Average Error: 27.1 → 0.8
Time: 6.6s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.9233272992807447 \cdot 10^{53}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{elif}\;x \le 127999625215081296:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x}\right) \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]
\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 -4.9233272992807447 \cdot 10^{53}:\\
\;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\

\mathbf{elif}\;x \le 127999625215081296:\\
\;\;\;\;\left(x - 2\right) \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(\sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x}\right) \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} + 313.399215894\right) \cdot x + 47.066876606000001}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\end{array}
double f(double x, double y, double z) {
        double r449945 = x;
        double r449946 = 2.0;
        double r449947 = r449945 - r449946;
        double r449948 = 4.16438922228;
        double r449949 = r449945 * r449948;
        double r449950 = 78.6994924154;
        double r449951 = r449949 + r449950;
        double r449952 = r449951 * r449945;
        double r449953 = 137.519416416;
        double r449954 = r449952 + r449953;
        double r449955 = r449954 * r449945;
        double r449956 = y;
        double r449957 = r449955 + r449956;
        double r449958 = r449957 * r449945;
        double r449959 = z;
        double r449960 = r449958 + r449959;
        double r449961 = r449947 * r449960;
        double r449962 = 43.3400022514;
        double r449963 = r449945 + r449962;
        double r449964 = r449963 * r449945;
        double r449965 = 263.505074721;
        double r449966 = r449964 + r449965;
        double r449967 = r449966 * r449945;
        double r449968 = 313.399215894;
        double r449969 = r449967 + r449968;
        double r449970 = r449969 * r449945;
        double r449971 = 47.066876606;
        double r449972 = r449970 + r449971;
        double r449973 = r449961 / r449972;
        return r449973;
}
↓
double f(double x, double y, double z) {
        double r449974 = x;
        double r449975 = -4.923327299280745e+53;
        bool r449976 = r449974 <= r449975;
        double r449977 = 2.0;
        double r449978 = r449974 - r449977;
        double r449979 = y;
        double r449980 = 3.0;
        double r449981 = pow(r449974, r449980);
        double r449982 = r449979 / r449981;
        double r449983 = 4.16438922228;
        double r449984 = r449982 + r449983;
        double r449985 = 101.7851458539211;
        double r449986 = 1.0;
        double r449987 = r449986 / r449974;
        double r449988 = r449985 * r449987;
        double r449989 = r449984 - r449988;
        double r449990 = r449978 * r449989;
        double r449991 = 1.279996252150813e+17;
        bool r449992 = r449974 <= r449991;
        double r449993 = r449974 * r449983;
        double r449994 = 78.6994924154;
        double r449995 = r449993 + r449994;
        double r449996 = r449995 * r449974;
        double r449997 = 137.519416416;
        double r449998 = r449996 + r449997;
        double r449999 = r449998 * r449974;
        double r450000 = r449999 + r449979;
        double r450001 = r450000 * r449974;
        double r450002 = z;
        double r450003 = r450001 + r450002;
        double r450004 = 43.3400022514;
        double r450005 = r449974 + r450004;
        double r450006 = r450005 * r449974;
        double r450007 = 263.505074721;
        double r450008 = r450006 + r450007;
        double r450009 = r450008 * r449974;
        double r450010 = cbrt(r450009);
        double r450011 = r450010 * r450010;
        double r450012 = r450011 * r450010;
        double r450013 = 313.399215894;
        double r450014 = r450012 + r450013;
        double r450015 = r450014 * r449974;
        double r450016 = 47.066876606;
        double r450017 = r450015 + r450016;
        double r450018 = r450003 / r450017;
        double r450019 = r449978 * r450018;
        double r450020 = 2.0;
        double r450021 = pow(r449974, r450020);
        double r450022 = r449979 / r450021;
        double r450023 = r449983 * r449974;
        double r450024 = r450022 + r450023;
        double r450025 = 110.1139242984811;
        double r450026 = r450024 - r450025;
        double r450027 = r449992 ? r450019 : r450026;
        double r450028 = r449976 ? r449990 : r450027;
        return r450028;
}

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

Original27.1
Target0.5
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -4.923327299280745e+53

    1. Initial program 62.7

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

    3. Applied *-un-lft-identity62.7

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

    4. Applied times-frac58.9

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

    5. Simplified58.9

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

    6. Taylor expanded around inf 0.5

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)}\]

    if -4.923327299280745e+53 < x < 1.279996252150813e+17

    1. Initial program 0.9

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

    3. Applied *-un-lft-identity0.9

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    7. Applied add-cube-cbrt0.5

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x}\right) \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x}} + 313.399215894\right) \cdot x + 47.066876606000001}\]

    if 1.279996252150813e+17 < x

    1. Initial program 55.2

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

    2. Taylor expanded around inf 1.6

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.9233272992807447 \cdot 10^{53}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{elif}\;x \le 127999625215081296:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x}\right) \cdot \sqrt[3]{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x} + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 
(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)))