c0 <= 8.8e-66):
		tmp = (c0 / (2.0 * w)) * (((d / D) * ((d / D) * ((c0 / w) / h))) + ((math.pow((d / D), 2.0) * (c0 / w)) / h))
	else:
		tmp = 0.0
	return tmp

Julia

function code(c0, w, h, D, d, M)
	tmp = 0.0
	if ((c0 <= -5.2e-101) || !(c0 <= 8.8e-66))
		tmp = Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64(d / D) * Float64(Float64(d / D) * Float64(Float64(c0 / w) / h))) + Float64(Float64((Float64(d / D) ^ 2.0) * Float64(c0 / w)) / h)));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, w, h, D, d, M)
	tmp = 0.0;
	if ((c0 <= -5.2e-101) || ~((c0 <= 8.8e-66)))
		tmp = (c0 / (2.0 * w)) * (((d / D) * ((d / D) * ((c0 / w) / h))) + ((((d / D) ^ 2.0) * (c0 / w)) / h));
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := If[Or[LessEqual[c0, -5.2e-101], N[Not[LessEqual[c0, 8.8e-66]], $MachinePrecision]], N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(d / D), $MachinePrecision] * N[(N[(d / D), $MachinePrecision] * N[(N[(c0 / w), $MachinePrecision] / h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision] * N[(c0 / w), $MachinePrecision]), $MachinePrecision] / h), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

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

Alternative 6: 33.2% 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 2023364 
(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))))))