Average Error: 5.9 → 6.0
Time: 8.2s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
↓
\[\left(\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}
↓
\left(\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}
double f(double x, double y, double z) {
        double r508915 = x;
        double r508916 = 0.5;
        double r508917 = r508915 - r508916;
        double r508918 = log(r508915);
        double r508919 = r508917 * r508918;
        double r508920 = r508919 - r508915;
        double r508921 = 0.91893853320467;
        double r508922 = r508920 + r508921;
        double r508923 = y;
        double r508924 = 0.0007936500793651;
        double r508925 = r508923 + r508924;
        double r508926 = z;
        double r508927 = r508925 * r508926;
        double r508928 = 0.0027777777777778;
        double r508929 = r508927 - r508928;
        double r508930 = r508929 * r508926;
        double r508931 = 0.083333333333333;
        double r508932 = r508930 + r508931;
        double r508933 = r508932 / r508915;
        double r508934 = r508922 + r508933;
        return r508934;
}
↓
double f(double x, double y, double z) {
        double r508935 = x;
        double r508936 = 0.5;
        double r508937 = r508935 - r508936;
        double r508938 = 2.0;
        double r508939 = cbrt(r508935);
        double r508940 = log(r508939);
        double r508941 = r508938 * r508940;
        double r508942 = sqrt(r508939);
        double r508943 = log(r508942);
        double r508944 = r508941 + r508943;
        double r508945 = r508937 * r508944;
        double r508946 = r508943 * r508937;
        double r508947 = r508945 + r508946;
        double r508948 = r508947 - r508935;
        double r508949 = 0.91893853320467;
        double r508950 = r508948 + r508949;
        double r508951 = y;
        double r508952 = 0.0007936500793651;
        double r508953 = r508951 + r508952;
        double r508954 = z;
        double r508955 = r508953 * r508954;
        double r508956 = 0.0027777777777778;
        double r508957 = r508955 - r508956;
        double r508958 = r508957 * r508954;
        double r508959 = 0.083333333333333;
        double r508960 = r508958 + r508959;
        double r508961 = r508960 / r508935;
        double r508962 = r508950 + r508961;
        return r508962;
}

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

Original5.9
Target1.2
Herbie6.0
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467001 - x\right)\right) + \frac{0.0833333333333329956}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.93650079365100015 \cdot 10^{-4}\right) - 0.0027777777777778\right)\]

Derivation

  1. Initial program 5.9

    \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt5.9

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  4. Applied log-prod6.0

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  5. Applied distribute-lft-in6.0

    \[\leadsto \left(\left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  6. Simplified6.0

    \[\leadsto \left(\left(\left(\color{blue}{\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right)} + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right)\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt5.9

    \[\leadsto \left(\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \left(x - 0.5\right) \cdot \log \color{blue}{\left(\sqrt{\sqrt[3]{x}} \cdot \sqrt{\sqrt[3]{x}}\right)}\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  9. Applied log-prod5.9

    \[\leadsto \left(\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt{\sqrt[3]{x}}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right)}\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  10. Applied distribute-rgt-in5.9

    \[\leadsto \left(\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \color{blue}{\left(\log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right) + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right)}\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  11. Applied associate-+r+6.0

    \[\leadsto \left(\left(\color{blue}{\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right) + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  12. Simplified6.0

    \[\leadsto \left(\left(\left(\color{blue}{\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right)} + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  13. Final simplification6.0

    \[\leadsto \left(\left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt{\sqrt[3]{x}}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))