Average Error: 25.1 → 0.7
Time: 17.6s
Precision: 64
\[\frac{\left(x - 2.0\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.2348757811419234 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{x \cdot x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \mathbf{elif}\;x \le 2.0084271042117127 \cdot 10^{+34}:\\ \;\;\;\;\frac{1}{\frac{47.066876606 + \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right) \cdot x}{x \cdot \left(y + \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x\right) + z}} \cdot \left(x - 2.0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \end{array}\]
\frac{\left(x - 2.0\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.2348757811419234 \cdot 10^{+47}:\\
\;\;\;\;\frac{y}{x \cdot x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\

\mathbf{elif}\;x \le 2.0084271042117127 \cdot 10^{+34}:\\
\;\;\;\;\frac{1}{\frac{47.066876606 + \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right) \cdot x}{x \cdot \left(y + \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x\right) + z}} \cdot \left(x - 2.0\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{x \cdot x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\

\end{array}
double f(double x, double y, double z) {
        double r7882087 = x;
        double r7882088 = 2.0;
        double r7882089 = r7882087 - r7882088;
        double r7882090 = 4.16438922228;
        double r7882091 = r7882087 * r7882090;
        double r7882092 = 78.6994924154;
        double r7882093 = r7882091 + r7882092;
        double r7882094 = r7882093 * r7882087;
        double r7882095 = 137.519416416;
        double r7882096 = r7882094 + r7882095;
        double r7882097 = r7882096 * r7882087;
        double r7882098 = y;
        double r7882099 = r7882097 + r7882098;
        double r7882100 = r7882099 * r7882087;
        double r7882101 = z;
        double r7882102 = r7882100 + r7882101;
        double r7882103 = r7882089 * r7882102;
        double r7882104 = 43.3400022514;
        double r7882105 = r7882087 + r7882104;
        double r7882106 = r7882105 * r7882087;
        double r7882107 = 263.505074721;
        double r7882108 = r7882106 + r7882107;
        double r7882109 = r7882108 * r7882087;
        double r7882110 = 313.399215894;
        double r7882111 = r7882109 + r7882110;
        double r7882112 = r7882111 * r7882087;
        double r7882113 = 47.066876606;
        double r7882114 = r7882112 + r7882113;
        double r7882115 = r7882103 / r7882114;
        return r7882115;
}
↓
double f(double x, double y, double z) {
        double r7882116 = x;
        double r7882117 = -1.2348757811419234e+47;
        bool r7882118 = r7882116 <= r7882117;
        double r7882119 = y;
        double r7882120 = r7882116 * r7882116;
        double r7882121 = r7882119 / r7882120;
        double r7882122 = 4.16438922228;
        double r7882123 = r7882116 * r7882122;
        double r7882124 = 110.1139242984811;
        double r7882125 = r7882123 - r7882124;
        double r7882126 = r7882121 + r7882125;
        double r7882127 = 2.0084271042117127e+34;
        bool r7882128 = r7882116 <= r7882127;
        double r7882129 = 1.0;
        double r7882130 = 47.066876606;
        double r7882131 = 313.399215894;
        double r7882132 = 263.505074721;
        double r7882133 = 43.3400022514;
        double r7882134 = r7882133 + r7882116;
        double r7882135 = r7882116 * r7882134;
        double r7882136 = r7882132 + r7882135;
        double r7882137 = r7882116 * r7882136;
        double r7882138 = r7882131 + r7882137;
        double r7882139 = r7882138 * r7882116;
        double r7882140 = r7882130 + r7882139;
        double r7882141 = 78.6994924154;
        double r7882142 = r7882123 + r7882141;
        double r7882143 = r7882142 * r7882116;
        double r7882144 = 137.519416416;
        double r7882145 = r7882143 + r7882144;
        double r7882146 = r7882145 * r7882116;
        double r7882147 = r7882119 + r7882146;
        double r7882148 = r7882116 * r7882147;
        double r7882149 = z;
        double r7882150 = r7882148 + r7882149;
        double r7882151 = r7882140 / r7882150;
        double r7882152 = r7882129 / r7882151;
        double r7882153 = 2.0;
        double r7882154 = r7882116 - r7882153;
        double r7882155 = r7882152 * r7882154;
        double r7882156 = r7882128 ? r7882155 : r7882126;
        double r7882157 = r7882118 ? r7882126 : r7882156;
        return r7882157;
}

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

Original25.1
Target0.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{elif}\;x \lt 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2.0}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.2348757811419234e+47 or 2.0084271042117127e+34 < x

    1. Initial program 58.5

      \[\frac{\left(x - 2.0\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]

    2. Taylor expanded around inf 1.0

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922228 \cdot x\right) - 110.1139242984811}\]

    3. Simplified1.0

      \[\leadsto \color{blue}{\frac{y}{x \cdot x} + \left(4.16438922228 \cdot x - 110.1139242984811\right)}\]

    if -1.2348757811419234e+47 < x < 2.0084271042117127e+34

    1. Initial program 0.7

      \[\frac{\left(x - 2.0\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity0.7

      \[\leadsto \frac{\left(x - 2.0\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606\right)}}\]

    4. Applied times-frac0.3

      \[\leadsto \color{blue}{\frac{x - 2.0}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}}\]

    5. Simplified0.3

      \[\leadsto \color{blue}{\left(x - 2.0\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]
    6. Using strategy rm

    7. Applied clear-num0.5

      \[\leadsto \left(x - 2.0\right) \cdot \color{blue}{\frac{1}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.2348757811419234 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{x \cdot x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \mathbf{elif}\;x \le 2.0084271042117127 \cdot 10^{+34}:\\ \;\;\;\;\frac{1}{\frac{47.066876606 + \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right) \cdot x}{x \cdot \left(y + \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x\right) + z}} \cdot \left(x - 2.0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 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 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))