Average Error: 26.3 → 1.0
Time: 10.6s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -26739016327637995500 \lor \neg \left(x \le 3.6330534504476709 \cdot 10^{40}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(78.6994924154000017 \cdot {x}^{2} + \left(137.51941641600001 \cdot x + 4.16438922227999964 \cdot {x}^{3}\right)\right) + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -26739016327637995500 \lor \neg \left(x \le 3.6330534504476709 \cdot 10^{40}\right):\\
\;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(78.6994924154000017 \cdot {x}^{2} + \left(137.51941641600001 \cdot x + 4.16438922227999964 \cdot {x}^{3}\right)\right) + 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}\\

\end{array}
double f(double x, double y, double z) {
        double r395876 = x;
        double r395877 = 2.0;
        double r395878 = r395876 - r395877;
        double r395879 = 4.16438922228;
        double r395880 = r395876 * r395879;
        double r395881 = 78.6994924154;
        double r395882 = r395880 + r395881;
        double r395883 = r395882 * r395876;
        double r395884 = 137.519416416;
        double r395885 = r395883 + r395884;
        double r395886 = r395885 * r395876;
        double r395887 = y;
        double r395888 = r395886 + r395887;
        double r395889 = r395888 * r395876;
        double r395890 = z;
        double r395891 = r395889 + r395890;
        double r395892 = r395878 * r395891;
        double r395893 = 43.3400022514;
        double r395894 = r395876 + r395893;
        double r395895 = r395894 * r395876;
        double r395896 = 263.505074721;
        double r395897 = r395895 + r395896;
        double r395898 = r395897 * r395876;
        double r395899 = 313.399215894;
        double r395900 = r395898 + r395899;
        double r395901 = r395900 * r395876;
        double r395902 = 47.066876606;
        double r395903 = r395901 + r395902;
        double r395904 = r395892 / r395903;
        return r395904;
}
↓
double f(double x, double y, double z) {
        double r395905 = x;
        double r395906 = -2.6739016327637996e+19;
        bool r395907 = r395905 <= r395906;
        double r395908 = 3.633053450447671e+40;
        bool r395909 = r395905 <= r395908;
        double r395910 = !r395909;
        bool r395911 = r395907 || r395910;
        double r395912 = 2.0;
        double r395913 = r395905 - r395912;
        double r395914 = y;
        double r395915 = 3.0;
        double r395916 = pow(r395905, r395915);
        double r395917 = r395914 / r395916;
        double r395918 = 4.16438922228;
        double r395919 = r395917 + r395918;
        double r395920 = 101.7851458539211;
        double r395921 = 1.0;
        double r395922 = r395921 / r395905;
        double r395923 = r395920 * r395922;
        double r395924 = r395919 - r395923;
        double r395925 = r395913 * r395924;
        double r395926 = 78.6994924154;
        double r395927 = 2.0;
        double r395928 = pow(r395905, r395927);
        double r395929 = r395926 * r395928;
        double r395930 = 137.519416416;
        double r395931 = r395930 * r395905;
        double r395932 = r395918 * r395916;
        double r395933 = r395931 + r395932;
        double r395934 = r395929 + r395933;
        double r395935 = r395934 + r395914;
        double r395936 = r395935 * r395905;
        double r395937 = z;
        double r395938 = r395936 + r395937;
        double r395939 = r395913 * r395938;
        double r395940 = 43.3400022514;
        double r395941 = r395905 + r395940;
        double r395942 = r395941 * r395905;
        double r395943 = 263.505074721;
        double r395944 = r395942 + r395943;
        double r395945 = r395944 * r395905;
        double r395946 = 313.399215894;
        double r395947 = r395945 + r395946;
        double r395948 = r395947 * r395905;
        double r395949 = 47.066876606;
        double r395950 = r395948 + r395949;
        double r395951 = r395939 / r395950;
        double r395952 = r395911 ? r395925 : r395951;
        return r395952;
}

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

Original26.3
Target0.5
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 < -2.6739016327637996e+19 or 3.633053450447671e+40 < 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. Using strategy rm

    3. Applied associate-/l*54.3

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

    5. Applied div-inv54.3

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

    6. Taylor expanded around inf 1.5

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

    if -2.6739016327637996e+19 < x < 3.633053450447671e+40

    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. Taylor expanded around 0 0.6

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

    3. Simplified0.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -26739016327637995500 \lor \neg \left(x \le 3.6330534504476709 \cdot 10^{40}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(78.6994924154000017 \cdot {x}^{2} + \left(137.51941641600001 \cdot x + 4.16438922227999964 \cdot {x}^{3}\right)\right) + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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)))