Average Error: 26.5 → 1.0
Time: 12.2s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r446084 = x;
        double r446085 = 2.0;
        double r446086 = r446084 - r446085;
        double r446087 = 4.16438922228;
        double r446088 = r446084 * r446087;
        double r446089 = 78.6994924154;
        double r446090 = r446088 + r446089;
        double r446091 = r446090 * r446084;
        double r446092 = 137.519416416;
        double r446093 = r446091 + r446092;
        double r446094 = r446093 * r446084;
        double r446095 = y;
        double r446096 = r446094 + r446095;
        double r446097 = r446096 * r446084;
        double r446098 = z;
        double r446099 = r446097 + r446098;
        double r446100 = r446086 * r446099;
        double r446101 = 43.3400022514;
        double r446102 = r446084 + r446101;
        double r446103 = r446102 * r446084;
        double r446104 = 263.505074721;
        double r446105 = r446103 + r446104;
        double r446106 = r446105 * r446084;
        double r446107 = 313.399215894;
        double r446108 = r446106 + r446107;
        double r446109 = r446108 * r446084;
        double r446110 = 47.066876606;
        double r446111 = r446109 + r446110;
        double r446112 = r446100 / r446111;
        return r446112;
}
↓
double f(double x, double y, double z) {
        double r446113 = x;
        double r446114 = -6.759357258045804e+26;
        bool r446115 = r446113 <= r446114;
        double r446116 = 2.3371063637595438e+32;
        bool r446117 = r446113 <= r446116;
        double r446118 = !r446117;
        bool r446119 = r446115 || r446118;
        double r446120 = y;
        double r446121 = 2.0;
        double r446122 = pow(r446113, r446121);
        double r446123 = r446120 / r446122;
        double r446124 = 4.16438922228;
        double r446125 = r446124 * r446113;
        double r446126 = r446123 + r446125;
        double r446127 = 110.1139242984811;
        double r446128 = r446126 - r446127;
        double r446129 = 2.0;
        double r446130 = r446113 - r446129;
        double r446131 = r446113 * r446124;
        double r446132 = 78.6994924154;
        double r446133 = r446131 + r446132;
        double r446134 = r446133 * r446113;
        double r446135 = 137.519416416;
        double r446136 = r446134 + r446135;
        double r446137 = r446136 * r446113;
        double r446138 = r446137 + r446120;
        double r446139 = r446138 * r446113;
        double r446140 = z;
        double r446141 = r446139 + r446140;
        double r446142 = r446130 * r446141;
        double r446143 = 1.0;
        double r446144 = 43.3400022514;
        double r446145 = r446113 + r446144;
        double r446146 = r446145 * r446113;
        double r446147 = 263.505074721;
        double r446148 = r446146 + r446147;
        double r446149 = r446148 * r446113;
        double r446150 = 313.399215894;
        double r446151 = r446149 + r446150;
        double r446152 = r446151 * r446113;
        double r446153 = 47.066876606;
        double r446154 = r446152 + r446153;
        double r446155 = r446143 / r446154;
        double r446156 = r446142 * r446155;
        double r446157 = r446119 ? r446128 : r446156;
        return r446157;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.5
Target0.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -6.759357258045804e+26 or 2.3371063637595438e+32 < x

    1. Initial program 58.3

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    2. Taylor expanded around inf 1.0

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]

    if -6.759357258045804e+26 < x < 2.3371063637595438e+32

    1. Initial program 0.6

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied div-inv0.9

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))