Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B

Percentage Accurate: 94.4% → 99.3%

Time: 15.3s

Alternatives: 15

Speedup: 1.0×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
  (/
   (+
    (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
    0.083333333333333)
   x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
  (/
   (+
    (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
    0.083333333333333)
   x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8.5e+64)
   (+
    (fma (+ x -0.5) (log x) (- 0.91893853320467 x))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (* (+ y 0.0007936500793651) (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.5e+64) {
		tmp = fma((x + -0.5), log(x), (0.91893853320467 - x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8.5e+64)
		tmp = Float64(fma(Float64(x + -0.5), log(x), Float64(0.91893853320467 - x)) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8.5e+64], N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.4999999999999998e64

   1. Initial program 99.7%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. remove-double-neg 99.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log x + \left(-x\right)\right)} + 0.91893853320467\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      3. associate-+l+ 99.7%

         \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log x + \left(\left(-x\right) + 0.91893853320467\right)\right)} + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      4. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - 0.5, \log x, \left(-x\right) + 0.91893853320467\right)} + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      5. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x + \left(-0.5\right)}, \log x, \left(-x\right) + 0.91893853320467\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x + \color{blue}{-0.5}, \log x, \left(-x\right) + 0.91893853320467\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      7. +-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0.91893853320467 + \left(-x\right)}\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      8. unsub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0.91893853320467 - x}\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      9. remove-double-neg 99.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \color{blue}{\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}} \]

      10. *-commutative 99.7%

          \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\color{blue}{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)} + 0.083333333333333}{x} \]

      11. fma-def 99.7%

          \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\color{blue}{\mathsf{fma}\left(z, \left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, 0.083333333333333\right)}}{x} \]

      12. fma-neg 99.7%

          \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, 0.083333333333333\right)}{x} \]

      13. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), 0.083333333333333\right)}{x} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}} \]

   if 8.4999999999999998e64 < x

   1. Initial program 87.0%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 87.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 89.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 89.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 89.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 90.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

      2. associate-/l* 99.4%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}}} \cdot \left(0.0007936500793651 + y\right) \]

      3. +-commutative 99.4%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z}{\frac{x}{z}} \cdot \color{blue}{\left(y + 0.0007936500793651\right)} \]

   6. Applied egg-rr 99.4%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 2: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -0.5\right) \cdot \log x - x\\ \mathbf{if}\;x \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{0.8444480278083504 - {t_0}^{2}}{0.91893853320467 - t_0} + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ x -0.5) (log x)) x)))
   (if (<= x 2e+17)
     (+
      (/ (- 0.8444480278083504 (pow t_0 2.0)) (- 0.91893853320467 t_0))
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+
      (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
      (* (+ y 0.0007936500793651) (/ z (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x + -0.5) * log(x)) - x;
	double tmp;
	if (x <= 2e+17) {
		tmp = ((0.8444480278083504 - pow(t_0, 2.0)) / (0.91893853320467 - t_0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x + (-0.5d0)) * log(x)) - x
    if (x <= 2d+17) then
        tmp = ((0.8444480278083504d0 - (t_0 ** 2.0d0)) / (0.91893853320467d0 - t_0)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((y + 0.0007936500793651d0) * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x + -0.5) * Math.log(x)) - x;
	double tmp;
	if (x <= 2e+17) {
		tmp = ((0.8444480278083504 - Math.pow(t_0, 2.0)) / (0.91893853320467 - t_0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x + -0.5) * math.log(x)) - x
	tmp = 0
	if x <= 2e+17:
		tmp = ((0.8444480278083504 - math.pow(t_0, 2.0)) / (0.91893853320467 - t_0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x + -0.5) * log(x)) - x)
	tmp = 0.0
	if (x <= 2e+17)
		tmp = Float64(Float64(Float64(0.8444480278083504 - (t_0 ^ 2.0)) / Float64(0.91893853320467 - t_0)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x + -0.5) * log(x)) - x;
	tmp = 0.0;
	if (x <= 2e+17)
		tmp = ((0.8444480278083504 - (t_0 ^ 2.0)) / (0.91893853320467 - t_0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, 2e+17], N[(N[(N[(0.8444480278083504 - N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] / N[(0.91893853320467 - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 2e17

   1. Initial program 99.7%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(0.91893853320467 + \left(\left(x - 0.5\right) \cdot \log x - x\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. flip-+ 99.7%

         \[\leadsto \color{blue}{\frac{0.91893853320467 \cdot 0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right) \cdot \left(\left(x - 0.5\right) \cdot \log x - x\right)}{0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right)}} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. metadata-eval 99.7%

         \[\leadsto \frac{\color{blue}{0.8444480278083504} - \left(\left(x - 0.5\right) \cdot \log x - x\right) \cdot \left(\left(x - 0.5\right) \cdot \log x - x\right)}{0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      4. pow2 99.7%

         \[\leadsto \frac{0.8444480278083504 - \color{blue}{{\left(\left(x - 0.5\right) \cdot \log x - x\right)}^{2}}}{0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      5. sub-neg 99.7%

         \[\leadsto \frac{0.8444480278083504 - {\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right)}^{2}}{0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      6. metadata-eval 99.7%

         \[\leadsto \frac{0.8444480278083504 - {\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right)}^{2}}{0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      7. *-commutative 99.7%

         \[\leadsto \frac{0.8444480278083504 - {\left(\color{blue}{\log x \cdot \left(x + -0.5\right)} - x\right)}^{2}}{0.91893853320467 - \left(\left(x - 0.5\right) \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      8. sub-neg 99.7%

         \[\leadsto \frac{0.8444480278083504 - {\left(\log x \cdot \left(x + -0.5\right) - x\right)}^{2}}{0.91893853320467 - \left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      9. metadata-eval 99.7%

         \[\leadsto \frac{0.8444480278083504 - {\left(\log x \cdot \left(x + -0.5\right) - x\right)}^{2}}{0.91893853320467 - \left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      10. *-commutative 99.7%

          \[\leadsto \frac{0.8444480278083504 - {\left(\log x \cdot \left(x + -0.5\right) - x\right)}^{2}}{0.91893853320467 - \left(\color{blue}{\log x \cdot \left(x + -0.5\right)} - x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{0.8444480278083504 - {\left(\log x \cdot \left(x + -0.5\right) - x\right)}^{2}}{0.91893853320467 - \left(\log x \cdot \left(x + -0.5\right) - x\right)}} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 2e17 < x

   1. Initial program 89.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 89.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 91.3%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 91.3%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 92.0%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

      2. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}}} \cdot \left(0.0007936500793651 + y\right) \]

      3. +-commutative 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z}{\frac{x}{z}} \cdot \color{blue}{\left(y + 0.0007936500793651\right)} \]

   6. Applied egg-rr 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{0.8444480278083504 - {\left(\left(x + -0.5\right) \cdot \log x - x\right)}^{2}}{0.91893853320467 - \left(\left(x + -0.5\right) \cdot \log x - x\right)} + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 3: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\\ \mathbf{if}\;x \leq 4 \cdot 10^{+16}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))))
   (if (<= x 4e+16)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+ t_0 (* (+ y 0.0007936500793651) (/ z (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((log(x) * (x - 0.5)) - x);
	double tmp;
	if (x <= 4e+16) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)
    if (x <= 4d+16) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((y + 0.0007936500793651d0) * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x);
	double tmp;
	if (x <= 4e+16) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)
	tmp = 0
	if x <= 4e+16:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x))
	tmp = 0.0
	if (x <= 4e+16)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + ((log(x) * (x - 0.5)) - x);
	tmp = 0.0;
	if (x <= 4e+16)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4e+16], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4e16

   1. Initial program 99.7%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 4e16 < x

   1. Initial program 89.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 89.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 91.3%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 91.3%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 92.0%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

      2. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}}} \cdot \left(0.0007936500793651 + y\right) \]

      3. +-commutative 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z}{\frac{x}{z}} \cdot \color{blue}{\left(y + 0.0007936500793651\right)} \]

   6. Applied egg-rr 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+16}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 4: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ t_1 := \left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-40}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (+ 0.91893853320467 (* -0.5 (log x)))
          (/ (* z z) (/ x (+ y 0.0007936500793651)))))
        (t_1
         (+ (+ 0.91893853320467 (* x (+ (log x) -1.0))) (/ y (/ x (* z z))))))
   (if (<= z -2.9e+101)
     t_0
     (if (<= z -3.8e-22)
       t_1
       (if (<= z 1.95e-40)
         (+
          (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
          (/ 0.083333333333333 x))
         (if (<= z 3e+42) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((z * z) / (x / (y + 0.0007936500793651)));
	double t_1 = (0.91893853320467 + (x * (log(x) + -1.0))) + (y / (x / (z * z)));
	double tmp;
	if (z <= -2.9e+101) {
		tmp = t_0;
	} else if (z <= -3.8e-22) {
		tmp = t_1;
	} else if (z <= 1.95e-40) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	} else if (z <= 3e+42) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((z * z) / (x / (y + 0.0007936500793651d0)))
    t_1 = (0.91893853320467d0 + (x * (log(x) + (-1.0d0)))) + (y / (x / (z * z)))
    if (z <= (-2.9d+101)) then
        tmp = t_0
    else if (z <= (-3.8d-22)) then
        tmp = t_1
    else if (z <= 1.95d-40) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    else if (z <= 3d+42) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * Math.log(x))) + ((z * z) / (x / (y + 0.0007936500793651)));
	double t_1 = (0.91893853320467 + (x * (Math.log(x) + -1.0))) + (y / (x / (z * z)));
	double tmp;
	if (z <= -2.9e+101) {
		tmp = t_0;
	} else if (z <= -3.8e-22) {
		tmp = t_1;
	} else if (z <= 1.95e-40) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	} else if (z <= 3e+42) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.91893853320467 + (-0.5 * math.log(x))) + ((z * z) / (x / (y + 0.0007936500793651)))
	t_1 = (0.91893853320467 + (x * (math.log(x) + -1.0))) + (y / (x / (z * z)))
	tmp = 0
	if z <= -2.9e+101:
		tmp = t_0
	elif z <= -3.8e-22:
		tmp = t_1
	elif z <= 1.95e-40:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	elif z <= 3e+42:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(z * z) / Float64(x / Float64(y + 0.0007936500793651))))
	t_1 = Float64(Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0))) + Float64(y / Float64(x / Float64(z * z))))
	tmp = 0.0
	if (z <= -2.9e+101)
		tmp = t_0;
	elseif (z <= -3.8e-22)
		tmp = t_1;
	elseif (z <= 1.95e-40)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	elseif (z <= 3e+42)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((z * z) / (x / (y + 0.0007936500793651)));
	t_1 = (0.91893853320467 + (x * (log(x) + -1.0))) + (y / (x / (z * z)));
	tmp = 0.0;
	if (z <= -2.9e+101)
		tmp = t_0;
	elseif (z <= -3.8e-22)
		tmp = t_1;
	elseif (z <= 1.95e-40)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	elseif (z <= 3e+42)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+101], t$95$0, If[LessEqual[z, -3.8e-22], t$95$1, If[LessEqual[z, 1.95e-40], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+42], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999987e101 or 3.00000000000000029e42 < z

   1. Initial program 86.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 86.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 89.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 89.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 89.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}} \]

   if -2.89999999999999987e101 < z < -3.80000000000000023e-22 or 1.9499999999999999e-40 < z < 3.00000000000000029e42

   1. Initial program 99.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 98.4%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 48.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 48.5%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 48.5%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 48.5%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 48.5%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 98.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in y around inf 81.3%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   6. Step-by-step derivation

      1. associate-/l* 81.3%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{y}{\frac{x}{{z}^{2}}}} \]

      2. unpow2 81.3%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{y}{\frac{x}{\color{blue}{z \cdot z}}} \]

   7. Simplified 81.3%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{y}{\frac{x}{z \cdot z}}} \]

   if -3.80000000000000023e-22 < z < 1.9499999999999999e-40

   1. Initial program 99.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0 96.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+101}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-40}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+42}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \]

Alternative 5: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-23} \lor \neg \left(z \leq 2.65 \cdot 10^{-40}\right):\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.4e-23) (not (<= z 2.65e-40)))
   (+
    (+ 0.91893853320467 (* x (+ (log x) -1.0)))
    (* (+ y 0.0007936500793651) (/ (* z z) x)))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.4e-23) || !(z <= 2.65e-40)) {
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.4d-23)) .or. (.not. (z <= 2.65d-40))) then
        tmp = (0.91893853320467d0 + (x * (log(x) + (-1.0d0)))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.4e-23) || !(z <= 2.65e-40)) {
		tmp = (0.91893853320467 + (x * (Math.log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.4e-23) or not (z <= 2.65e-40):
		tmp = (0.91893853320467 + (x * (math.log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.4e-23) || !(z <= 2.65e-40))
		tmp = Float64(Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.4e-23) || ~((z <= 2.65e-40)))
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.4e-23], N[Not[LessEqual[z, 2.65e-40]], $MachinePrecision]], N[(N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4000000000000005e-23 or 2.6500000000000001e-40 < z

   1. Initial program 89.9%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 89.6%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 27.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 27.1%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 27.1%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 27.1%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 27.1%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 89.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in z around inf 87.9%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   6. Step-by-step derivation

      1. associate-/l* 89.9%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. +-commutative 89.9%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{{z}^{2}}{\frac{x}{\color{blue}{y + 0.0007936500793651}}} \]

      3. associate-/r/ 90.7%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

      4. unpow2 90.7%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{x} \cdot \left(y + 0.0007936500793651\right) \]

      5. +-commutative 90.7%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{z \cdot z}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   7. Simplified 90.7%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

   if -7.4000000000000005e-23 < z < 2.6500000000000001e-40

   1. Initial program 99.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0 96.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-23} \lor \neg \left(z \leq 2.65 \cdot 10^{-40}\right):\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 6: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -400 \lor \neg \left(z \leq 0.116\right):\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot y\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (* x (+ (log x) -1.0)))))
   (if (or (<= z -400.0) (not (<= z 0.116)))
     (+ t_0 (* (+ y 0.0007936500793651) (/ (* z z) x)))
     (+ t_0 (/ (+ 0.083333333333333 (* z (* z y))) x)))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (x * (log(x) + -1.0));
	double tmp;
	if ((z <= -400.0) || !(z <= 0.116)) {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * (z * y))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + (x * (log(x) + (-1.0d0)))
    if ((z <= (-400.0d0)) .or. (.not. (z <= 0.116d0))) then
        tmp = t_0 + ((y + 0.0007936500793651d0) * ((z * z) / x))
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * (z * y))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (x * (Math.log(x) + -1.0));
	double tmp;
	if ((z <= -400.0) || !(z <= 0.116)) {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * (z * y))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + (x * (math.log(x) + -1.0))
	tmp = 0
	if (z <= -400.0) or not (z <= 0.116):
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x))
	else:
		tmp = t_0 + ((0.083333333333333 + (z * (z * y))) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0)))
	tmp = 0.0
	if ((z <= -400.0) || !(z <= 0.116))
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(z * y))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + (x * (log(x) + -1.0));
	tmp = 0.0;
	if ((z <= -400.0) || ~((z <= 0.116)))
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	else
		tmp = t_0 + ((0.083333333333333 + (z * (z * y))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -400.0], N[Not[LessEqual[z, 0.116]], $MachinePrecision]], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -400 or 0.116000000000000006 < z

   1. Initial program 89.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 26.7%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 26.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 26.7%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 26.7%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 26.7%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 26.7%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 89.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in z around inf 88.0%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   6. Step-by-step derivation

      1. associate-/l* 90.1%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. +-commutative 90.1%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{{z}^{2}}{\frac{x}{\color{blue}{y + 0.0007936500793651}}} \]

      3. associate-/r/ 90.9%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

      4. unpow2 90.9%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{x} \cdot \left(y + 0.0007936500793651\right) \]

      5. +-commutative 90.9%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{z \cdot z}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   7. Simplified 90.9%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

   if -400 < z < 0.116000000000000006

   1. Initial program 99.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 97.2%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 90.4%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 90.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 90.4%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 90.4%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 90.4%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 90.4%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 97.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in y around inf 96.8%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{y \cdot {z}^{2}} + 0.083333333333333}{x} \]
   6. Step-by-step derivation

      1. *-commutative 96.8%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{{z}^{2} \cdot y} + 0.083333333333333}{x} \]

      2. unpow2 96.8%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(z \cdot z\right)} \cdot y + 0.083333333333333}{x} \]

      3. associate-*l* 96.8%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot \left(z \cdot y\right)} + 0.083333333333333}{x} \]

   7. Simplified 96.8%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot \left(z \cdot y\right)} + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -400 \lor \neg \left(z \leq 0.116\right):\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot y\right)}{x}\\ \end{array} \]

Alternative 7: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0015:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(0.91893853320467 + -0.5 \cdot \log x\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+159}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + 0.0007936500793651 \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0015)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    (+ 0.91893853320467 (* -0.5 (log x))))
   (if (<= x 7e+159)
     (+
      (+ 0.91893853320467 (* x (+ (log x) -1.0)))
      (* (+ y 0.0007936500793651) (/ (* z z) x)))
     (+
      (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
      (* 0.0007936500793651 (* z (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0015) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * log(x)));
	} else if (x <= 7e+159) {
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.0007936500793651 * (z * (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 0.0015d0) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (0.91893853320467d0 + ((-0.5d0) * log(x)))
    else if (x <= 7d+159) then
        tmp = (0.91893853320467d0 + (x * (log(x) + (-1.0d0)))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.0007936500793651d0 * (z * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0015) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * Math.log(x)));
	} else if (x <= 7e+159) {
		tmp = (0.91893853320467 + (x * (Math.log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.0007936500793651 * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.0015:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * math.log(x)))
	elif x <= 7e+159:
		tmp = (0.91893853320467 + (x * (math.log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.0007936500793651 * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0015)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(0.91893853320467 + Float64(-0.5 * log(x))));
	elseif (x <= 7e+159)
		tmp = Float64(Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.0007936500793651 * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.0015)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * log(x)));
	elseif (x <= 7e+159)
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + ((y + 0.0007936500793651) * ((z * z) / x));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.0007936500793651 * (z * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0015], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+159], N[(N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.0007936500793651 * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 0.0015

   1. Initial program 99.7%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 0.0015 < x < 6.9999999999999999e159

   1. Initial program 95.8%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 94.4%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 54.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 54.2%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 54.2%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 54.2%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 54.2%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 94.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in z around inf 94.5%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   6. Step-by-step derivation

      1. associate-/l* 97.0%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. +-commutative 97.0%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{{z}^{2}}{\frac{x}{\color{blue}{y + 0.0007936500793651}}} \]

      3. associate-/r/ 97.0%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

      4. unpow2 97.0%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{x} \cdot \left(y + 0.0007936500793651\right) \]

      5. +-commutative 97.0%

         \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{z \cdot z}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   7. Simplified 97.0%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

   if 6.9999999999999999e159 < x

   1. Initial program 82.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 82.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 84.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 84.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 84.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Taylor expanded in y around 0 85.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{0.0007936500793651 \cdot \frac{{z}^{2}}{x}} \]
   6. Step-by-step derivation

      1. unpow2 85.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + 0.0007936500793651 \cdot \frac{\color{blue}{z \cdot z}}{x} \]

      2. associate-*l/ 96.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + 0.0007936500793651 \cdot \color{blue}{\left(\frac{z}{x} \cdot z\right)} \]

   7. Simplified 96.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{0.0007936500793651 \cdot \left(\frac{z}{x} \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0015:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(0.91893853320467 + -0.5 \cdot \log x\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+159}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + 0.0007936500793651 \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 8: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0015:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(0.91893853320467 + -0.5 \cdot \log x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0015)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    (+ 0.91893853320467 (* -0.5 (log x))))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (* (+ y 0.0007936500793651) (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0015) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * log(x)));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 0.0015d0) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (0.91893853320467d0 + ((-0.5d0) * log(x)))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((y + 0.0007936500793651d0) * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0015) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * Math.log(x)));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.0015:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * math.log(x)))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0015)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(0.91893853320467 + Float64(-0.5 * log(x))));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.0015)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (0.91893853320467 + (-0.5 * log(x)));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0015], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0015

   1. Initial program 99.7%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 0.0015 < x

   1. Initial program 89.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 89.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 91.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 91.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 91.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 91.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right)} \]

      2. associate-/l* 99.0%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}}} \cdot \left(0.0007936500793651 + y\right) \]

      3. +-commutative 99.0%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z}{\frac{x}{z}} \cdot \color{blue}{\left(y + 0.0007936500793651\right)} \]

   6. Applied egg-rr 99.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0015:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(0.91893853320467 + -0.5 \cdot \log x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 9: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+70} \lor \neg \left(z \leq 7.2 \cdot 10^{-31}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e+70) (not (<= z 7.2e-31)))
   (+
    (+ 0.91893853320467 (* -0.5 (log x)))
    (/ (* z z) (/ x (+ y 0.0007936500793651))))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+70) || !(z <= 7.2e-31)) {
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((z * z) / (x / (y + 0.0007936500793651)));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3d+70)) .or. (.not. (z <= 7.2d-31))) then
        tmp = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((z * z) / (x / (y + 0.0007936500793651d0)))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+70) || !(z <= 7.2e-31)) {
		tmp = (0.91893853320467 + (-0.5 * Math.log(x))) + ((z * z) / (x / (y + 0.0007936500793651)));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e+70) or not (z <= 7.2e-31):
		tmp = (0.91893853320467 + (-0.5 * math.log(x))) + ((z * z) / (x / (y + 0.0007936500793651)))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e+70) || !(z <= 7.2e-31))
		tmp = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(z * z) / Float64(x / Float64(y + 0.0007936500793651))));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e+70) || ~((z <= 7.2e-31)))
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((z * z) / (x / (y + 0.0007936500793651)));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e+70], N[Not[LessEqual[z, 7.2e-31]], $MachinePrecision]], N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999976e70 or 7.20000000000000007e-31 < z

   1. Initial program 88.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf 87.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   3. Step-by-step derivation

      1. associate-/l* 89.3%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

      2. unpow2 89.3%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   4. Simplified 89.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Taylor expanded in x around 0 75.6%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}} \]

   if -2.99999999999999976e70 < z < 7.20000000000000007e-31

   1. Initial program 99.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+70} \lor \neg \left(z \leq 7.2 \cdot 10^{-31}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 10: 60.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-22}:\\ \;\;\;\;t_0 + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (* x (+ (log x) -1.0)))))
   (if (<= z -3.9e-22)
     (+ t_0 (* -0.0027777777777778 (/ z x)))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (x * (log(x) + -1.0));
	double tmp;
	if (z <= -3.9e-22) {
		tmp = t_0 + (-0.0027777777777778 * (z / x));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + (x * (log(x) + (-1.0d0)))
    if (z <= (-3.9d-22)) then
        tmp = t_0 + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (x * (Math.log(x) + -1.0));
	double tmp;
	if (z <= -3.9e-22) {
		tmp = t_0 + (-0.0027777777777778 * (z / x));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + (x * (math.log(x) + -1.0))
	tmp = 0
	if z <= -3.9e-22:
		tmp = t_0 + (-0.0027777777777778 * (z / x))
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0)))
	tmp = 0.0
	if (z <= -3.9e-22)
		tmp = Float64(t_0 + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + (x * (log(x) + -1.0));
	tmp = 0.0;
	if (z <= -3.9e-22)
		tmp = t_0 + (-0.0027777777777778 * (z / x));
	else
		tmp = t_0 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e-22], N[(t$95$0 + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999998e-22

   1. Initial program 89.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 89.2%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 28.9%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 28.9%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 28.9%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 28.9%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 28.9%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 28.9%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 89.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in z around 0 46.1%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{-0.0027777777777778 \cdot z} + 0.083333333333333}{x} \]

   6. Taylor expanded in z around inf 46.1%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{-0.0027777777777778 \cdot \frac{z}{x}} \]

   if -3.89999999999999998e-22 < z

   1. Initial program 96.0%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0 68.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   3. Taylor expanded in x around inf 67.1%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 67.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 67.1%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 67.1%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 67.1%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 67.1%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   5. Simplified 67.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-22}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 11: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+41)
   (+
    (+ 0.91893853320467 (* x (+ (log x) -1.0)))
    (* -0.0027777777777778 (/ z x)))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+41) {
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.5d+41)) then
        tmp = (0.91893853320467d0 + (x * (log(x) + (-1.0d0)))) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+41) {
		tmp = (0.91893853320467 + (x * (Math.log(x) + -1.0))) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+41:
		tmp = (0.91893853320467 + (x * (math.log(x) + -1.0))) + (-0.0027777777777778 * (z / x))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+41)
		tmp = Float64(Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0))) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+41)
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + (-0.0027777777777778 * (z / x));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+41], N[(N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000011e41

   1. Initial program 87.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 87.5%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 25.3%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 25.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 25.3%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 25.3%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 25.3%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 25.3%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 87.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in z around 0 45.3%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{-0.0027777777777778 \cdot z} + 0.083333333333333}{x} \]

   6. Taylor expanded in z around inf 45.3%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{-0.0027777777777778 \cdot \frac{z}{x}} \]

   if -2.50000000000000011e41 < z

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0 67.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 12: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+41)
   (+
    (+ 0.91893853320467 (* x (+ (log x) -1.0)))
    (* -0.0027777777777778 (/ z x)))
   (+
    (/ 0.083333333333333 x)
    (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+41) {
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.083333333333333 / x) + (((x + -0.5) * log(x)) - (x + -0.91893853320467));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.5d+41)) then
        tmp = (0.91893853320467d0 + (x * (log(x) + (-1.0d0)))) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = (0.083333333333333d0 / x) + (((x + (-0.5d0)) * log(x)) - (x + (-0.91893853320467d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+41) {
		tmp = (0.91893853320467 + (x * (Math.log(x) + -1.0))) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.083333333333333 / x) + (((x + -0.5) * Math.log(x)) - (x + -0.91893853320467));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+41:
		tmp = (0.91893853320467 + (x * (math.log(x) + -1.0))) + (-0.0027777777777778 * (z / x))
	else:
		tmp = (0.083333333333333 / x) + (((x + -0.5) * math.log(x)) - (x + -0.91893853320467))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+41)
		tmp = Float64(Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0))) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+41)
		tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + (-0.0027777777777778 * (z / x));
	else
		tmp = (0.083333333333333 / x) + (((x + -0.5) * log(x)) - (x + -0.91893853320467));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+41], N[(N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000011e41

   1. Initial program 87.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around inf 87.5%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. *-commutative 25.3%

         \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. sub-neg 25.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. mul-1-neg 25.3%

         \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. log-rec 25.3%

         \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      5. remove-double-neg 25.3%

         \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 25.3%

         \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Simplified 87.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   5. Taylor expanded in z around 0 45.3%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \frac{\color{blue}{-0.0027777777777778 \cdot z} + 0.083333333333333}{x} \]

   6. Taylor expanded in z around inf 45.3%

      \[\leadsto \left(x \cdot \left(\log x + -1\right) + 0.91893853320467\right) + \color{blue}{-0.0027777777777778 \cdot \frac{z}{x}} \]

   if -2.50000000000000011e41 < z

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0 67.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
   3. Step-by-step derivation

      1. associate-+l- 67.6%

         \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log x - \left(x - 0.91893853320467\right)\right)} + \frac{0.083333333333333}{x} \]

      2. sub-neg 67.6%

         \[\leadsto \left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - \left(x - 0.91893853320467\right)\right) + \frac{0.083333333333333}{x} \]

      3. metadata-eval 67.6%

         \[\leadsto \left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - \left(x - 0.91893853320467\right)\right) + \frac{0.083333333333333}{x} \]

      4. *-commutative 67.6%

         \[\leadsto \left(\color{blue}{\log x \cdot \left(x + -0.5\right)} - \left(x - 0.91893853320467\right)\right) + \frac{0.083333333333333}{x} \]

      5. sub-neg 67.6%

         \[\leadsto \left(\log x \cdot \left(x + -0.5\right) - \color{blue}{\left(x + \left(-0.91893853320467\right)\right)}\right) + \frac{0.083333333333333}{x} \]

      6. metadata-eval 67.6%

         \[\leadsto \left(\log x \cdot \left(x + -0.5\right) - \left(x + \color{blue}{-0.91893853320467}\right)\right) + \frac{0.083333333333333}{x} \]

   4. Applied egg-rr 67.6%

      \[\leadsto \color{blue}{\left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)} + \frac{0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right)\\ \end{array} \]

Alternative 13: 55.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (+ 0.91893853320467 (* x (+ (log x) -1.0))) (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	return (0.91893853320467 + (x * (log(x) + -1.0))) + (0.083333333333333 / x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (0.91893853320467d0 + (x * (log(x) + (-1.0d0)))) + (0.083333333333333d0 / x)
end function

Java

public static double code(double x, double y, double z) {
	return (0.91893853320467 + (x * (Math.log(x) + -1.0))) + (0.083333333333333 / x);
}

Python

def code(x, y, z):
	return (0.91893853320467 + (x * (math.log(x) + -1.0))) + (0.083333333333333 / x)

Julia

function code(x, y, z)
	return Float64(Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0))) + Float64(0.083333333333333 / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (0.91893853320467 + (x * (log(x) + -1.0))) + (0.083333333333333 / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(0.91893853320467 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

2. Taylor expanded in z around 0 57.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

3. Taylor expanded in x around inf 56.5%

   \[\leadsto \left(\color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot x} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
4. Step-by-step derivation

   1. *-commutative 56.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   2. sub-neg 56.5%

      \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   3. mul-1-neg 56.5%

      \[\leadsto \left(x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. log-rec 56.5%

      \[\leadsto \left(x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   5. remove-double-neg 56.5%

      \[\leadsto \left(x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   6. metadata-eval 56.5%

      \[\leadsto \left(x \cdot \left(\log x + \color{blue}{-1}\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

5. Simplified 56.5%

   \[\leadsto \left(\color{blue}{x \cdot \left(\log x + -1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

6. Final simplification 56.5%

   \[\leadsto \left(0.91893853320467 + x \cdot \left(\log x + -1\right)\right) + \frac{0.083333333333333}{x} \]

Alternative 14: 22.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (+ 0.91893853320467 (* -0.5 (log x))) (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	return (0.91893853320467 + (-0.5 * log(x))) + (0.083333333333333 / x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (0.91893853320467d0 + ((-0.5d0) * log(x))) + (0.083333333333333d0 / x)
end function

Java

public static double code(double x, double y, double z) {
	return (0.91893853320467 + (-0.5 * Math.log(x))) + (0.083333333333333 / x);
}

Python

def code(x, y, z):
	return (0.91893853320467 + (-0.5 * math.log(x))) + (0.083333333333333 / x)

Julia

function code(x, y, z)
	return Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(0.083333333333333 / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (0.91893853320467 + (-0.5 * log(x))) + (0.083333333333333 / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

2. Taylor expanded in z around 0 57.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

3. Taylor expanded in x around 0 19.5%

   \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{0.083333333333333}{x} \]

4. Final simplification 19.5%

   \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{0.083333333333333}{x} \]

Alternative 15: 2.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 - \log x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 0.91893853320467 (* (log x) 0.5)))

C

double code(double x, double y, double z) {
	return 0.91893853320467 - (log(x) * 0.5);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.91893853320467d0 - (log(x) * 0.5d0)
end function

Java

public static double code(double x, double y, double z) {
	return 0.91893853320467 - (Math.log(x) * 0.5);
}

Python

def code(x, y, z):
	return 0.91893853320467 - (math.log(x) * 0.5)

Julia

function code(x, y, z)
	return Float64(0.91893853320467 - Float64(log(x) * 0.5))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.91893853320467 - (log(x) * 0.5);
end

Wolfram

code[x_, y_, z_] := N[(0.91893853320467 - N[(N[Log[x], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

2. Taylor expanded in z around 0 57.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

3. Taylor expanded in x around 0 19.5%

   \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{0.083333333333333}{x} \]
4. Step-by-step derivation

   1. div-inv 19.4%

      \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \color{blue}{0.083333333333333 \cdot \frac{1}{x}} \]

5. Applied egg-rr 19.4%

   \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \color{blue}{0.083333333333333 \cdot \frac{1}{x}} \]

6. Taylor expanded in x around inf 2.5%

   \[\leadsto \color{blue}{0.91893853320467 + 0.5 \cdot \log \left(\frac{1}{x}\right)} \]
7. Step-by-step derivation

   1. *-commutative 2.5%

      \[\leadsto 0.91893853320467 + \color{blue}{\log \left(\frac{1}{x}\right) \cdot 0.5} \]

   2. log-rec 2.5%

      \[\leadsto 0.91893853320467 + \color{blue}{\left(-\log x\right)} \cdot 0.5 \]

   3. distribute-lft-neg-out 2.5%

      \[\leadsto 0.91893853320467 + \color{blue}{\left(-\log x \cdot 0.5\right)} \]

   4. unsub-neg 2.5%

      \[\leadsto \color{blue}{0.91893853320467 - \log x \cdot 0.5} \]

8. Simplified 2.5%

   \[\leadsto \color{blue}{0.91893853320467 - \log x \cdot 0.5} \]

9. Final simplification 2.5%

   \[\leadsto 0.91893853320467 - \log x \cdot 0.5 \]

Developer target: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x))
  (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)) + ((z / x) * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x)) + Float64(Float64(z / x) * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023178 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))