Average Error: 7.9 → 5.7
Time: 3.8s
Precision: 64
\[x0 = 1.854999999999999982236431605997495353222 \land x1 = 2.090000000000000115064208161541614572343 \cdot 10^{-4} \lor x0 = 2.984999999999999875655021241982467472553 \land x1 = 0.01859999999999999847899445626353553961962\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{e^{\log \left(\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0\right)}}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{e^{\log \left(\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}}
double f(double x0, double x1) {
        double r158279 = x0;
        double r158280 = 1.0;
        double r158281 = x1;
        double r158282 = r158280 - r158281;
        double r158283 = r158279 / r158282;
        double r158284 = r158283 - r158279;
        return r158284;
}
↓
double f(double x0, double x1) {
        double r158285 = x0;
        double r158286 = 1.0;
        double r158287 = x1;
        double r158288 = r158286 - r158287;
        double r158289 = r158285 / r158288;
        double r158290 = 1.0;
        double r158291 = r158290 / r158288;
        double r158292 = r158285 * r158291;
        double r158293 = r158289 * r158292;
        double r158294 = r158285 * r158285;
        double r158295 = r158293 - r158294;
        double r158296 = log(r158295);
        double r158297 = exp(r158296);
        double r158298 = r158289 + r158285;
        double r158299 = cbrt(r158298);
        double r158300 = r158299 * r158299;
        double r158301 = r158300 * r158299;
        double r158302 = r158297 / r158301;
        return r158302;
}

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
Herbie5.7
\[\frac{x0 \cdot x1}{1 - x1}\]

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-exp-log5.7

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

  10. Final simplification5.7

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

Reproduce

herbie shell --seed 2019318 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :precision binary64
  :pre (or (and (== x0 1.855) (== x1 2.09000000000000012e-4)) (and (== x0 2.98499999999999988) (== x1 0.018599999999999998)))

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

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