VandenBroeck and Keller, Equation (20)

Percentage Accurate: 6.7% → 96.7%

Time: 20.7s

Alternatives: 14

Speedup: 1027.0×

• could not determine a ground truth

  1. f = 2.00000000000000007e154

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{4} \cdot f\\ t_1 := e^{t_0}\\ t_2 := e^{-t_0}\\ -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{t_1 + t_2}{t_1 - t_2}\right) \end{array} \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (let* ((t_0 (* (/ PI 4.0) f)) (t_1 (exp t_0)) (t_2 (exp (- t_0))))
   (- (* (/ 1.0 (/ PI 4.0)) (log (/ (+ t_1 t_2) (- t_1 t_2)))))))

C

double code(double f) {
	double t_0 = (((double) M_PI) / 4.0) * f;
	double t_1 = exp(t_0);
	double t_2 = exp(-t_0);
	return -((1.0 / (((double) M_PI) / 4.0)) * log(((t_1 + t_2) / (t_1 - t_2))));
}

Java

public static double code(double f) {
	double t_0 = (Math.PI / 4.0) * f;
	double t_1 = Math.exp(t_0);
	double t_2 = Math.exp(-t_0);
	return -((1.0 / (Math.PI / 4.0)) * Math.log(((t_1 + t_2) / (t_1 - t_2))));
}

Python

def code(f):
	t_0 = (math.pi / 4.0) * f
	t_1 = math.exp(t_0)
	t_2 = math.exp(-t_0)
	return -((1.0 / (math.pi / 4.0)) * math.log(((t_1 + t_2) / (t_1 - t_2))))

Julia

function code(f)
	t_0 = Float64(Float64(pi / 4.0) * f)
	t_1 = exp(t_0)
	t_2 = exp(Float64(-t_0))
	return Float64(-Float64(Float64(1.0 / Float64(pi / 4.0)) * log(Float64(Float64(t_1 + t_2) / Float64(t_1 - t_2)))))
end

MATLAB

function tmp = code(f)
	t_0 = (pi / 4.0) * f;
	t_1 = exp(t_0);
	t_2 = exp(-t_0);
	tmp = -((1.0 / (pi / 4.0)) * log(((t_1 + t_2) / (t_1 - t_2))));
end

Wolfram

code[f_] := Block[{t$95$0 = N[(N[(Pi / 4.0), $MachinePrecision] * f), $MachinePrecision]}, Block[{t$95$1 = N[Exp[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Exp[(-t$95$0)], $MachinePrecision]}, (-N[(N[(1.0 / N[(Pi / 4.0), $MachinePrecision]), $MachinePrecision] * N[Log[N[(N[(t$95$1 + t$95$2), $MachinePrecision] / N[(t$95$1 - t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision])]]]

Initial Program: 6.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{4} \cdot f\\ t_1 := e^{t_0}\\ t_2 := e^{-t_0}\\ -\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{t_1 + t_2}{t_1 - t_2}\right) \end{array} \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (let* ((t_0 (* (/ PI 4.0) f)) (t_1 (exp t_0)) (t_2 (exp (- t_0))))
   (- (* (/ 1.0 (/ PI 4.0)) (log (/ (+ t_1 t_2) (- t_1 t_2)))))))

C

double code(double f) {
	double t_0 = (((double) M_PI) / 4.0) * f;
	double t_1 = exp(t_0);
	double t_2 = exp(-t_0);
	return -((1.0 / (((double) M_PI) / 4.0)) * log(((t_1 + t_2) / (t_1 - t_2))));
}

Java

public static double code(double f) {
	double t_0 = (Math.PI / 4.0) * f;
	double t_1 = Math.exp(t_0);
	double t_2 = Math.exp(-t_0);
	return -((1.0 / (Math.PI / 4.0)) * Math.log(((t_1 + t_2) / (t_1 - t_2))));
}

Python

def code(f):
	t_0 = (math.pi / 4.0) * f
	t_1 = math.exp(t_0)
	t_2 = math.exp(-t_0)
	return -((1.0 / (math.pi / 4.0)) * math.log(((t_1 + t_2) / (t_1 - t_2))))

Julia

function code(f)
	t_0 = Float64(Float64(pi / 4.0) * f)
	t_1 = exp(t_0)
	t_2 = exp(Float64(-t_0))
	return Float64(-Float64(Float64(1.0 / Float64(pi / 4.0)) * log(Float64(Float64(t_1 + t_2) / Float64(t_1 - t_2)))))
end

MATLAB

function tmp = code(f)
	t_0 = (pi / 4.0) * f;
	t_1 = exp(t_0);
	t_2 = exp(-t_0);
	tmp = -((1.0 / (pi / 4.0)) * log(((t_1 + t_2) / (t_1 - t_2))));
end

Wolfram

code[f_] := Block[{t$95$0 = N[(N[(Pi / 4.0), $MachinePrecision] * f), $MachinePrecision]}, Block[{t$95$1 = N[Exp[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Exp[(-t$95$0)], $MachinePrecision]}, (-N[(N[(1.0 / N[(Pi / 4.0), $MachinePrecision]), $MachinePrecision] * N[Log[N[(N[(t$95$1 + t$95$2), $MachinePrecision] / N[(t$95$1 - t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision])]]]

Alternative 1: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{\log \left(\frac{e^{0.25 \cdot \left(\pi \cdot \left(-f\right)\right)} + e^{0.25 \cdot \left(f \cdot \pi\right)}}{\mathsf{fma}\left(f, \pi \cdot 0.5, \mathsf{fma}\left({f}^{3}, {\pi}^{3} \cdot 0.005208333333333333, \mathsf{fma}\left({f}^{7}, {\pi}^{7} \cdot 2.422030009920635 \cdot 10^{-8}, 1.6276041666666666 \cdot 10^{-5} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)\right)\right)}\right)}{\pi} \cdot -4 \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (*
  (/
   (log
    (/
     (+ (exp (* 0.25 (* PI (- f)))) (exp (* 0.25 (* f PI))))
     (fma
      f
      (* PI 0.5)
      (fma
       (pow f 3.0)
       (* (pow PI 3.0) 0.005208333333333333)
       (fma
        (pow f 7.0)
        (* (pow PI 7.0) 2.422030009920635e-8)
        (* 1.6276041666666666e-5 (* (pow f 5.0) (pow PI 5.0))))))))
   PI)
  -4.0))

C

double code(double f) {
	return (log(((exp((0.25 * (((double) M_PI) * -f))) + exp((0.25 * (f * ((double) M_PI))))) / fma(f, (((double) M_PI) * 0.5), fma(pow(f, 3.0), (pow(((double) M_PI), 3.0) * 0.005208333333333333), fma(pow(f, 7.0), (pow(((double) M_PI), 7.0) * 2.422030009920635e-8), (1.6276041666666666e-5 * (pow(f, 5.0) * pow(((double) M_PI), 5.0)))))))) / ((double) M_PI)) * -4.0;
}

Julia

function code(f)
	return Float64(Float64(log(Float64(Float64(exp(Float64(0.25 * Float64(pi * Float64(-f)))) + exp(Float64(0.25 * Float64(f * pi)))) / fma(f, Float64(pi * 0.5), fma((f ^ 3.0), Float64((pi ^ 3.0) * 0.005208333333333333), fma((f ^ 7.0), Float64((pi ^ 7.0) * 2.422030009920635e-8), Float64(1.6276041666666666e-5 * Float64((f ^ 5.0) * (pi ^ 5.0)))))))) / pi) * -4.0)
end

Wolfram

code[f_] := N[(N[(N[Log[N[(N[(N[Exp[N[(0.25 * N[(Pi * (-f)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(0.25 * N[(f * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(f * N[(Pi * 0.5), $MachinePrecision] + N[(N[Power[f, 3.0], $MachinePrecision] * N[(N[Power[Pi, 3.0], $MachinePrecision] * 0.005208333333333333), $MachinePrecision] + N[(N[Power[f, 7.0], $MachinePrecision] * N[(N[Power[Pi, 7.0], $MachinePrecision] * 2.422030009920635e-8), $MachinePrecision] + N[(1.6276041666666666e-5 * N[(N[Power[f, 5.0], $MachinePrecision] * N[Power[Pi, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

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Alternative 2: 96.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{\log \left(\frac{e^{0.25 \cdot \left(\pi \cdot \left(-f\right)\right)} + e^{0.25 \cdot \left(f \cdot \pi\right)}}{\mathsf{fma}\left(f, \pi \cdot 0.5, \mathsf{fma}\left({f}^{3}, {\pi}^{3} \cdot 0.005208333333333333, {f}^{5} \cdot \left(1.6276041666666666 \cdot 10^{-5} \cdot {\pi}^{5}\right)\right)\right)}\right)}{\pi} \cdot -4 \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (*
  (/
   (log
    (/
     (+ (exp (* 0.25 (* PI (- f)))) (exp (* 0.25 (* f PI))))
     (fma
      f
      (* PI 0.5)
      (fma
       (pow f 3.0)
       (* (pow PI 3.0) 0.005208333333333333)
       (* (pow f 5.0) (* 1.6276041666666666e-5 (pow PI 5.0)))))))
   PI)
  -4.0))

C

double code(double f) {
	return (log(((exp((0.25 * (((double) M_PI) * -f))) + exp((0.25 * (f * ((double) M_PI))))) / fma(f, (((double) M_PI) * 0.5), fma(pow(f, 3.0), (pow(((double) M_PI), 3.0) * 0.005208333333333333), (pow(f, 5.0) * (1.6276041666666666e-5 * pow(((double) M_PI), 5.0))))))) / ((double) M_PI)) * -4.0;
}

Julia

function code(f)
	return Float64(Float64(log(Float64(Float64(exp(Float64(0.25 * Float64(pi * Float64(-f)))) + exp(Float64(0.25 * Float64(f * pi)))) / fma(f, Float64(pi * 0.5), fma((f ^ 3.0), Float64((pi ^ 3.0) * 0.005208333333333333), Float64((f ^ 5.0) * Float64(1.6276041666666666e-5 * (pi ^ 5.0))))))) / pi) * -4.0)
end

Wolfram

code[f_] := N[(N[(N[Log[N[(N[(N[Exp[N[(0.25 * N[(Pi * (-f)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(0.25 * N[(f * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(f * N[(Pi * 0.5), $MachinePrecision] + N[(N[Power[f, 3.0], $MachinePrecision] * N[(N[Power[Pi, 3.0], $MachinePrecision] * 0.005208333333333333), $MachinePrecision] + N[(N[Power[f, 5.0], $MachinePrecision] * N[(1.6276041666666666e-5 * N[Power[Pi, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

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Alternative 3: 96.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{\log \left(\frac{e^{0.25 \cdot \left(\pi \cdot \left(-f\right)\right)} + e^{0.25 \cdot \left(f \cdot \pi\right)}}{\mathsf{fma}\left(f, \pi \cdot 0.5, {f}^{3} \cdot \left({\pi}^{3} \cdot 0.005208333333333333\right)\right)}\right)}{\pi} \cdot -4 \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (*
  (/
   (log
    (/
     (+ (exp (* 0.25 (* PI (- f)))) (exp (* 0.25 (* f PI))))
     (fma f (* PI 0.5) (* (pow f 3.0) (* (pow PI 3.0) 0.005208333333333333)))))
   PI)
  -4.0))

C

double code(double f) {
	return (log(((exp((0.25 * (((double) M_PI) * -f))) + exp((0.25 * (f * ((double) M_PI))))) / fma(f, (((double) M_PI) * 0.5), (pow(f, 3.0) * (pow(((double) M_PI), 3.0) * 0.005208333333333333))))) / ((double) M_PI)) * -4.0;
}

Julia

function code(f)
	return Float64(Float64(log(Float64(Float64(exp(Float64(0.25 * Float64(pi * Float64(-f)))) + exp(Float64(0.25 * Float64(f * pi)))) / fma(f, Float64(pi * 0.5), Float64((f ^ 3.0) * Float64((pi ^ 3.0) * 0.005208333333333333))))) / pi) * -4.0)
end

Wolfram

code[f_] := N[(N[(N[Log[N[(N[(N[Exp[N[(0.25 * N[(Pi * (-f)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(0.25 * N[(f * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(f * N[(Pi * 0.5), $MachinePrecision] + N[(N[Power[f, 3.0], $MachinePrecision] * N[(N[Power[Pi, 3.0], $MachinePrecision] * 0.005208333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

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Alternative 4: 96.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ -\mathsf{fma}\left(4, \frac{\log \left(\frac{4}{\pi}\right) - \log f}{\pi}, {f}^{2} \cdot \left(\pi \cdot 0.08333333333333333\right)\right) \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (-
  (fma
   4.0
   (/ (- (log (/ 4.0 PI)) (log f)) PI)
   (* (pow f 2.0) (* PI 0.08333333333333333)))))

C

double code(double f) {
	return -fma(4.0, ((log((4.0 / ((double) M_PI))) - log(f)) / ((double) M_PI)), (pow(f, 2.0) * (((double) M_PI) * 0.08333333333333333)));
}

Julia

function code(f)
	return Float64(-fma(4.0, Float64(Float64(log(Float64(4.0 / pi)) - log(f)) / pi), Float64((f ^ 2.0) * Float64(pi * 0.08333333333333333))))
end

Wolfram

code[f_] := (-N[(4.0 * N[(N[(N[Log[N[(4.0 / Pi), $MachinePrecision]], $MachinePrecision] - N[Log[f], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision] + N[(N[Power[f, 2.0], $MachinePrecision] * N[(Pi * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])

Derivation

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Alternative 5: 96.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{\log f - \log \left(\frac{4}{\pi}\right)}{\pi} - 0.125 \cdot \left(\pi \cdot {f}^{2}\right) \end{array} \]

FPCore

(FPCore (f)
 :precision binary64
 (- (* 4.0 (/ (- (log f) (log (/ 4.0 PI))) PI)) (* 0.125 (* PI (pow f 2.0)))))

C

double code(double f) {
	return (4.0 * ((log(f) - log((4.0 / ((double) M_PI)))) / ((double) M_PI))) - (0.125 * (((double) M_PI) * pow(f, 2.0)));
}

Java

public static double code(double f) {
	return (4.0 * ((Math.log(f) - Math.log((4.0 / Math.PI))) / Math.PI)) - (0.125 * (Math.PI * Math.pow(f, 2.0)));
}

Python

def code(f):
	return (4.0 * ((math.log(f) - math.log((4.0 / math.pi))) / math.pi)) - (0.125 * (math.pi * math.pow(f, 2.0)))

Julia

function code(f)
	return Float64(Float64(4.0 * Float64(Float64(log(f) - log(Float64(4.0 / pi))) / pi)) - Float64(0.125 * Float64(pi * (f ^ 2.0))))
end

MATLAB

function tmp = code(f)
	tmp = (4.0 * ((log(f) - log((4.0 / pi))) / pi)) - (0.125 * (pi * (f ^ 2.0)));
end

Wolfram

code[f_] := N[(N[(4.0 * N[(N[(N[Log[f], $MachinePrecision] - N[Log[N[(4.0 / Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(Pi * N[Power[f, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 6: 96.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{\log f - \log \left(\frac{4}{\pi}\right)}{\pi} \end{array} \]

FPCore

(FPCore (f) :precision binary64 (* 4.0 (/ (- (log f) (log (/ 4.0 PI))) PI)))

C

double code(double f) {
	return 4.0 * ((log(f) - log((4.0 / ((double) M_PI)))) / ((double) M_PI));
}

Java

public static double code(double f) {
	return 4.0 * ((Math.log(f) - Math.log((4.0 / Math.PI))) / Math.PI);
}

Python

def code(f):
	return 4.0 * ((math.log(f) - math.log((4.0 / math.pi))) / math.pi)

Julia

function code(f)
	return Float64(4.0 * Float64(Float64(log(f) - log(Float64(4.0 / pi))) / pi))
end

MATLAB

function tmp = code(f)
	tmp = 4.0 * ((log(f) - log((4.0 / pi))) / pi);
end

Wolfram

code[f_] := N[(4.0 * N[(N[(N[Log[f], $MachinePrecision] - N[Log[N[(4.0 / Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 7: 96.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \frac{\log \left(\frac{\frac{4}{\pi}}{f}\right)}{\pi} \cdot -4 \end{array} \]

FPCore

(FPCore (f) :precision binary64 (* (/ (log (/ (/ 4.0 PI) f)) PI) -4.0))

C

double code(double f) {
	return (log(((4.0 / ((double) M_PI)) / f)) / ((double) M_PI)) * -4.0;
}

Java

public static double code(double f) {
	return (Math.log(((4.0 / Math.PI) / f)) / Math.PI) * -4.0;
}

Python

def code(f):
	return (math.log(((4.0 / math.pi) / f)) / math.pi) * -4.0

Julia

function code(f)
	return Float64(Float64(log(Float64(Float64(4.0 / pi) / f)) / pi) * -4.0)
end

MATLAB

function tmp = code(f)
	tmp = (log(((4.0 / pi) / f)) / pi) * -4.0;
end

Wolfram

code[f_] := N[(N[(N[Log[N[(N[(4.0 / Pi), $MachinePrecision] / f), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

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Alternative 8: 40.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{\log f - 0.25}{\pi} \end{array} \]

FPCore

(FPCore (f) :precision binary64 (* 4.0 (/ (- (log f) 0.25) PI)))

C

double code(double f) {
	return 4.0 * ((log(f) - 0.25) / ((double) M_PI));
}

Java

public static double code(double f) {
	return 4.0 * ((Math.log(f) - 0.25) / Math.PI);
}

Python

def code(f):
	return 4.0 * ((math.log(f) - 0.25) / math.pi)

Julia

function code(f)
	return Float64(4.0 * Float64(Float64(log(f) - 0.25) / pi))
end

MATLAB

function tmp = code(f)
	tmp = 4.0 * ((log(f) - 0.25) / pi);
end

Wolfram

code[f_] := N[(4.0 * N[(N[(N[Log[f], $MachinePrecision] - 0.25), $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 9: 5.1% accurate, 1027.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (f) :precision binary64 0.0)

C

double code(double f) {
	return 0.0;
}

Fortran

real(8) function code(f)
    real(8), intent (in) :: f
    code = 0.0d0
end function

Java

public static double code(double f) {
	return 0.0;
}

Python

def code(f):
	return 0.0

Julia

function code(f)
	return 0.0
end

MATLAB

function tmp = code(f)
	tmp = 0.0;
end

Wolfram

code[f_] := 0.0

Derivation

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Alternative 10: 12.1% accurate, 1027.0× speedup

Math

\[\begin{array}{l} \\ -0.001953125 \end{array} \]

FPCore

(FPCore (f) :precision binary64 -0.001953125)

C

double code(double f) {
	return -0.001953125;
}

Fortran

real(8) function code(f)
    real(8), intent (in) :: f
    code = -0.001953125d0
end function

Java

public static double code(double f) {
	return -0.001953125;
}

Python

def code(f):
	return -0.001953125

Julia

function code(f)
	return -0.001953125
end

MATLAB

function tmp = code(f)
	tmp = -0.001953125;
end

Wolfram

code[f_] := -0.001953125

Derivation

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Alternative 11: 14.4% accurate, 1027.0× speedup

Math

\[\begin{array}{l} \\ -4 \end{array} \]

FPCore

(FPCore (f) :precision binary64 -4.0)

C

double code(double f) {
	return -4.0;
}

Fortran

real(8) function code(f)
    real(8), intent (in) :: f
    code = -4.0d0
end function

Java

public static double code(double f) {
	return -4.0;
}

Python

def code(f):
	return -4.0

Julia

function code(f)
	return -4.0
end

MATLAB

function tmp = code(f)
	tmp = -4.0;
end

Wolfram

code[f_] := -4.0

Derivation

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Alternative 12: 14.6% accurate, 1027.0× speedup

Math

\[\begin{array}{l} \\ -6 \end{array} \]

FPCore

(FPCore (f) :precision binary64 -6.0)

C

double code(double f) {
	return -6.0;
}

Fortran

real(8) function code(f)
    real(8), intent (in) :: f
    code = -6.0d0
end function

Java

public static double code(double f) {
	return -6.0;
}

Python

def code(f):
	return -6.0

Julia

function code(f)
	return -6.0
end

MATLAB

function tmp = code(f)
	tmp = -6.0;
end

Wolfram

code[f_] := -6.0

Derivation

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Alternative 13: 15.3% accurate, 1027.0× speedup

Math

\[\begin{array}{l} \\ -16 \end{array} \]

FPCore

(FPCore (f) :precision binary64 -16.0)

C

double code(double f) {
	return -16.0;
}

Fortran

real(8) function code(f)
    real(8), intent (in) :: f
    code = -16.0d0
end function

Java

public static double code(double f) {
	return -16.0;
}

Python

def code(f):
	return -16.0

Julia

function code(f)
	return -16.0
end

MATLAB

function tmp = code(f)
	tmp = -16.0;
end

Wolfram

code[f_] := -16.0

Derivation

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

Alternative 14: 16.7% accurate, 1027.0× speedup

Math

\[\begin{array}{l} \\ -64 \end{array} \]

FPCore

(FPCore (f) :precision binary64 -64.0)

C

double code(double f) {
	return -64.0;
}

Fortran

real(8) function code(f)
    real(8), intent (in) :: f
    code = -64.0d0
end function

Java

public static double code(double f) {
	return -64.0;
}

Python

def code(f):
	return -64.0

Julia

function code(f)
	return -64.0
end

MATLAB

function tmp = code(f)
	tmp = -64.0;
end

Wolfram

code[f_] := -64.0

Derivation

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

Reproduce

herbie shell --seed 2024010 
(FPCore (f)
  :name "VandenBroeck and Keller, Equation (20)"
  :precision binary64
  (- (* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (- (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (- (* (/ PI 4.0) f)))))))))