Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B

Average Error: 31.63% → 0.12%

Time: 13.4s

Precision: binary64

Cost: 14152

Math

\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{-15.646356830292042}{z}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-0.279195317918525 - z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}{-3.350343815022304 + z \cdot \left(-6.012459259764103 - z\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

↓

(FPCore (x y z)
 :precision binary64
 (if (<= z -480000000.0)
   (+ x (/ y (+ 14.431876219268936 (/ -15.646356830292042 z))))
   (if (<= z 1.12e+16)
     (fma
      (/
       (-
        -0.279195317918525
        (* z (fma z 0.0692910599291889 0.4917317610505968)))
       (+ -3.350343815022304 (* z (- -6.012459259764103 z))))
      y
      x)
     (+ x (/ y 14.431876219268936)))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

↓

double code(double x, double y, double z) {
	double tmp;
	if (z <= -480000000.0) {
		tmp = x + (y / (14.431876219268936 + (-15.646356830292042 / z)));
	} else if (z <= 1.12e+16) {
		tmp = fma(((-0.279195317918525 - (z * fma(z, 0.0692910599291889, 0.4917317610505968))) / (-3.350343815022304 + (z * (-6.012459259764103 - z)))), y, x);
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	return tmp;
}

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

↓

function code(x, y, z)
	tmp = 0.0
	if (z <= -480000000.0)
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 + Float64(-15.646356830292042 / z))));
	elseif (z <= 1.12e+16)
		tmp = fma(Float64(Float64(-0.279195317918525 - Float64(z * fma(z, 0.0692910599291889, 0.4917317610505968))) / Float64(-3.350343815022304 + Float64(z * Float64(-6.012459259764103 - z)))), y, x);
	else
		tmp = Float64(x + Float64(y / 14.431876219268936));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := If[LessEqual[z, -480000000.0], N[(x + N[(y / N[(14.431876219268936 + N[(-15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+16], N[(N[(N[(-0.279195317918525 - N[(z * N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-3.350343815022304 + N[(z * N[(-6.012459259764103 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]]]

Target

Original	31.63%
Target	0.56%
Herbie	0.12%

\[\begin{array}{l} \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e8

   1. Initial program 63.22

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   2. Simplified 50.21

      \[\leadsto \color{blue}{x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}}} \]
      Proof

      [Start] 63.22	\[ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
      associate-/l* [=>] 50.21	\[ x + \color{blue}{\frac{y}{\frac{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}}} \]
      fma-def [=>] 50.21	\[ x + \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}}{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}} \]
      fma-def [=>] 50.21	\[ x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}} \]
      fma-def [=>] 50.21	\[ x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}} \]

   3. Taylor expanded in z around inf 0.06

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]

   4. Simplified 0.06

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]
      Proof

      [Start] 0.06	\[ x + \frac{y}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}} \]
      associate-*r/ [=>] 0.06	\[ x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]
      metadata-eval [=>] 0.06	\[ x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   if -4.8e8 < z < 1.12e16

   1. Initial program 0.41

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   2. Simplified 0.17

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, y, x\right)} \]
      Proof

      [Start] 0.41	\[ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
      +-commutative [=>] 0.41	\[ \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]
      associate-*r/ [<=] 0.17	\[ \color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]
      *-commutative [<=] 0.17	\[ \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \cdot y} + x \]
      fma-def [=>] 0.16	\[ \color{blue}{\mathsf{fma}\left(\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, y, x\right)} \]
      *-commutative [=>] 0.16	\[ \mathsf{fma}\left(\frac{\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, y, x\right) \]
      fma-def [=>] 0.16	\[ \mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, y, x\right) \]
      fma-def [=>] 0.16	\[ \mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, y, x\right) \]
      *-commutative [=>] 0.16	\[ \mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, y, x\right) \]
      fma-def [=>] 0.17	\[ \mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, y, x\right) \]

   3. Applied egg-rr 0.16

      \[\leadsto \mathsf{fma}\left(\color{blue}{-\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}}, y, x\right) \]

   4. Simplified 0.16

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-0.279195317918525 - z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}}, y, x\right) \]
      Proof

      [Start] 0.16	\[ \mathsf{fma}\left(-\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      distribute-frac-neg [<=] 0.16	\[ \mathsf{fma}\left(\color{blue}{\frac{-\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}}, y, x\right) \]
      fma-udef [=>] 0.16	\[ \mathsf{fma}\left(\frac{-\color{blue}{\left(z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right) + 0.279195317918525\right)}}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      fma-udef [=>] 0.16	\[ \mathsf{fma}\left(\frac{-\left(z \cdot \color{blue}{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      *-commutative [<=] 0.16	\[ \mathsf{fma}\left(\frac{-\left(z \cdot \left(\color{blue}{0.0692910599291889 \cdot z} + 0.4917317610505968\right) + 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      +-commutative [<=] 0.16	\[ \mathsf{fma}\left(\frac{-\left(z \cdot \color{blue}{\left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)} + 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      *-commutative [<=] 0.16	\[ \mathsf{fma}\left(\frac{-\left(\color{blue}{\left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z} + 0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      distribute-neg-in [=>] 0.16	\[ \mathsf{fma}\left(\frac{\color{blue}{\left(-\left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) \cdot z\right) + \left(-0.279195317918525\right)}}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      *-commutative [=>] 0.16	\[ \mathsf{fma}\left(\frac{\left(-\color{blue}{z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)}\right) + \left(-0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      +-commutative [=>] 0.16	\[ \mathsf{fma}\left(\frac{\left(-z \cdot \color{blue}{\left(0.0692910599291889 \cdot z + 0.4917317610505968\right)}\right) + \left(-0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      *-commutative [=>] 0.16	\[ \mathsf{fma}\left(\frac{\left(-z \cdot \left(\color{blue}{z \cdot 0.0692910599291889} + 0.4917317610505968\right)\right) + \left(-0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      fma-udef [<=] 0.16	\[ \mathsf{fma}\left(\frac{\left(-z \cdot \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}\right) + \left(-0.279195317918525\right)}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      metadata-eval [=>] 0.16	\[ \mathsf{fma}\left(\frac{\left(-z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)\right) + \color{blue}{-0.279195317918525}}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      +-commutative [<=] 0.16	\[ \mathsf{fma}\left(\frac{\color{blue}{-0.279195317918525 + \left(-z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)\right)}}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]
      sub-neg [<=] 0.16	\[ \mathsf{fma}\left(\frac{\color{blue}{-0.279195317918525 - z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}}{-3.350343815022304 - z \cdot \left(z + 6.012459259764103\right)}, y, x\right) \]

   if 1.12e16 < z

   1. Initial program 66.19

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   2. Simplified 52.99

      \[\leadsto \color{blue}{x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}}} \]
      Proof

      [Start] 66.19	\[ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
      associate-/l* [=>] 52.99	\[ x + \color{blue}{\frac{y}{\frac{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}}} \]
      fma-def [=>] 52.99	\[ x + \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}}{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}} \]
      fma-def [=>] 52.99	\[ x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}} \]
      fma-def [=>] 52.99	\[ x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}} \]

   3. Taylor expanded in z around inf 0.08

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.12

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{-15.646356830292042}{z}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-0.279195317918525 - z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}{-3.350343815022304 + z \cdot \left(-6.012459259764103 - z\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.12%
Cost	7880

\[\begin{array}{l} \mathbf{if}\;z \leq -24500000000:\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{-15.646356830292042}{z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{-0.279195317918525 - z \cdot \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}{-3.350343815022304 + z \cdot \left(-6.012459259764103 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

Alternative 2
Error	0.25%
Cost	1608

\[\begin{array}{l} \mathbf{if}\;z \leq -600000000:\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{-15.646356830292042}{z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

Alternative 3
Error	39.71%
Cost	852

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-213}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-261}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-238}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	39.71%
Cost	852

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-213}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-261}:\\ \;\;\;\;\frac{y}{12.000000000000014}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-238}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	0.77%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \end{array} \]

Alternative 6
Error	0.53%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 6.5\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{-15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \end{array} \]

Alternative 7
Error	40.94%
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+147}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-60}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \end{array} \]

Alternative 8
Error	0.99%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 6\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \]

Alternative 9
Error	23.74%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+61}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \end{array} \]

Alternative 10
Error	50.12%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))