Average Error: 0.1 → 0.2
Time: 19.3s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(3 \cdot y + 1.5\right) \cdot \left(\frac{1}{3} \cdot \log y\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(3 \cdot y + 1.5\right) \cdot \left(\frac{1}{3} \cdot \log y\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r321769 = x;
        double r321770 = y;
        double r321771 = 0.5;
        double r321772 = r321770 + r321771;
        double r321773 = log(r321770);
        double r321774 = r321772 * r321773;
        double r321775 = r321769 - r321774;
        double r321776 = r321775 + r321770;
        double r321777 = z;
        double r321778 = r321776 - r321777;
        return r321778;
}
↓
double f(double x, double y, double z) {
        double r321779 = x;
        double r321780 = 3.0;
        double r321781 = y;
        double r321782 = r321780 * r321781;
        double r321783 = 1.5;
        double r321784 = r321782 + r321783;
        double r321785 = 0.3333333333333333;
        double r321786 = log(r321781);
        double r321787 = r321785 * r321786;
        double r321788 = r321784 * r321787;
        double r321789 = r321779 - r321788;
        double r321790 = r321789 + r321781;
        double r321791 = z;
        double r321792 = r321790 - r321791;
        return r321792;
}

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. Simplified0.2

    \[\leadsto \left(\left(x - \left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right)} + \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right)\right) + y\right) - z\]

  7. Simplified0.2

    \[\leadsto \left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \color{blue}{\log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)}\right)\right) + y\right) - z\]

  8. Taylor expanded around inf 0.2

    \[\leadsto \left(\left(x - \color{blue}{\left(3 \cdot \left(y \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) + 1.5 \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right)}\right) + y\right) - z\]

  9. Simplified0.2

    \[\leadsto \left(\left(x - \color{blue}{\left(\frac{-1}{3} \cdot \left(-\log y\right)\right) \cdot \left(3 \cdot y + 1.5\right)}\right) + y\right) - z\]

  10. Final simplification0.2

    \[\leadsto \left(\left(x - \left(3 \cdot y + 1.5\right) \cdot \left(\frac{1}{3} \cdot \log y\right)\right) + y\right) - z\]

Reproduce

herbie shell --seed 2019235 
(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))