Average Error: 0.1 → 0.2
Time: 5.9s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r359767 = x;
        double r359768 = y;
        double r359769 = 0.5;
        double r359770 = r359768 + r359769;
        double r359771 = log(r359768);
        double r359772 = r359770 * r359771;
        double r359773 = r359767 - r359772;
        double r359774 = r359773 + r359768;
        double r359775 = z;
        double r359776 = r359774 - r359775;
        return r359776;
}
↓
double f(double x, double y, double z) {
        double r359777 = x;
        double r359778 = y;
        double r359779 = cbrt(r359778);
        double r359780 = r359779 * r359779;
        double r359781 = log(r359780);
        double r359782 = 0.5;
        double r359783 = r359778 + r359782;
        double r359784 = r359781 * r359783;
        double r359785 = r359777 - r359784;
        double r359786 = 1.0;
        double r359787 = 0.3333333333333333;
        double r359788 = pow(r359778, r359787);
        double r359789 = r359786 * r359788;
        double r359790 = log(r359789);
        double r359791 = r359783 * r359790;
        double r359792 = r359785 - r359791;
        double r359793 = r359792 + r359778;
        double r359794 = z;
        double r359795 = r359793 - r359794;
        return r359795;
}

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

Original0.1
Target0.1
Herbie0.2
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)}\right) + y\right) - z\]

  4. Applied log-prod0.2

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)}\right) + y\right) - z\]

  5. Applied distribute-lft-in0.2

    \[\leadsto \left(\left(x - \color{blue}{\left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right)}\right) + y\right) - z\]

  6. Applied associate--r+0.2

    \[\leadsto \left(\color{blue}{\left(\left(x - \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) - \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right)} + y\right) - z\]

  7. Simplified0.2

    \[\leadsto \left(\left(\color{blue}{\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right)} - \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right) + y\right) - z\]
  8. Using strategy rm

  9. Applied *-un-lft-identity0.2

    \[\leadsto \left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{\color{blue}{1 \cdot y}}\right)\right) + y\right) - z\]

  10. Applied cbrt-prod0.2

    \[\leadsto \left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{y}\right)}\right) + y\right) - z\]

  11. Simplified0.2

    \[\leadsto \left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(\color{blue}{1} \cdot \sqrt[3]{y}\right)\right) + y\right) - z\]

  12. Simplified0.2

    \[\leadsto \left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(1 \cdot \color{blue}{{y}^{\frac{1}{3}}}\right)\right) + y\right) - z\]

  13. Final simplification0.2

    \[\leadsto \left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + y\right) - z\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))