Average Error: 7.9 → 6.4
Time: 7.8s
Precision: 64
\[x0 = 1.854999999999999982236431605997495353222 \land x1 = 2.090000000000000115064208161541614572343 \cdot 10^{-4} \lor x0 = 2.984999999999999875655021241982467472553 \land x1 = 0.01859999999999999847899445626353553961962\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\frac{x0}{1 - x1} \cdot \frac{1}{1 - x1} - x0}{1 + \frac{1}{1 - x1}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\frac{x0}{1 - x1} \cdot \frac{1}{1 - x1} - x0}{1 + \frac{1}{1 - x1}}
double f(double x0, double x1) {
        double r151412 = x0;
        double r151413 = 1.0;
        double r151414 = x1;
        double r151415 = r151413 - r151414;
        double r151416 = r151412 / r151415;
        double r151417 = r151416 - r151412;
        return r151417;
}
↓
double f(double x0, double x1) {
        double r151418 = x0;
        double r151419 = 1.0;
        double r151420 = x1;
        double r151421 = r151419 - r151420;
        double r151422 = r151418 / r151421;
        double r151423 = 1.0;
        double r151424 = r151423 / r151421;
        double r151425 = r151422 * r151424;
        double r151426 = r151425 - r151418;
        double r151427 = r151423 + r151424;
        double r151428 = r151426 / r151427;
        return r151428;
}

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
Herbie6.4
\[\frac{x0 \cdot x1}{1 - x1}\]

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 simplification6.4

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \frac{1}{1 - x1} - x0}{1 + \frac{1}{1 - x1}}\]

Reproduce

herbie shell --seed 2019294 
(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))