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

Percentage Accurate: 93.7% → 99.6%

Time: 23.7s

Precision: binary64

Cost: 26820

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{y + 0.0007936500793651}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

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 2e+20)
   (+
    (fma (+ x -0.5) (log x) (- 0.91893853320467 x))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ (+ y 0.0007936500793651) (/ (/ x z) 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 <= 2e+20) {
		tmp = fma((x + -0.5), log(x), (0.91893853320467 - x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((y + 0.0007936500793651) / ((x / z) / 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 <= 2e+20)
		tmp = Float64(fma(Float64(x + -0.5), log(x), Float64(0.91893853320467 - x)) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(y + 0.0007936500793651) / Float64(Float64(x / z) / 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, 2e+20], N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	93.7%
Target	98.6%
Herbie	99.6%

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

Derivation

1. Split input into 2 regimes

2. if x < 2e20

   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%

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

   if 2e20 < x

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 87.8%

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

   3. Simplified 91.8%

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

      [Start] 87.8%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x} \]
      associate-/l* [=>] 91.0%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]
      +-commutative [<=] 91.0%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{{z}^{2}}{\frac{x}{\color{blue}{y + 0.0007936500793651}}} \]
      associate-/r/ [=>] 91.8%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]
      unpow2 [=>] 91.8%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{x} \cdot \left(y + 0.0007936500793651\right) \]
      +-commutative [=>] 91.8%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z \cdot z}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   4. Taylor expanded in z around 0 91.8%

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

   5. Simplified 98.9%

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

      [Start] 91.8%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right) \]
      unpow2 [=>] 91.8%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot z}}{x} \cdot \left(0.0007936500793651 + y\right) \]
      associate-/l* [=>] 98.9%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{z}{\frac{x}{z}}} \cdot \left(0.0007936500793651 + y\right) \]

   6. Applied egg-rr 99.5%

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

      [Start] 98.9%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z}{\frac{x}{z}} \cdot \left(0.0007936500793651 + y\right) \]
      *-commutative [=>] 98.9%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(0.0007936500793651 + y\right) \cdot \frac{z}{\frac{x}{z}}} \]
      clear-num [=>] 98.9%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(0.0007936500793651 + y\right) \cdot \color{blue}{\frac{1}{\frac{\frac{x}{z}}{z}}} \]
      un-div-inv [=>] 99.5%	\[ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.0007936500793651 + y}{\frac{\frac{x}{z}}{z}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{y + 0.0007936500793651}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.6%
Cost	26820

\[\begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{y + 0.0007936500793651}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

Alternative 2
Accuracy	99.5%
Cost	8004

\[\begin{array}{l} t_0 := 0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\\ \mathbf{if}\;x \leq 5000:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{y + 0.0007936500793651}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

Alternative 3
Accuracy	97.9%
Cost	7753

\[\begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+16} \lor \neg \left(z \leq 7.6\right):\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \end{array} \]

Alternative 4
Accuracy	98.3%
Cost	7748

\[\begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 5
Accuracy	98.7%
Cost	7748

\[\begin{array}{l} \mathbf{if}\;x \leq 0.37:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 6
Accuracy	98.7%
Cost	7748

\[\begin{array}{l} \mathbf{if}\;x \leq 0.37:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{y + 0.0007936500793651}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

Alternative 7
Accuracy	95.8%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-50} \lor \neg \left(z \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8
Accuracy	97.9%
Cost	7625

\[\begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+16} \lor \neg \left(z \leq 6.4\right):\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot y\right)}{x}\\ \end{array} \]

Alternative 9
Accuracy	81.4%
Cost	7496

\[\begin{array}{l} \mathbf{if}\;z \leq -6800000000000:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + 0.0007936500793651\right) \cdot {z}^{2}}{x}\\ \end{array} \]

Alternative 10
Accuracy	82.4%
Cost	7496

\[\begin{array}{l} \mathbf{if}\;z \leq -680000000000:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+61}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + 0.0007936500793651\right) \cdot {z}^{2}}{x}\\ \end{array} \]

Alternative 11
Accuracy	81.4%
Cost	7368

\[\begin{array}{l} \mathbf{if}\;z \leq -37000000000:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+61}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + 0.0007936500793651\right) \cdot {z}^{2}}{x}\\ \end{array} \]

Alternative 12
Accuracy	81.4%
Cost	7240

\[\begin{array}{l} \mathbf{if}\;z \leq -1320000000000:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + 0.0007936500793651\right) \cdot {z}^{2}}{x}\\ \end{array} \]

Alternative 13
Accuracy	60.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-28} \lor \neg \left(z \leq 1.35 \cdot 10^{-13}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 14
Accuracy	48.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-27} \lor \neg \left(z \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \left(y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 15
Accuracy	48.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-50} \lor \neg \left(z \leq 8.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{y \cdot \left(z \cdot z\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 16
Accuracy	23.6%
Cost	192

\[\frac{0.083333333333333}{x} \]

Reproduce

herbie shell --seed 2023263 
(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)))