Average Error: 0.1 → 0.1
Time: 23.1s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \left(\left(y + 0.5\right) \cdot \frac{1}{3}\right) \cdot \log y\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \left(\left(y + 0.5\right) \cdot \frac{1}{3}\right) \cdot \log y\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r371755 = x;
        double r371756 = y;
        double r371757 = 0.5;
        double r371758 = r371756 + r371757;
        double r371759 = log(r371756);
        double r371760 = r371758 * r371759;
        double r371761 = r371755 - r371760;
        double r371762 = r371761 + r371756;
        double r371763 = z;
        double r371764 = r371762 - r371763;
        return r371764;
}
↓
double f(double x, double y, double z) {
        double r371765 = x;
        double r371766 = 2.0;
        double r371767 = y;
        double r371768 = cbrt(r371767);
        double r371769 = log(r371768);
        double r371770 = r371766 * r371769;
        double r371771 = 0.5;
        double r371772 = r371767 + r371771;
        double r371773 = r371770 * r371772;
        double r371774 = 0.3333333333333333;
        double r371775 = r371772 * r371774;
        double r371776 = log(r371767);
        double r371777 = r371775 * r371776;
        double r371778 = r371773 + r371777;
        double r371779 = r371765 - r371778;
        double r371780 = r371779 + r371767;
        double r371781 = z;
        double r371782 = r371780 - r371781;
        return r371782;
}

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

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. Using strategy rm

  8. Applied pow1/30.2

    \[\leadsto \left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \left(y + 0.5\right) \cdot \log \color{blue}{\left({y}^{\frac{1}{3}}\right)}\right)\right) + y\right) - z\]

  9. Applied log-pow0.1

    \[\leadsto \left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \left(y + 0.5\right) \cdot \color{blue}{\left(\frac{1}{3} \cdot \log y\right)}\right)\right) + y\right) - z\]

  10. Applied associate-*r*0.1

    \[\leadsto \left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \color{blue}{\left(\left(y + 0.5\right) \cdot \frac{1}{3}\right) \cdot \log y}\right)\right) + y\right) - z\]

  11. Final simplification0.1

    \[\leadsto \left(\left(x - \left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right) + \left(\left(y + 0.5\right) \cdot \frac{1}{3}\right) \cdot \log y\right)\right) + y\right) - z\]

Reproduce

herbie shell --seed 2020045 
(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))