Average Error: 26.0 → 0.7
Time: 6.5s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.3208084680443081 \cdot 10^{63} \lor \neg \left(x \le 7.097511826692136 \cdot 10^{66}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -1.3208084680443081 \cdot 10^{63} \lor \neg \left(x \le 7.097511826692136 \cdot 10^{66}\right):\\
\;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\

\mathbf{else}:\\
\;\;\;\;\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(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r302909 = x;
        double r302910 = 2.0;
        double r302911 = r302909 - r302910;
        double r302912 = 4.16438922228;
        double r302913 = r302909 * r302912;
        double r302914 = 78.6994924154;
        double r302915 = r302913 + r302914;
        double r302916 = r302915 * r302909;
        double r302917 = 137.519416416;
        double r302918 = r302916 + r302917;
        double r302919 = r302918 * r302909;
        double r302920 = y;
        double r302921 = r302919 + r302920;
        double r302922 = r302921 * r302909;
        double r302923 = z;
        double r302924 = r302922 + r302923;
        double r302925 = r302911 * r302924;
        double r302926 = 43.3400022514;
        double r302927 = r302909 + r302926;
        double r302928 = r302927 * r302909;
        double r302929 = 263.505074721;
        double r302930 = r302928 + r302929;
        double r302931 = r302930 * r302909;
        double r302932 = 313.399215894;
        double r302933 = r302931 + r302932;
        double r302934 = r302933 * r302909;
        double r302935 = 47.066876606;
        double r302936 = r302934 + r302935;
        double r302937 = r302925 / r302936;
        return r302937;
}
↓
double f(double x, double y, double z) {
        double r302938 = x;
        double r302939 = -1.3208084680443081e+63;
        bool r302940 = r302938 <= r302939;
        double r302941 = 7.097511826692136e+66;
        bool r302942 = r302938 <= r302941;
        double r302943 = !r302942;
        bool r302944 = r302940 || r302943;
        double r302945 = 2.0;
        double r302946 = r302938 - r302945;
        double r302947 = y;
        double r302948 = 3.0;
        double r302949 = pow(r302938, r302948);
        double r302950 = r302947 / r302949;
        double r302951 = 4.16438922228;
        double r302952 = r302950 + r302951;
        double r302953 = 101.7851458539211;
        double r302954 = 1.0;
        double r302955 = r302954 / r302938;
        double r302956 = r302953 * r302955;
        double r302957 = r302952 - r302956;
        double r302958 = r302946 * r302957;
        double r302959 = r302938 * r302951;
        double r302960 = 78.6994924154;
        double r302961 = r302959 + r302960;
        double r302962 = r302961 * r302938;
        double r302963 = 137.519416416;
        double r302964 = r302962 + r302963;
        double r302965 = r302964 * r302938;
        double r302966 = r302965 + r302947;
        double r302967 = r302966 * r302938;
        double r302968 = z;
        double r302969 = r302967 + r302968;
        double r302970 = 43.3400022514;
        double r302971 = r302938 + r302970;
        double r302972 = r302971 * r302938;
        double r302973 = 263.505074721;
        double r302974 = r302972 + r302973;
        double r302975 = cbrt(r302974);
        double r302976 = r302975 * r302975;
        double r302977 = r302975 * r302938;
        double r302978 = r302976 * r302977;
        double r302979 = 313.399215894;
        double r302980 = r302978 + r302979;
        double r302981 = r302980 * r302938;
        double r302982 = 47.066876606;
        double r302983 = r302981 + r302982;
        double r302984 = r302969 / r302983;
        double r302985 = r302946 * r302984;
        double r302986 = r302944 ? r302958 : r302985;
        return r302986;
}

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

Original26.0
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.3208084680443081e+63 or 7.097511826692136e+66 < x

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac61.4

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

    5. Simplified61.4

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

    6. Taylor expanded around inf 0.2

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

    if -1.3208084680443081e+63 < x < 7.097511826692136e+66

    1. Initial program 2.3

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

    3. Applied *-un-lft-identity2.3

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

    7. Applied add-cube-cbrt1.0

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

    8. Applied associate-*l*1.0

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.3208084680443081 \cdot 10^{63} \lor \neg \left(x \le 7.097511826692136 \cdot 10^{66}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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)))