Average Error: 5.9 → 6.0
Time: 32.4s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]
↓
\[\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(\left(0.91893853320467 + \left(\left(\sqrt{x} - \sqrt{0.5}\right) \cdot \left(\left(\sqrt{x} + \sqrt{0.5}\right) \cdot \log \left(\sqrt{x}\right)\right) - x\right)\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right)\right)\]
\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}
↓
\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(\left(0.91893853320467 + \left(\left(\sqrt{x} - \sqrt{0.5}\right) \cdot \left(\left(\sqrt{x} + \sqrt{0.5}\right) \cdot \log \left(\sqrt{x}\right)\right) - x\right)\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right)\right)
double f(double x, double y, double z) {
        double r21787839 = x;
        double r21787840 = 0.5;
        double r21787841 = r21787839 - r21787840;
        double r21787842 = log(r21787839);
        double r21787843 = r21787841 * r21787842;
        double r21787844 = r21787843 - r21787839;
        double r21787845 = 0.91893853320467;
        double r21787846 = r21787844 + r21787845;
        double r21787847 = y;
        double r21787848 = 0.0007936500793651;
        double r21787849 = r21787847 + r21787848;
        double r21787850 = z;
        double r21787851 = r21787849 * r21787850;
        double r21787852 = 0.0027777777777778;
        double r21787853 = r21787851 - r21787852;
        double r21787854 = r21787853 * r21787850;
        double r21787855 = 0.083333333333333;
        double r21787856 = r21787854 + r21787855;
        double r21787857 = r21787856 / r21787839;
        double r21787858 = r21787846 + r21787857;
        return r21787858;
}
↓
double f(double x, double y, double z) {
        double r21787859 = 0.083333333333333;
        double r21787860 = z;
        double r21787861 = y;
        double r21787862 = 0.0007936500793651;
        double r21787863 = r21787861 + r21787862;
        double r21787864 = r21787860 * r21787863;
        double r21787865 = 0.0027777777777778;
        double r21787866 = r21787864 - r21787865;
        double r21787867 = r21787860 * r21787866;
        double r21787868 = r21787859 + r21787867;
        double r21787869 = x;
        double r21787870 = r21787868 / r21787869;
        double r21787871 = 0.91893853320467;
        double r21787872 = sqrt(r21787869);
        double r21787873 = 0.5;
        double r21787874 = sqrt(r21787873);
        double r21787875 = r21787872 - r21787874;
        double r21787876 = r21787872 + r21787874;
        double r21787877 = log(r21787872);
        double r21787878 = r21787876 * r21787877;
        double r21787879 = r21787875 * r21787878;
        double r21787880 = r21787879 - r21787869;
        double r21787881 = r21787871 + r21787880;
        double r21787882 = r21787869 - r21787873;
        double r21787883 = r21787882 * r21787877;
        double r21787884 = r21787881 + r21787883;
        double r21787885 = r21787870 + r21787884;
        return r21787885;
}

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
Target1.1
Herbie6.0
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)\]

Derivation

  1. Initial program 5.9

    \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt5.9

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  4. Applied log-prod5.9

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt{x}\right) + \log \left(\sqrt{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  5. Applied distribute-rgt-in5.9

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right)\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  6. Applied associate--l+5.9

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  7. Applied associate-+l+5.9

    \[\leadsto \color{blue}{\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \left(\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt5.9

    \[\leadsto \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \left(\left(\log \left(\sqrt{x}\right) \cdot \left(x - \color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}\right) - x\right) + 0.91893853320467\right)\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  10. Applied add-sqr-sqrt6.0

    \[\leadsto \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \left(\left(\log \left(\sqrt{x}\right) \cdot \left(\color{blue}{\sqrt{x} \cdot \sqrt{x}} - \sqrt{0.5} \cdot \sqrt{0.5}\right) - x\right) + 0.91893853320467\right)\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  11. Applied difference-of-squares6.0

    \[\leadsto \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \left(\left(\log \left(\sqrt{x}\right) \cdot \color{blue}{\left(\left(\sqrt{x} + \sqrt{0.5}\right) \cdot \left(\sqrt{x} - \sqrt{0.5}\right)\right)} - x\right) + 0.91893853320467\right)\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  12. Applied associate-*r*6.0

    \[\leadsto \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) + \left(\left(\color{blue}{\left(\log \left(\sqrt{x}\right) \cdot \left(\sqrt{x} + \sqrt{0.5}\right)\right) \cdot \left(\sqrt{x} - \sqrt{0.5}\right)} - x\right) + 0.91893853320467\right)\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

  13. Final simplification6.0

    \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(\left(0.91893853320467 + \left(\left(\sqrt{x} - \sqrt{0.5}\right) \cdot \left(\left(\sqrt{x} + \sqrt{0.5}\right) \cdot \log \left(\sqrt{x}\right)\right) - x\right)\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right)\right)\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"

  :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)))