Average Error: 7.9 → 4.8
Time: 10.5s
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 r5061253 = x0;
        double r5061254 = 1.0;
        double r5061255 = x1;
        double r5061256 = r5061254 - r5061255;
        double r5061257 = r5061253 / r5061256;
        double r5061258 = r5061257 - r5061253;
        return r5061258;
}
↓
double f(double x0, double x1) {
        double r5061259 = x0;
        double r5061260 = r5061259 * r5061259;
        double r5061261 = 1.0;
        double r5061262 = x1;
        double r5061263 = r5061261 - r5061262;
        double r5061264 = r5061263 * r5061263;
        double r5061265 = r5061260 / r5061264;
        double r5061266 = r5061265 - r5061260;
        double r5061267 = exp(r5061266);
        double r5061268 = log(r5061267);
        double r5061269 = r5061259 / r5061263;
        double r5061270 = r5061259 + r5061269;
        double r5061271 = cbrt(r5061270);
        double r5061272 = r5061271 * r5061271;
        double r5061273 = r5061272 * r5061271;
        double r5061274 = r5061268 / r5061273;
        return r5061274;
}

Error

Bits error versus x0

Bits error versus x1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.9
Target0.3
Herbie4.8
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 7.9

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

  3. Applied flip--7.3

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

  5. Applied div-inv5.6

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \color{blue}{\left(x0 \cdot \frac{1}{1 - x1}\right)} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
  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-exp4.8

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

  10. Simplified4.8

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

  11. Final simplification4.8

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

Reproduce

herbie shell --seed 2019149 
(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))