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

Percentage Accurate: 93.8% → 99.2%

Time: 18.0s

Alternatives: 11

Speedup: 1.0×

• 31.4% 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: 93.8% 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: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 110:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, -x\right) + \left(0.91893853320467 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 110.0)
   (+
    (fma (+ x -0.5) (log x) (- x))
    (+
     0.91893853320467
     (/
      (fma
       (fma (+ y 0.0007936500793651) z -0.0027777777777778)
       z
       0.083333333333333)
      x)))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* z (/ (+ y 0.0007936500793651) (/ x z)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 110.0) {
		tmp = fma((x + -0.5), log(x), -x) + (0.91893853320467 + (fma(fma((y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x));
	} else {
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) / (x / z))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 110.0)
		tmp = Float64(fma(Float64(x + -0.5), log(x), Float64(-x)) + Float64(0.91893853320467 + Float64(fma(fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x)));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) / Float64(x / z))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 110.0], N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + (-x)), $MachinePrecision] + N[(0.91893853320467 + N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 110

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. fma-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. fma-define 99.8%

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

      6. fma-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   if 110 < x

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-*r/ 88.3%

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

      3. metadata-eval 88.3%

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

      4. unpow2 88.3%

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

      5. associate-*l* 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. associate-*l/ 96.5%

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

      8. associate-/l* 99.6%

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

      9. associate-*l/ 99.6%

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

      10. associate-*r/ 99.6%

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

      11. distribute-rgt-out 99.6%

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

      12. +-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around 0 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*l/ 99.6%

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

      3. associate-/r/ 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around inf 99.8%

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

       1. sub-neg 99.8%

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

       2. mul-1-neg 99.8%

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

       3. log-rec 99.8%

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

       4. remove-double-neg 99.8%

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

       5. metadata-eval 99.8%

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

       6. +-commutative 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 110:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, -x\right) + \left(0.91893853320467 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 110:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 110.0)
   (+
    (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) (/ x z)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 110.0) {
		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) / (x / z))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 110.0)
		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(x / z))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 110.0], 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[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 110

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      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 99.7%

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

      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 110 < x

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-*r/ 88.3%

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

      3. metadata-eval 88.3%

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

      4. unpow2 88.3%

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

      5. associate-*l* 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. associate-*l/ 96.5%

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

      8. associate-/l* 99.6%

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

      9. associate-*l/ 99.6%

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

      10. associate-*r/ 99.6%

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

      11. distribute-rgt-out 99.6%

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

      12. +-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around 0 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*l/ 99.6%

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

      3. associate-/r/ 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around inf 99.8%

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

       1. sub-neg 99.8%

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

       2. mul-1-neg 99.8%

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

       3. log-rec 99.8%

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

       4. remove-double-neg 99.8%

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

       5. metadata-eval 99.8%

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

       6. +-commutative 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 110:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 110:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 110.0)
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* z (/ (+ y 0.0007936500793651) (/ x z)))
     (* 0.083333333333333 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 110.0) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) / (x / z))) + (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 <= 110.0d0) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((z * ((y + 0.0007936500793651d0) / (x / z))) + (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 <= 110.0) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) / (x / z))) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 110.0:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) / (x / z))) + (0.083333333333333 * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 110.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + 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(x / z))) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 110.0)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (x * (log(x) + -1.0)) + ((z * ((y + 0.0007936500793651) / (x / z))) + (0.083333333333333 * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 110.0], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $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[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 110

   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

   if 110 < x

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-*r/ 88.3%

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

      3. metadata-eval 88.3%

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

      4. unpow2 88.3%

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

      5. associate-*l* 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. associate-*l/ 96.5%

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

      8. associate-/l* 99.6%

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

      9. associate-*l/ 99.6%

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

      10. associate-*r/ 99.6%

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

      11. distribute-rgt-out 99.6%

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

      12. +-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around 0 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*l/ 99.6%

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

      3. associate-/r/ 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around inf 99.8%

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

       1. sub-neg 99.8%

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

       2. mul-1-neg 99.8%

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

       3. log-rec 99.8%

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

       4. remove-double-neg 99.8%

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

       5. metadata-eval 99.8%

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

       6. +-commutative 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 110:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;y \leq -0.0008 \lor \neg \left(y \leq 1.02 \cdot 10^{+43}\right):\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= y -0.0008) (not (<= y 1.02e+43)))
     (+ t_0 (/ (+ 0.083333333333333 (* z (- (* y z) 0.0027777777777778))) x))
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
       x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((y <= -0.0008) || !(y <= 1.02e+43)) {
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / 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 ((y <= (-0.0008d0)) .or. (.not. (y <= 1.02d+43))) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((y * z) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * z) - 0.0027777777777778d0))) / 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 ((y <= -0.0008) || !(y <= 1.02e+43)) {
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (y <= -0.0008) or not (y <= 1.02e+43):
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((y <= -0.0008) || !(y <= 1.02e+43))
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(y * z) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((y <= -0.0008) || ~((y <= 1.02e+43)))
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / 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[Or[LessEqual[y, -0.0008], N[Not[LessEqual[y, 1.02e+43]], $MachinePrecision]], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(y * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000038e-4 or 1.02e43 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. sub-neg 97.1%

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

      2. mul-1-neg 97.1%

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

      3. log-rec 97.1%

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

      4. remove-double-neg 97.1%

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

      5. metadata-eval 97.1%

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

      6. +-commutative 97.1%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in y around inf 91.0%

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

      1. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   if -8.00000000000000038e-4 < y < 1.02e43

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 90.3%

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

      1. sub-neg 97.5%

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

      2. mul-1-neg 97.5%

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

      3. log-rec 97.5%

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

      4. remove-double-neg 97.5%

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

      5. metadata-eval 97.5%

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

      6. +-commutative 97.5%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

   8. Simplified 91.0%

      \[\leadsto x \cdot \left(-1 + \log x\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0008 \lor \neg \left(y \leq 1.02 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 1.5 \cdot 10^{-91}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 1.5e-91)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+
      t_0
      (+
       (* 0.083333333333333 (/ 1.0 x))
       (* z (* (+ y 0.0007936500793651) (/ z x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (x <= 1.5e-91) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 * (1.0 / x)) + (z * ((y + 0.0007936500793651) * (z / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (x <= 1.5d-91) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((0.083333333333333d0 * (1.0d0 / x)) + (z * ((y + 0.0007936500793651d0) * (z / 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 <= 1.5e-91) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 * (1.0 / x)) + (z * ((y + 0.0007936500793651) * (z / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if x <= 1.5e-91:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((0.083333333333333 * (1.0 / x)) + (z * ((y + 0.0007936500793651) * (z / x))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (x <= 1.5e-91)
		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(0.083333333333333 * Float64(1.0 / x)) + Float64(z * Float64(Float64(y + 0.0007936500793651) * Float64(z / 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 <= 1.5e-91)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((0.083333333333333 * (1.0 / x)) + (z * ((y + 0.0007936500793651) * (z / 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, 1.5e-91], 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[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.5000000000000001e-91

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. sub-neg 95.1%

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

      2. mul-1-neg 95.1%

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

      3. log-rec 95.1%

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

      4. remove-double-neg 95.1%

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

      5. metadata-eval 95.1%

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

      6. +-commutative 95.1%

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

   5. Simplified 99.8%

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

   if 1.5000000000000001e-91 < x

   1. Initial program 85.5%

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

   3. Taylor expanded in z around 0 97.7%

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

   4. Taylor expanded in z around inf 88.5%

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

      1. +-commutative 88.5%

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

      2. associate-*r/ 88.5%

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

      3. metadata-eval 88.5%

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

      4. unpow2 88.5%

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

      5. associate-*l* 97.6%

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

      6. distribute-rgt-in 96.9%

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

      7. associate-*l/ 96.3%

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

      8. associate-/l* 97.5%

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

      9. associate-*l/ 97.4%

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

      10. associate-*r/ 97.5%

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

      11. distribute-rgt-out 99.5%

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

      12. +-commutative 99.5%

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

   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 98.9%

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

      1. sub-neg 99.0%

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

      2. mul-1-neg 99.0%

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

      3. log-rec 99.0%

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

      4. remove-double-neg 99.0%

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

      5. metadata-eval 99.0%

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

      6. +-commutative 99.0%

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

   9. Simplified 98.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(\left(y + 0.0007936500793651\right) \cdot \frac{z}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 100:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 100.0)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+
      t_0
      (+
       (* z (/ (+ y 0.0007936500793651) (/ x z)))
       (* 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 <= 100.0) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((z * ((y + 0.0007936500793651) / (x / z))) + (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 <= 100.0d0) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((z * ((y + 0.0007936500793651d0) / (x / z))) + (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 <= 100.0) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((z * ((y + 0.0007936500793651) / (x / z))) + (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 <= 100.0:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((z * ((y + 0.0007936500793651) / (x / z))) + (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 <= 100.0)
		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(x / z))) + 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 <= 100.0)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((z * ((y + 0.0007936500793651) / (x / z))) + (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, 100.0], 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[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 100

   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 98.9%

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

      1. sub-neg 95.2%

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

      2. mul-1-neg 95.2%

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

      3. log-rec 95.2%

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

      4. remove-double-neg 95.2%

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

      5. metadata-eval 95.2%

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

      6. +-commutative 95.2%

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

   5. Simplified 98.9%

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

   if 100 < x

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-*r/ 88.3%

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

      3. metadata-eval 88.3%

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

      4. unpow2 88.3%

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

      5. associate-*l* 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. associate-*l/ 96.5%

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

      8. associate-/l* 99.6%

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

      9. associate-*l/ 99.6%

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

      10. associate-*r/ 99.6%

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

      11. distribute-rgt-out 99.6%

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

      12. +-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around 0 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*l/ 99.6%

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

      3. associate-/r/ 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around inf 99.8%

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

       1. sub-neg 99.8%

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

       2. mul-1-neg 99.8%

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

       3. log-rec 99.8%

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

       4. remove-double-neg 99.8%

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

       5. metadata-eval 99.8%

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

       6. +-commutative 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 100:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{y + 0.0007936500793651}{\frac{x}{z}} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 1.32 \cdot 10^{+241}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 1.32e+241)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (x <= 1.32e+241) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (x <= 1.32d+241) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if (x <= 1.32e+241) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if x <= 1.32e+241:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (x <= 1.32e+241)
		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(0.083333333333333 / 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 <= 1.32e+241)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + (0.083333333333333 / 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, 1.32e+241], 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[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.3199999999999999e241

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 95.1%

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

      1. sub-neg 97.0%

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

      2. mul-1-neg 97.0%

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

      3. log-rec 97.0%

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

      4. remove-double-neg 97.0%

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

      5. metadata-eval 97.0%

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

      6. +-commutative 97.0%

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

   5. Simplified 95.1%

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

   if 1.3199999999999999e241 < x

   1. Initial program 59.4%

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

   3. Taylor expanded in z around 0 96.5%

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

   4. Taylor expanded in x around inf 96.7%

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

      1. sub-neg 99.7%

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

      2. mul-1-neg 99.7%

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

      3. log-rec 99.7%

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

      4. remove-double-neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. +-commutative 99.7%

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

   6. Simplified 96.7%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.32 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 2.4 \cdot 10^{+178}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 2.4e+178)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
       x))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (x <= 2.4e+178) {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (x <= 2.4d+178) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * z) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if (x <= 2.4e+178) {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if x <= 2.4e+178:
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (x <= 2.4e+178)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(0.083333333333333 / 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 <= 2.4e+178)
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + (0.083333333333333 / 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, 2.4e+178], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 2.4e178

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 97.7%

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

      1. sub-neg 96.6%

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

      2. mul-1-neg 96.6%

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

      3. log-rec 96.6%

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

      4. remove-double-neg 96.6%

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

      5. metadata-eval 96.6%

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

      6. +-commutative 96.6%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around 0 79.5%

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

      1. *-commutative 79.5%

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

   8. Simplified 79.5%

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

   if 2.4e178 < x

   1. Initial program 70.2%

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

   3. Taylor expanded in z around 0 86.2%

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

   4. Taylor expanded in x around inf 86.4%

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

      1. sub-neg 99.8%

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

      2. mul-1-neg 99.8%

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

      3. log-rec 99.8%

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

      4. remove-double-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. +-commutative 99.8%

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

   6. Simplified 86.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (log(x) + -1.0)) + ((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 = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 + (z * (-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 * -0.0027777777777778)) / x);
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * -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 * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.4%

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

3. Taylor expanded in x around inf 91.0%

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

   1. sub-neg 97.4%

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

   2. mul-1-neg 97.4%

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

   3. log-rec 97.4%

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

   4. remove-double-neg 97.4%

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

   5. metadata-eval 97.4%

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

   6. +-commutative 97.4%

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

5. Simplified 91.0%

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

6. Taylor expanded in z around 0 62.8%

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

   1. *-commutative 62.8%

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

8. Simplified 62.8%

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

9. Final simplification 62.8%

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

Alternative 10: 56.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.4%

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

3. Taylor expanded in z around 0 59.0%

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

4. Taylor expanded in x around inf 58.7%

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

   1. sub-neg 97.4%

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

   2. mul-1-neg 97.4%

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

   3. log-rec 97.4%

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

   4. remove-double-neg 97.4%

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

   5. metadata-eval 97.4%

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

   6. +-commutative 97.4%

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

6. Simplified 58.7%

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

7. Final simplification 58.7%

   \[\leadsto x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x} \]
8. Add Preprocessing

Alternative 11: 23.2% 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 91.4%

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

3. Taylor expanded in z around 0 59.0%

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

   1. add-cbrt-cube 37.9%

      \[\leadsto \left(\left(\color{blue}{\sqrt[3]{\left(\left(\left(x - 0.5\right) \cdot \log x\right) \cdot \left(\left(x - 0.5\right) \cdot \log x\right)\right) \cdot \left(\left(x - 0.5\right) \cdot \log x\right)}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   2. pow3 37.9%

      \[\leadsto \left(\left(\sqrt[3]{\color{blue}{{\left(\left(x - 0.5\right) \cdot \log x\right)}^{3}}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   3. sub-neg 37.9%

      \[\leadsto \left(\left(\sqrt[3]{{\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. metadata-eval 37.9%

      \[\leadsto \left(\left(\sqrt[3]{{\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   5. *-commutative 37.9%

      \[\leadsto \left(\left(\sqrt[3]{{\color{blue}{\left(\log x \cdot \left(x + -0.5\right)\right)}}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

5. Applied egg-rr 37.9%

   \[\leadsto \left(\left(\color{blue}{\sqrt[3]{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3}}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

6. Taylor expanded in x around 0 25.7%

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

   1. +-commutative 25.7%

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

   2. *-commutative 25.7%

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

8. Simplified 25.7%

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

9. Taylor expanded in x around 0 26.2%

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

10. Final simplification 26.2%

    \[\leadsto \frac{0.083333333333333}{x} \]
11. 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 2024072 
(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)))