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

Percentage Accurate: 93.9% → 99.5%

Time: 15.3s

Alternatives: 19

Speedup: 1.0×

• 32.0% 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: 93.9% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+33}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e+33)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (pow
     (/
      x
      (fma
       z
       (fma (+ y 0.0007936500793651) z -0.0027777777777778)
       0.083333333333333))
     -1.0))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* z (* (+ y 0.0007936500793651) (/ z x)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+33) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + pow((x / fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333)), -1.0);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e+33)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + (Float64(x / fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333)) ^ -1.0));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) * Float64(z / x))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e+33], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[Power[N[(x / N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999995e32

   1. Initial program 99.6%

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

      1. clear-num 99.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{\frac{x}{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}}} \]

      2. inv-pow 99.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{{\left(\frac{x}{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}\right)}^{-1}} \]

      3. *-commutative 99.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\color{blue}{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)} + 0.083333333333333}\right)}^{-1} \]

      4. fma-undefine 99.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\color{blue}{\mathsf{fma}\left(z, \left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, 0.083333333333333\right)}}\right)}^{-1} \]

      5. fma-neg 99.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, 0.083333333333333\right)}\right)}^{-1} \]

      6. metadata-eval 99.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), 0.083333333333333\right)}\right)}^{-1} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{{\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}} \]

   if 9.9999999999999995e32 < x

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]

   4. Taylor expanded in z around inf 89.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
   5. Step-by-step derivation

      1. unpow2 89.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      2. associate-*l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      3. distribute-rgt-in 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\left(0.0007936500793651 \cdot \frac{1}{x}\right) \cdot z + \frac{y}{x} \cdot z\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      4. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot 1}{x}} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\frac{\color{blue}{0.0007936500793651}}{x} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      6. associate-*l/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      7. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{0.0007936500793651 \cdot \frac{z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      8. associate-*l/ 98.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{\frac{y \cdot z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      9. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{y \cdot \frac{z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      10. distribute-rgt-out 99.5%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   6. Simplified 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   7. Taylor expanded in x around inf 99.6%

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

      1. sub-neg 99.6%

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

      2. mul-1-neg 99.6%

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

      3. log-rec 99.6%

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

      4. remove-double-neg 99.6%

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

      5. metadata-eval 99.6%

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

      6. +-commutative 99.6%

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

   9. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \left(-1 + \log x\right)} + \left(z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+33}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e+88)
   (+
    (fma (+ x -0.5) (log x) (- 0.91893853320467 x))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* z (* (+ y 0.0007936500793651) (/ z x)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+88) {
		tmp = fma((x + -0.5), log(x), (0.91893853320467 - x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e+88)
		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(x * Float64(log(x) + -1.0)) + Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) * Float64(z / x))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e+88], 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[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.99999999999999959e87

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. associate-+l+ 99.6%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. +-commutative 99.7%

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

      7. unsub-neg 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-define 99.6%

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

      10. fma-neg 99.7%

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

      11. 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%

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

   if 9.99999999999999959e87 < x

   1. Initial program 83.3%

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

   3. Taylor expanded in z around 0 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]

   4. Taylor expanded in z around inf 87.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
   5. Step-by-step derivation

      1. unpow2 87.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      2. associate-*l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      3. distribute-rgt-in 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\left(0.0007936500793651 \cdot \frac{1}{x}\right) \cdot z + \frac{y}{x} \cdot z\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      4. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot 1}{x}} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\frac{\color{blue}{0.0007936500793651}}{x} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      6. associate-*l/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      7. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{0.0007936500793651 \cdot \frac{z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      8. associate-*l/ 98.4%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{\frac{y \cdot z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      9. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{y \cdot \frac{z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      10. distribute-rgt-out 99.5%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   6. Simplified 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   7. Taylor expanded in x around inf 99.5%

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

      1. sub-neg 99.5%

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

      2. mul-1-neg 99.5%

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

      3. log-rec 99.5%

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

      4. remove-double-neg 99.5%

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

      5. metadata-eval 99.5%

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

      6. +-commutative 99.5%

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

   9. Simplified 99.5%

      \[\leadsto \color{blue}{x \cdot \left(-1 + \log x\right)} + \left(z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+33}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e+33)
   (+
    (- (* (log x) (+ x -0.5)) (+ x -0.91893853320467))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* z (* (+ y 0.0007936500793651) (/ z x)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+33) {
		tmp = ((log(x) * (x + -0.5)) - (x + -0.91893853320467)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / 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 <= 1d+33) then
        tmp = ((log(x) * (x + (-0.5d0))) - (x + (-0.91893853320467d0))) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((z * ((y + 0.0007936500793651d0) * (z / x))) + (0.083333333333333d0 * (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+33) {
		tmp = ((Math.log(x) * (x + -0.5)) - (x + -0.91893853320467)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1e+33:
		tmp = ((math.log(x) * (x + -0.5)) - (x + -0.91893853320467)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e+33)
		tmp = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) - Float64(x + -0.91893853320467)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) * Float64(z / x))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1e+33)
		tmp = ((log(x) * (x + -0.5)) - (x + -0.91893853320467)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e+33], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $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[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999995e32

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   4. Applied egg-rr 99.6%

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

   if 9.9999999999999995e32 < x

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]

   4. Taylor expanded in z around inf 89.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
   5. Step-by-step derivation

      1. unpow2 89.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      2. associate-*l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      3. distribute-rgt-in 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\left(0.0007936500793651 \cdot \frac{1}{x}\right) \cdot z + \frac{y}{x} \cdot z\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      4. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot 1}{x}} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\frac{\color{blue}{0.0007936500793651}}{x} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      6. associate-*l/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      7. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{0.0007936500793651 \cdot \frac{z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      8. associate-*l/ 98.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{\frac{y \cdot z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      9. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{y \cdot \frac{z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      10. distribute-rgt-out 99.5%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   6. Simplified 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   7. Taylor expanded in x around inf 99.6%

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

      1. sub-neg 99.6%

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

      2. mul-1-neg 99.6%

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

      3. log-rec 99.6%

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

      4. remove-double-neg 99.6%

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

      5. metadata-eval 99.6%

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

      6. +-commutative 99.6%

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

   9. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \left(-1 + \log x\right)} + \left(z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+33}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7.5e+32)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* z (* (+ y 0.0007936500793651) (/ z x)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7.5e+32) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / 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 <= 7.5d+32) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((z * ((y + 0.0007936500793651d0) * (z / x))) + (0.083333333333333d0 * (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 7.5e+32) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7.5e+32:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7.5e+32)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) * Float64(z / x))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7.5e+32)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7.5e+32], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $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[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.49999999999999959e32

   1. Initial program 99.6%

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

   if 7.49999999999999959e32 < x

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]

   4. Taylor expanded in z around inf 89.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
   5. Step-by-step derivation

      1. unpow2 89.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      2. associate-*l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      3. distribute-rgt-in 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\left(0.0007936500793651 \cdot \frac{1}{x}\right) \cdot z + \frac{y}{x} \cdot z\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      4. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot 1}{x}} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\frac{\color{blue}{0.0007936500793651}}{x} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      6. associate-*l/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      7. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{0.0007936500793651 \cdot \frac{z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      8. associate-*l/ 98.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{\frac{y \cdot z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      9. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{y \cdot \frac{z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      10. distribute-rgt-out 99.5%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   6. Simplified 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   7. Taylor expanded in x around inf 99.6%

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

      1. sub-neg 99.6%

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

      2. mul-1-neg 99.6%

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

      3. log-rec 99.6%

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

      4. remove-double-neg 99.6%

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

      5. metadata-eval 99.6%

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

      6. +-commutative 99.6%

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

   9. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \left(-1 + \log x\right)} + \left(z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{if}\;x \leq 3.2 \cdot 10^{-252}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.083333333333333 \cdot \frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          0.91893853320467
          (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))))
   (if (<= x 3.2e-252)
     t_0
     (if (<= x 8.5e-210)
       (* x (/ 0.083333333333333 (pow x 2.0)))
       (if (<= x 1.0)
         t_0
         (+ (* x (+ (log x) -1.0)) (* 0.083333333333333 (/ 1.0 x))))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 3.2e-252) {
		tmp = t_0;
	} else if (x <= 8.5e-210) {
		tmp = x * (0.083333333333333 / pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 * (1.0 / 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 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    if (x <= 3.2d-252) then
        tmp = t_0
    else if (x <= 8.5d-210) then
        tmp = x * (0.083333333333333d0 / (x ** 2.0d0))
    else if (x <= 1.0d0) then
        tmp = t_0
    else
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 * (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 3.2e-252) {
		tmp = t_0;
	} else if (x <= 8.5e-210) {
		tmp = x * (0.083333333333333 / Math.pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 * (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	tmp = 0
	if x <= 3.2e-252:
		tmp = t_0
	elif x <= 8.5e-210:
		tmp = x * (0.083333333333333 / math.pow(x, 2.0))
	elif x <= 1.0:
		tmp = t_0
	else:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 * (1.0 / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x))
	tmp = 0.0
	if (x <= 3.2e-252)
		tmp = t_0;
	elseif (x <= 8.5e-210)
		tmp = Float64(x * Float64(0.083333333333333 / (x ^ 2.0)));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 * Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	tmp = 0.0;
	if (x <= 3.2e-252)
		tmp = t_0;
	elseif (x <= 8.5e-210)
		tmp = x * (0.083333333333333 / (x ^ 2.0));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 * (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 3.2e-252], t$95$0, If[LessEqual[x, 8.5e-210], N[(x * N[(0.083333333333333 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], t$95$0, N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.2000000000000002e-252 or 8.4999999999999997e-210 < x < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. log-rec 98.9%

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

      4. remove-double-neg 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 56.2%

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

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

   if 3.2000000000000002e-252 < x < 8.4999999999999997e-210

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 15.7%

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

   4. Taylor expanded in x around inf 15.7%

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

      1. sub-neg 89.7%

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

      2. mul-1-neg 89.7%

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

      3. log-rec 89.7%

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

      4. remove-double-neg 89.7%

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

      5. metadata-eval 89.7%

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

      6. +-commutative 89.7%

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

   6. Simplified 15.7%

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

   7. Taylor expanded in x around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. mul-1-neg 57.9%

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

      3. log-rec 57.9%

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

      4. remove-double-neg 57.9%

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

      5. sub-neg 57.9%

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

      6. associate-*r/ 57.9%

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

      7. metadata-eval 57.9%

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

      8. metadata-eval 57.9%

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

   9. Simplified 57.9%

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

   10. Taylor expanded in x around 0 57.9%

       \[\leadsto x \cdot \color{blue}{\frac{0.083333333333333}{{x}^{2}}} \]

   if 1 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 76.0%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. log-rec 98.6%

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

      4. remove-double-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. +-commutative 98.6%

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

   6. Simplified 75.2%

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

      1. div-inv 75.2%

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

      2. *-commutative 75.2%

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

   8. Applied egg-rr 75.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-252}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.083333333333333 \cdot \frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 10^{+88}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 1e+88)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+
      t_0
      (+
       (* z (* (+ y 0.0007936500793651) (/ z x)))
       (* 0.083333333333333 (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (x <= 1e+88) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / 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 = x * (log(x) + (-1.0d0))
    if (x <= 1d+88) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((z * ((y + 0.0007936500793651d0) * (z / x))) + (0.083333333333333d0 * (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if (x <= 1e+88) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if x <= 1e+88:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (x <= 1e+88)
		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(z * Float64(Float64(y + 0.0007936500793651) * Float64(z / x))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (x <= 1e+88)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((z * ((y + 0.0007936500793651) * (z / x))) + (0.083333333333333 * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1e+88], 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[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 9.99999999999999959e87

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. sub-neg 95.3%

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

      2. mul-1-neg 95.3%

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

      3. log-rec 95.3%

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

      4. remove-double-neg 95.3%

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

      5. metadata-eval 95.3%

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

      6. +-commutative 95.3%

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

   5. Simplified 98.5%

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

   if 9.99999999999999959e87 < x

   1. Initial program 83.3%

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

   3. Taylor expanded in z around 0 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]

   4. Taylor expanded in z around inf 87.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
   5. Step-by-step derivation

      1. unpow2 87.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      2. associate-*l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      3. distribute-rgt-in 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\left(0.0007936500793651 \cdot \frac{1}{x}\right) \cdot z + \frac{y}{x} \cdot z\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      4. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot 1}{x}} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\frac{\color{blue}{0.0007936500793651}}{x} \cdot z + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      6. associate-*l/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      7. associate-*r/ 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(\color{blue}{0.0007936500793651 \cdot \frac{z}{x}} + \frac{y}{x} \cdot z\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      8. associate-*l/ 98.4%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{\frac{y \cdot z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      9. associate-/l* 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(0.0007936500793651 \cdot \frac{z}{x} + \color{blue}{y \cdot \frac{z}{x}}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]

      10. distribute-rgt-out 99.5%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \color{blue}{\left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   6. Simplified 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right)} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   7. Taylor expanded in x around inf 99.5%

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

      1. sub-neg 99.5%

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

      2. mul-1-neg 99.5%

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

      3. log-rec 99.5%

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

      4. remove-double-neg 99.5%

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

      5. metadata-eval 99.5%

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

      6. +-commutative 99.5%

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

   9. Simplified 99.5%

      \[\leadsto \color{blue}{x \cdot \left(-1 + \log x\right)} + \left(z \cdot \left(\frac{z}{x} \cdot \left(0.0007936500793651 + y\right)\right) + 0.083333333333333 \cdot \frac{1}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+88}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{if}\;x \leq 8.8 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          0.91893853320467
          (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))))
   (if (<= x 8.8e-251)
     t_0
     (if (<= x 1.35e-209)
       (* x (/ 0.083333333333333 (pow x 2.0)))
       (if (<= x 1.0)
         t_0
         (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 8.8e-251) {
		tmp = t_0;
	} else if (x <= 1.35e-209) {
		tmp = x * (0.083333333333333 / pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = (x * (log(x) + -1.0)) + (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 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    if (x <= 8.8d-251) then
        tmp = t_0
    else if (x <= 1.35d-209) then
        tmp = x * (0.083333333333333d0 / (x ** 2.0d0))
    else if (x <= 1.0d0) then
        tmp = t_0
    else
        tmp = (x * (log(x) + (-1.0d0))) + (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 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 8.8e-251) {
		tmp = t_0;
	} else if (x <= 1.35e-209) {
		tmp = x * (0.083333333333333 / Math.pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	tmp = 0
	if x <= 8.8e-251:
		tmp = t_0
	elif x <= 1.35e-209:
		tmp = x * (0.083333333333333 / math.pow(x, 2.0))
	elif x <= 1.0:
		tmp = t_0
	else:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x))
	tmp = 0.0
	if (x <= 8.8e-251)
		tmp = t_0;
	elseif (x <= 1.35e-209)
		tmp = Float64(x * Float64(0.083333333333333 / (x ^ 2.0)));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	tmp = 0.0;
	if (x <= 8.8e-251)
		tmp = t_0;
	elseif (x <= 1.35e-209)
		tmp = x * (0.083333333333333 / (x ^ 2.0));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 8.8e-251], t$95$0, If[LessEqual[x, 1.35e-209], N[(x * N[(0.083333333333333 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], t$95$0, N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 8.8e-251 or 1.34999999999999999e-209 < x < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. log-rec 98.9%

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

      4. remove-double-neg 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 56.2%

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

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

   if 8.8e-251 < x < 1.34999999999999999e-209

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 15.7%

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

   4. Taylor expanded in x around inf 15.7%

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

      1. sub-neg 89.7%

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

      2. mul-1-neg 89.7%

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

      3. log-rec 89.7%

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

      4. remove-double-neg 89.7%

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

      5. metadata-eval 89.7%

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

      6. +-commutative 89.7%

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

   6. Simplified 15.7%

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

   7. Taylor expanded in x around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. mul-1-neg 57.9%

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

      3. log-rec 57.9%

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

      4. remove-double-neg 57.9%

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

      5. sub-neg 57.9%

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

      6. associate-*r/ 57.9%

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

      7. metadata-eval 57.9%

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

      8. metadata-eval 57.9%

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

   9. Simplified 57.9%

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

   10. Taylor expanded in x around 0 57.9%

       \[\leadsto x \cdot \color{blue}{\frac{0.083333333333333}{{x}^{2}}} \]

   if 1 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 76.0%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. log-rec 98.6%

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

      4. remove-double-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. +-commutative 98.6%

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

   6. Simplified 75.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{-251}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{if}\;x \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 - \log \left(\frac{1}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          0.91893853320467
          (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))))
   (if (<= x 6.8e-251)
     t_0
     (if (<= x 8.5e-210)
       (* x (/ 0.083333333333333 (pow x 2.0)))
       (if (<= x 1.0) t_0 (* x (- -1.0 (log (/ 1.0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 6.8e-251) {
		tmp = t_0;
	} else if (x <= 8.5e-210) {
		tmp = x * (0.083333333333333 / pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x * (-1.0 - log((1.0 / 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 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    if (x <= 6.8d-251) then
        tmp = t_0
    else if (x <= 8.5d-210) then
        tmp = x * (0.083333333333333d0 / (x ** 2.0d0))
    else if (x <= 1.0d0) then
        tmp = t_0
    else
        tmp = x * ((-1.0d0) - log((1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 6.8e-251) {
		tmp = t_0;
	} else if (x <= 8.5e-210) {
		tmp = x * (0.083333333333333 / Math.pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x * (-1.0 - Math.log((1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	tmp = 0
	if x <= 6.8e-251:
		tmp = t_0
	elif x <= 8.5e-210:
		tmp = x * (0.083333333333333 / math.pow(x, 2.0))
	elif x <= 1.0:
		tmp = t_0
	else:
		tmp = x * (-1.0 - math.log((1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x))
	tmp = 0.0
	if (x <= 6.8e-251)
		tmp = t_0;
	elseif (x <= 8.5e-210)
		tmp = Float64(x * Float64(0.083333333333333 / (x ^ 2.0)));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(-1.0 - log(Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	tmp = 0.0;
	if (x <= 6.8e-251)
		tmp = t_0;
	elseif (x <= 8.5e-210)
		tmp = x * (0.083333333333333 / (x ^ 2.0));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = x * (-1.0 - log((1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 6.8e-251], t$95$0, If[LessEqual[x, 8.5e-210], N[(x * N[(0.083333333333333 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], t$95$0, N[(x * N[(-1.0 - N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 6.80000000000000034e-251 or 8.4999999999999997e-210 < x < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. log-rec 98.9%

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

      4. remove-double-neg 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 56.2%

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

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

   if 6.80000000000000034e-251 < x < 8.4999999999999997e-210

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 15.7%

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

   4. Taylor expanded in x around inf 15.7%

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

      1. sub-neg 89.7%

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

      2. mul-1-neg 89.7%

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

      3. log-rec 89.7%

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

      4. remove-double-neg 89.7%

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

      5. metadata-eval 89.7%

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

      6. +-commutative 89.7%

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

   6. Simplified 15.7%

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

   7. Taylor expanded in x around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. mul-1-neg 57.9%

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

      3. log-rec 57.9%

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

      4. remove-double-neg 57.9%

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

      5. sub-neg 57.9%

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

      6. associate-*r/ 57.9%

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

      7. metadata-eval 57.9%

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

      8. metadata-eval 57.9%

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

   9. Simplified 57.9%

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

   10. Taylor expanded in x around 0 57.9%

       \[\leadsto x \cdot \color{blue}{\frac{0.083333333333333}{{x}^{2}}} \]

   if 1 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 76.0%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. log-rec 98.6%

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

      4. remove-double-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. +-commutative 98.6%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in x around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. mul-1-neg 75.2%

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

      3. log-rec 75.2%

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

      4. remove-double-neg 75.2%

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

      5. sub-neg 75.2%

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

      6. associate-*r/ 75.2%

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

      7. metadata-eval 75.2%

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

      8. metadata-eval 75.2%

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

   9. Simplified 75.2%

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

   10. Taylor expanded in x around inf 75.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 - \log \left(\frac{1}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{if}\;x \leq 8.8 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          0.91893853320467
          (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))))
   (if (<= x 8.8e-251)
     t_0
     (if (<= x 2.1e-209)
       (* x (/ 0.083333333333333 (pow x 2.0)))
       (if (<= x 1.0) t_0 (* x (+ (log x) -1.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 8.8e-251) {
		tmp = t_0;
	} else if (x <= 2.1e-209) {
		tmp = x * (0.083333333333333 / pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x * (log(x) + -1.0);
	}
	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) :: tmp
    t_0 = 0.91893853320467d0 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    if (x <= 8.8d-251) then
        tmp = t_0
    else if (x <= 2.1d-209) then
        tmp = x * (0.083333333333333d0 / (x ** 2.0d0))
    else if (x <= 1.0d0) then
        tmp = t_0
    else
        tmp = x * (log(x) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	double tmp;
	if (x <= 8.8e-251) {
		tmp = t_0;
	} else if (x <= 2.1e-209) {
		tmp = x * (0.083333333333333 / Math.pow(x, 2.0));
	} else if (x <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x * (Math.log(x) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	tmp = 0
	if x <= 8.8e-251:
		tmp = t_0
	elif x <= 2.1e-209:
		tmp = x * (0.083333333333333 / math.pow(x, 2.0))
	elif x <= 1.0:
		tmp = t_0
	else:
		tmp = x * (math.log(x) + -1.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x))
	tmp = 0.0
	if (x <= 8.8e-251)
		tmp = t_0;
	elseif (x <= 2.1e-209)
		tmp = Float64(x * Float64(0.083333333333333 / (x ^ 2.0)));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(log(x) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	tmp = 0.0;
	if (x <= 8.8e-251)
		tmp = t_0;
	elseif (x <= 2.1e-209)
		tmp = x * (0.083333333333333 / (x ^ 2.0));
	elseif (x <= 1.0)
		tmp = t_0;
	else
		tmp = x * (log(x) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 8.8e-251], t$95$0, If[LessEqual[x, 2.1e-209], N[(x * N[(0.083333333333333 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], t$95$0, N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 8.8e-251 or 2.09999999999999996e-209 < x < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. log-rec 98.9%

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

      4. remove-double-neg 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 56.2%

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

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

   if 8.8e-251 < x < 2.09999999999999996e-209

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 15.7%

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

   4. Taylor expanded in x around inf 15.7%

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

      1. sub-neg 89.7%

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

      2. mul-1-neg 89.7%

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

      3. log-rec 89.7%

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

      4. remove-double-neg 89.7%

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

      5. metadata-eval 89.7%

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

      6. +-commutative 89.7%

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

   6. Simplified 15.7%

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

   7. Taylor expanded in x around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. mul-1-neg 57.9%

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

      3. log-rec 57.9%

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

      4. remove-double-neg 57.9%

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

      5. sub-neg 57.9%

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

      6. associate-*r/ 57.9%

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

      7. metadata-eval 57.9%

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

      8. metadata-eval 57.9%

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

   9. Simplified 57.9%

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

   10. Taylor expanded in x around 0 57.9%

       \[\leadsto x \cdot \color{blue}{\frac{0.083333333333333}{{x}^{2}}} \]

   if 1 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 76.0%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. log-rec 98.6%

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

      4. remove-double-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. +-commutative 98.6%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in x around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. mul-1-neg 75.2%

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

      3. log-rec 75.2%

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

      4. remove-double-neg 75.2%

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

      5. sub-neg 75.2%

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

      6. associate-*r/ 75.2%

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

      7. metadata-eval 75.2%

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

      8. metadata-eval 75.2%

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

   9. Simplified 75.2%

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

   10. Taylor expanded in x around inf 75.2%

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

       1. sub-neg 75.2%

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

       2. mul-1-neg 75.2%

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

       3. log-rec 75.2%

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

       4. remove-double-neg 75.2%

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

       5. metadata-eval 75.2%

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

       6. +-commutative 75.2%

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

   12. Simplified 75.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{-251}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{0.083333333333333}{{x}^{2}}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (* x (+ (log x) -1.0))
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
   x)))

C

double code(double x, double y, double z) {
	return (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / 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 * (log(x) + (-1.0d0))) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (Math.log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
}

Python

def code(x, y, z):
	return (x * (math.log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
end

Wolfram

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

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. Add Preprocessing

3. Taylor expanded in x around inf 93.4%

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

   1. sub-neg 96.7%

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

   2. mul-1-neg 96.7%

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

   3. log-rec 96.7%

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

   4. remove-double-neg 96.7%

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

   5. metadata-eval 96.7%

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

   6. +-commutative 96.7%

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

5. Simplified 93.4%

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

6. Final simplification 93.4%

   \[\leadsto x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} \]
7. Add Preprocessing

Alternative 11: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -13.0)
   (+ (+ 0.91893853320467 (- (* x (log x)) x)) (* -0.0027777777777778 (/ z x)))
   (+
    (- (* (log x) (+ x -0.5)) (+ x -0.91893853320467))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -13.0) {
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = ((log(x) * (x + -0.5)) - (x + -0.91893853320467)) + (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 <= (-13.0d0)) then
        tmp = (0.91893853320467d0 + ((x * log(x)) - x)) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = ((log(x) * (x + (-0.5d0))) - (x + (-0.91893853320467d0))) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -13.0) {
		tmp = (0.91893853320467 + ((x * Math.log(x)) - x)) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = ((Math.log(x) * (x + -0.5)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -13.0:
		tmp = (0.91893853320467 + ((x * math.log(x)) - x)) + (-0.0027777777777778 * (z / x))
	else:
		tmp = ((math.log(x) * (x + -0.5)) - (x + -0.91893853320467)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -13.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(x * log(x)) - x)) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) - Float64(x + -0.91893853320467)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -13.0)
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + (-0.0027777777777778 * (z / x));
	else
		tmp = ((log(x) * (x + -0.5)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -13.0], N[(N[(0.91893853320467 + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -13

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-in 87.3%

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

      3. log-rec 87.3%

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

      4. remove-double-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around 0 40.5%

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

      1. *-commutative 40.5%

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

   8. Simplified 40.5%

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

   9. Taylor expanded in z around inf 41.6%

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

   if -13 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 72.3%

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

      1. associate-+l- 97.0%

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

      2. sub-neg 97.0%

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

      3. metadata-eval 97.0%

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

      4. sub-neg 97.0%

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

      5. metadata-eval 97.0%

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

   5. Applied egg-rr 72.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -13.0)
   (+ (+ 0.91893853320467 (- (* x (log x)) x)) (* -0.0027777777777778 (/ z x)))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -13.0) {
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (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 <= (-13.0d0)) then
        tmp = (0.91893853320467d0 + ((x * log(x)) - x)) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -13.0) {
		tmp = (0.91893853320467 + ((x * Math.log(x)) - x)) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -13.0:
		tmp = (0.91893853320467 + ((x * math.log(x)) - x)) + (-0.0027777777777778 * (z / x))
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -13.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(x * log(x)) - x)) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -13.0)
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + (-0.0027777777777778 * (z / x));
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -13.0], N[(N[(0.91893853320467 + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -13

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-in 87.3%

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

      3. log-rec 87.3%

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

      4. remove-double-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around 0 40.5%

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

      1. *-commutative 40.5%

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

   8. Simplified 40.5%

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

   9. Taylor expanded in z around inf 41.6%

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

   if -13 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+96}:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(-1 - \log \left(\frac{1}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+96)
   (+ (+ 0.91893853320467 (- (* x (log x)) x)) (* -0.0027777777777778 (/ z x)))
   (+ (/ 0.083333333333333 x) (* x (- -1.0 (log (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+96) {
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.083333333333333 / x) + (x * (-1.0 - log((1.0 / 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 <= (-3.6d+96)) then
        tmp = (0.91893853320467d0 + ((x * log(x)) - x)) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = (0.083333333333333d0 / x) + (x * ((-1.0d0) - log((1.0d0 / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+96) {
		tmp = (0.91893853320467 + ((x * Math.log(x)) - x)) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.083333333333333 / x) + (x * (-1.0 - Math.log((1.0 / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.6e+96:
		tmp = (0.91893853320467 + ((x * math.log(x)) - x)) + (-0.0027777777777778 * (z / x))
	else:
		tmp = (0.083333333333333 / x) + (x * (-1.0 - math.log((1.0 / x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+96)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(x * log(x)) - x)) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(x * Float64(-1.0 - log(Float64(1.0 / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e+96)
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + (-0.0027777777777778 * (z / x));
	else
		tmp = (0.083333333333333 / x) + (x * (-1.0 - log((1.0 / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e+96], N[(N[(0.91893853320467 + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(x * N[(-1.0 - N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000013e96

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-rgt-neg-in 85.9%

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

      3. log-rec 85.9%

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

      4. remove-double-neg 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in z around 0 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

   9. Taylor expanded in z around inf 40.8%

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

   if -3.60000000000000013e96 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 69.1%

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

   4. Taylor expanded in x around inf 68.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+96}:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(-1 - \log \left(\frac{1}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+123}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(-1 - \log \left(\frac{1}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+123)
   (+ 0.91893853320467 (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))
   (+ (/ 0.083333333333333 x) (* x (- -1.0 (log (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+123) {
		tmp = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = (0.083333333333333 / x) + (x * (-1.0 - log((1.0 / 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 <= (-1.1d+123)) then
        tmp = 0.91893853320467d0 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    else
        tmp = (0.083333333333333d0 / x) + (x * ((-1.0d0) - log((1.0d0 / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+123) {
		tmp = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = (0.083333333333333 / x) + (x * (-1.0 - Math.log((1.0 / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+123:
		tmp = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	else:
		tmp = (0.083333333333333 / x) + (x * (-1.0 - math.log((1.0 / x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+123)
		tmp = Float64(0.91893853320467 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(x * Float64(-1.0 - log(Float64(1.0 / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+123)
		tmp = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	else
		tmp = (0.083333333333333 / x) + (x * (-1.0 - log((1.0 / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+123], N[(0.91893853320467 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(x * N[(-1.0 - N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999996e123

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. distribute-rgt-neg-in 85.8%

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

      3. log-rec 85.8%

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

      4. remove-double-neg 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in z around 0 40.4%

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

      1. *-commutative 40.4%

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

   8. Simplified 40.4%

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

   9. Taylor expanded in x around 0 37.7%

      \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

   if -1.09999999999999996e123 < z

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 67.9%

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

   4. Taylor expanded in x around inf 67.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+123}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(-1 - \log \left(\frac{1}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (0.91893853320467 + ((x * log(x)) - x)) + ((0.083333333333333 + (z * -0.0027777777777778)) / 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)) - x)) + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in x around inf 93.3%

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

   1. mul-1-neg 93.3%

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

   2. distribute-rgt-neg-in 93.3%

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

   3. log-rec 93.3%

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

   4. remove-double-neg 93.3%

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

5. Simplified 93.3%

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

6. Taylor expanded in z around 0 63.2%

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

   1. *-commutative 63.2%

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

8. Simplified 63.2%

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

9. Final simplification 63.2%

   \[\leadsto \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} \]
10. Add Preprocessing

Alternative 16: 61.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.0) {
		tmp = 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = x * (log(x) + -1.0);
	}
	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) :: tmp
    if (x <= 1.0d0) then
        tmp = 0.91893853320467d0 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    else
        tmp = x * (log(x) + (-1.0d0))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1

   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. Add Preprocessing

   3. Taylor expanded in x around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. distribute-rgt-neg-in 99.1%

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

      3. log-rec 99.1%

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

      4. remove-double-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in z around 0 53.3%

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

      1. *-commutative 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in x around 0 53.3%

      \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

   if 1 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 76.0%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. log-rec 98.6%

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

      4. remove-double-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. +-commutative 98.6%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in x around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. mul-1-neg 75.2%

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

      3. log-rec 75.2%

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

      4. remove-double-neg 75.2%

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

      5. sub-neg 75.2%

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

      6. associate-*r/ 75.2%

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

      7. metadata-eval 75.2%

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

      8. metadata-eval 75.2%

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

   9. Simplified 75.2%

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

   10. Taylor expanded in x around inf 75.2%

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

       1. sub-neg 75.2%

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

       2. mul-1-neg 75.2%

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

       3. log-rec 75.2%

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

       4. remove-double-neg 75.2%

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

       5. metadata-eval 75.2%

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

       6. +-commutative 75.2%

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

   12. Simplified 75.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / 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 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
end function

Java

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

Python

def code(x, y, z):
	return 0.91893853320467 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(0.91893853320467 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / 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. Add Preprocessing

3. Taylor expanded in x around inf 93.3%

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

   1. mul-1-neg 93.3%

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

   2. distribute-rgt-neg-in 93.3%

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

   3. log-rec 93.3%

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

   4. remove-double-neg 93.3%

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

5. Simplified 93.3%

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

6. Taylor expanded in z around 0 63.2%

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

   1. *-commutative 63.2%

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

8. Simplified 63.2%

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

9. Taylor expanded in x around 0 30.9%

   \[\leadsto \color{blue}{0.91893853320467} + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x} \]

10. Final simplification 30.9%

    \[\leadsto 0.91893853320467 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} \]
11. Add Preprocessing

Alternative 18: 22.8% accurate, 24.6× speedup

Math

\[\begin{array}{l} \\ 0.083333333333333 \cdot \frac{1}{x} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.083333333333333 (/ 1.0 x)))

C

double code(double x, double y, double z) {
	return 0.083333333333333 * (1.0 / 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 = 0.083333333333333d0 * (1.0d0 / x)
end function

Java

public static double code(double x, double y, double z) {
	return 0.083333333333333 * (1.0 / x);
}

Python

def code(x, y, z):
	return 0.083333333333333 * (1.0 / x)

Julia

function code(x, y, z)
	return Float64(0.083333333333333 * Float64(1.0 / x))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(0.083333333333333 * N[(1.0 / 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. Add Preprocessing

3. Taylor expanded in z around 0 57.0%

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

4. Taylor expanded in x around inf 56.7%

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

   1. sub-neg 96.7%

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

   2. mul-1-neg 96.7%

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

   3. log-rec 96.7%

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

   4. remove-double-neg 96.7%

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

   5. metadata-eval 96.7%

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

   6. +-commutative 96.7%

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

6. Simplified 56.3%

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

7. Taylor expanded in x around 0 23.4%

   \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]
8. Step-by-step derivation

   1. div-inv 56.3%

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

   2. *-commutative 56.3%

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

9. Applied egg-rr 23.4%

   \[\leadsto \color{blue}{\frac{1}{x} \cdot 0.083333333333333} \]

10. Final simplification 23.4%

    \[\leadsto 0.083333333333333 \cdot \frac{1}{x} \]
11. Add Preprocessing

Alternative 19: 22.8% accurate, 41.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ 0.083333333333333 x))

C

double code(double x, double y, double z) {
	return 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 = 0.083333333333333d0 / x
end function

Java

public static double code(double x, double y, double z) {
	return 0.083333333333333 / x;
}

Python

def code(x, y, z):
	return 0.083333333333333 / x

Julia

function code(x, y, z)
	return Float64(0.083333333333333 / x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.083333333333333 / x;
end

Wolfram

code[x_, y_, z_] := N[(0.083333333333333 / x), $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. Add Preprocessing

3. Taylor expanded in z around 0 57.0%

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

4. Taylor expanded in x around inf 56.7%

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

   1. sub-neg 96.7%

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

   2. mul-1-neg 96.7%

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

   3. log-rec 96.7%

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

   4. remove-double-neg 96.7%

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

   5. metadata-eval 96.7%

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

   6. +-commutative 96.7%

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

6. Simplified 56.3%

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

7. Taylor expanded in x around 0 23.4%

   \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]
8. Add Preprocessing

Developer target: 98.6% 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 2024103 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (+ (+ (+ (* (- 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)))