Average Error: 8.0 → 4.9
Time: 8.8s
Precision: 64
\[x0 = 1.855 \land x1 = 0.000209 \lor x0 = 2.985 \land x1 = 0.0186\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\log \left(e^{\frac{x0 \cdot x0}{\left(1 - x1\right) \cdot \left(1 - x1\right)} - x0 \cdot x0}\right)}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\log \left(e^{\frac{x0 \cdot x0}{\left(1 - x1\right) \cdot \left(1 - x1\right)} - x0 \cdot x0}\right)}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}
double f(double x0, double x1) {
        double r6517847 = x0;
        double r6517848 = 1.0;
        double r6517849 = x1;
        double r6517850 = r6517848 - r6517849;
        double r6517851 = r6517847 / r6517850;
        double r6517852 = r6517851 - r6517847;
        return r6517852;
}
↓
double f(double x0, double x1) {
        double r6517853 = x0;
        double r6517854 = r6517853 * r6517853;
        double r6517855 = 1.0;
        double r6517856 = x1;
        double r6517857 = r6517855 - r6517856;
        double r6517858 = r6517857 * r6517857;
        double r6517859 = r6517854 / r6517858;
        double r6517860 = r6517859 - r6517854;
        double r6517861 = exp(r6517860);
        double r6517862 = log(r6517861);
        double r6517863 = r6517853 / r6517857;
        double r6517864 = r6517853 + r6517863;
        double r6517865 = cbrt(r6517864);
        double r6517866 = r6517865 * r6517865;
        double r6517867 = r6517866 * r6517865;
        double r6517868 = r6517862 / r6517867;
        return r6517868;
}

Error

Bits error versus x0

Bits error versus x1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.0
Target0.2
Herbie4.9
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 8.0

    \[\frac{x0}{1 - x1} - x0\]
  2. Using strategy rm

  3. Applied flip--7.4

    \[\leadsto \color{blue}{\frac{\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}}\]
  4. Using strategy rm

  5. Applied div-inv5.7

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \color{blue}{\left(x0 \cdot \frac{1}{1 - x1}\right)} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt5.7

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0}{\color{blue}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}}\]
  8. Using strategy rm

  9. Applied add-log-exp5.7

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - \color{blue}{\log \left(e^{x0 \cdot x0}\right)}}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]

  10. Applied add-log-exp5.7

    \[\leadsto \frac{\color{blue}{\log \left(e^{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right)}\right)} - \log \left(e^{x0 \cdot x0}\right)}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]

  11. Applied diff-log5.6

    \[\leadsto \frac{\color{blue}{\log \left(\frac{e^{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right)}}{e^{x0 \cdot x0}}\right)}}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]

  12. Simplified4.9

    \[\leadsto \frac{\log \color{blue}{\left(e^{\frac{x0 \cdot x0}{\left(1 - x1\right) \cdot \left(1 - x1\right)} - x0 \cdot x0}\right)}}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]

  13. Final simplification4.9

    \[\leadsto \frac{\log \left(e^{\frac{x0 \cdot x0}{\left(1 - x1\right) \cdot \left(1 - x1\right)} - x0 \cdot x0}\right)}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :pre (or (and (== x0 1.855) (== x1 0.000209)) (and (== x0 2.985) (== x1 0.0186)))

  :herbie-target
  (/ (* x0 x1) (- 1 x1))

  (- (/ x0 (- 1 x1)) x0))