Average Error: 0.1 → 0.2
Time: 5.6s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right) + y\right) - z\]
\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(\sqrt[3]{y}\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r254759 = x;
        double r254760 = y;
        double r254761 = 0.5;
        double r254762 = r254760 + r254761;
        double r254763 = log(r254760);
        double r254764 = r254762 * r254763;
        double r254765 = r254759 - r254764;
        double r254766 = r254765 + r254760;
        double r254767 = z;
        double r254768 = r254766 - r254767;
        return r254768;
}
↓
double f(double x, double y, double z) {
        double r254769 = x;
        double r254770 = y;
        double r254771 = cbrt(r254770);
        double r254772 = r254771 * r254771;
        double r254773 = log(r254772);
        double r254774 = 0.5;
        double r254775 = r254770 + r254774;
        double r254776 = r254773 * r254775;
        double r254777 = r254769 - r254776;
        double r254778 = log(r254771);
        double r254779 = r254775 * r254778;
        double r254780 = r254777 - r254779;
        double r254781 = r254780 + r254770;
        double r254782 = z;
        double r254783 = r254781 - r254782;
        return r254783;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020021 
(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))