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

Percentage Accurate: 93.8% → 99.0%

Time: 21.3s

Precision: binary64

Cost: 14020

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;0.91893853320467 + \left(-0.5 \cdot \log x + \left(\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + 0.083333333333333 \cdot \frac{1}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x + -0.5, 0.91893853320467 - x\right) + \left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

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)))

↓

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.1e-5)
   (+
    0.91893853320467
    (+
     (* -0.5 (log x))
     (+
      (/ (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)) x)
      (* 0.083333333333333 (/ 1.0 x)))))
   (+
    (fma (log x) (+ x -0.5) (- 0.91893853320467 x))
    (* (+ 0.0007936500793651 y) (/ z (/ x z))))))

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);
}

↓

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.1e-5) {
		tmp = 0.91893853320467 + ((-0.5 * log(x)) + (((z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778)) / x) + (0.083333333333333 * (1.0 / x))));
	} else {
		tmp = fma(log(x), (x + -0.5), (0.91893853320467 - x)) + ((0.0007936500793651 + y) * (z / (x / z)));
	}
	return tmp;
}

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

↓

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.1e-5)
		tmp = Float64(0.91893853320467 + Float64(Float64(-0.5 * log(x)) + Float64(Float64(Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778)) / x) + Float64(0.083333333333333 * Float64(1.0 / x)))));
	else
		tmp = Float64(fma(log(x), Float64(x + -0.5), Float64(0.91893853320467 - x)) + Float64(Float64(0.0007936500793651 + y) * Float64(z / Float64(x / z))));
	end
	return tmp
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]

↓

code[x_, y_, z_] := If[LessEqual[x, 2.1e-5], N[(0.91893853320467 + N[(N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	93.8%
Target	98.7%
Herbie	99.0%

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

Derivation

1. Split input into 2 regimes

2. if x < 2.09999999999999988e-5

   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. Simplified 99.7%

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

      [Start] 99.7%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      remove-double-neg [<=] 99.7%	\[ \left(\left(\color{blue}{\left(-\left(-\left(x - 0.5\right)\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      remove-double-neg [=>] 99.7%	\[ \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      sub-neg [=>] 99.7%	\[ \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      metadata-eval [=>] 99.7%	\[ \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      *-commutative [=>] 99.7%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)} + 0.083333333333333}{x} \]
      fma-def [=>] 99.7%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(z, \left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, 0.083333333333333\right)}}{x} \]
      fma-neg [=>] 99.7%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, 0.083333333333333\right)}{x} \]
      metadata-eval [=>] 99.7%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), 0.083333333333333\right)}{x} \]

   3. Taylor expanded in x around 0 99.7%

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

   if 2.09999999999999988e-5 < x

   1. Initial program 87.2%

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

   2. Simplified 87.2%

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

      [Start] 87.2%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      remove-double-neg [<=] 87.2%	\[ \left(\left(\color{blue}{\left(-\left(-\left(x - 0.5\right)\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      remove-double-neg [=>] 87.2%	\[ \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      sub-neg [=>] 87.2%	\[ \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      metadata-eval [=>] 87.2%	\[ \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
      *-commutative [=>] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)} + 0.083333333333333}{x} \]
      fma-def [=>] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(z, \left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, 0.083333333333333\right)}}{x} \]
      fma-neg [=>] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, 0.083333333333333\right)}{x} \]
      metadata-eval [=>] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), 0.083333333333333\right)}{x} \]

   3. Taylor expanded in z around inf 87.2%

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

   4. Simplified 87.2%

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

      [Start] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x} \]
      unpow2 [=>] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 + y\right)}{x} \]
      +-commutative [<=] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(z \cdot z\right) \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

   5. Applied egg-rr 87.2%

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

      [Start] 87.2%	\[ \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(z \cdot z\right) \cdot \left(y + 0.0007936500793651\right)}{x} \]
      *-un-lft-identity [=>] 87.2%	\[ \color{blue}{1 \cdot \left(\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(z \cdot z\right) \cdot \left(y + 0.0007936500793651\right)}{x}\right)} \]
      +-commutative [=>] 87.2%	\[ 1 \cdot \color{blue}{\left(\frac{\left(z \cdot z\right) \cdot \left(y + 0.0007936500793651\right)}{x} + \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right)\right)} \]
      *-commutative [=>] 87.2%	\[ 1 \cdot \left(\frac{\color{blue}{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}}{x} + \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right)\right) \]
      +-commutative [=>] 87.2%	\[ 1 \cdot \left(\frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} + \color{blue}{\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right)}\right) \]

   6. Simplified 98.2%

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

      [Start] 87.2%	\[ 1 \cdot \left(\frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} + \left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right)\right) \]
      *-lft-identity [=>] 87.2%	\[ \color{blue}{\frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} + \left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right)} \]
      +-commutative [=>] 87.2%	\[ \color{blue}{\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x}} \]
      associate-+r- [=>] 87.2%	\[ \color{blue}{\left(\left(0.91893853320467 + \left(x + -0.5\right) \cdot \log x\right) - x\right)} + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      +-commutative [=>] 87.2%	\[ \left(\color{blue}{\left(\left(x + -0.5\right) \cdot \log x + 0.91893853320467\right)} - x\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      associate-+r- [<=] 87.2%	\[ \color{blue}{\left(\left(x + -0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right)} + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      metadata-eval [<=] 87.2%	\[ \left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      sub-neg [<=] 87.2%	\[ \left(\color{blue}{\left(x - 0.5\right)} \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      *-commutative [=>] 87.2%	\[ \left(\color{blue}{\log x \cdot \left(x - 0.5\right)} + \left(0.91893853320467 - x\right)\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      fma-def [=>] 87.3%	\[ \color{blue}{\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right)} + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      sub-neg [=>] 87.3%	\[ \mathsf{fma}\left(\log x, \color{blue}{x + \left(-0.5\right)}, 0.91893853320467 - x\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      metadata-eval [=>] 87.3%	\[ \mathsf{fma}\left(\log x, x + \color{blue}{-0.5}, 0.91893853320467 - x\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      +-commutative [=>] 87.3%	\[ \mathsf{fma}\left(\log x, \color{blue}{-0.5 + x}, 0.91893853320467 - x\right) + \frac{\left(y + 0.0007936500793651\right) \cdot \left(z \cdot z\right)}{x} \]
      *-commutative [=>] 87.3%	\[ \mathsf{fma}\left(\log x, -0.5 + x, 0.91893853320467 - x\right) + \frac{\color{blue}{\left(z \cdot z\right) \cdot \left(y + 0.0007936500793651\right)}}{x} \]
      associate-/l* [=>] 90.9%	\[ \mathsf{fma}\left(\log x, -0.5 + x, 0.91893853320467 - x\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}} \]
      associate-/r/ [=>] 90.9%	\[ \mathsf{fma}\left(\log x, -0.5 + x, 0.91893853320467 - x\right) + \color{blue}{\frac{z \cdot z}{x} \cdot \left(y + 0.0007936500793651\right)} \]
      associate-/l* [=>] 98.2%	\[ \mathsf{fma}\left(\log x, -0.5 + x, 0.91893853320467 - x\right) + \color{blue}{\frac{z}{\frac{x}{z}}} \cdot \left(y + 0.0007936500793651\right) \]
      +-commutative [=>] 98.2%	\[ \mathsf{fma}\left(\log x, -0.5 + x, 0.91893853320467 - x\right) + \frac{z}{\frac{x}{z}} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;0.91893853320467 + \left(-0.5 \cdot \log x + \left(\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + 0.083333333333333 \cdot \frac{1}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x + -0.5, 0.91893853320467 - x\right) + \left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.0%
Cost	14020

\[\begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;0.91893853320467 + \left(-0.5 \cdot \log x + \left(\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + 0.083333333333333 \cdot \frac{1}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x + -0.5, 0.91893853320467 - x\right) + \left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 2
Accuracy	99.0%
Cost	8004

\[\begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;0.91893853320467 + \left(-0.5 \cdot \log x + \left(\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + 0.083333333333333 \cdot \frac{1}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}} + \left(\left(0.91893853320467 - x\right) + \log x \cdot \left(x + -0.5\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	90.4%
Cost	7752

\[\begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+143}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x + -0.5\right) - x\right)\right) + y \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 4
Accuracy	98.7%
Cost	7748

\[\begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}} + \left(\left(0.91893853320467 - x\right) + \log x \cdot \left(x + -0.5\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	83.4%
Cost	7496

\[\begin{array}{l} \mathbf{if}\;x \leq 780000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{+43}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x + -0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 6
Accuracy	83.4%
Cost	7240

\[\begin{array}{l} \mathbf{if}\;x \leq 950000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot \left(x - 0.5\right)\right) - x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 7
Accuracy	83.4%
Cost	7117

\[\begin{array}{l} \mathbf{if}\;x \leq 860000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+44} \lor \neg \left(x \leq 5 \cdot 10^{+100}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	65.0%
Cost	964

\[\begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	42.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+24} \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(0.0007936500793651 \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 10
Accuracy	42.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;y \leq 0.00078:\\ \;\;\;\;z \cdot \left(0.0007936500793651 \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 11
Accuracy	43.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;y \leq 0.00078:\\ \;\;\;\;z \cdot \left(0.0007936500793651 \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 12
Accuracy	44.2%
Cost	576

\[z \cdot \left(\left(0.0007936500793651 + y\right) \cdot \frac{z}{x}\right) \]

Alternative 13
Accuracy	44.4%
Cost	576

\[\left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}} \]

Alternative 14
Accuracy	44.5%
Cost	576

\[\frac{0.0007936500793651 + y}{\frac{\frac{x}{z}}{z}} \]

Alternative 15
Accuracy	25.7%
Cost	448

\[0.0007936500793651 \cdot \left(z \cdot \frac{z}{x}\right) \]

Alternative 16
Accuracy	25.9%
Cost	448

\[z \cdot \left(0.0007936500793651 \cdot \frac{z}{x}\right) \]

Reproduce

herbie shell --seed 2023272 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

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

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