Average Error: 7.9 → 5.7
Time: 3.0s
Precision: 64
\[x0 = 1.855 \land x1 = 2.09000000000000012 \cdot 10^{-4} \lor x0 = 2.98499999999999988 \land x1 = 0.018599999999999998\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\frac{x0}{1 - x1} \cdot \frac{\frac{x0}{\sqrt{1 - x1}}}{\sqrt{1 - x1}} - x0 \cdot x0}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\frac{x0}{1 - x1} \cdot \frac{\frac{x0}{\sqrt{1 - x1}}}{\sqrt{1 - x1}} - x0 \cdot x0}{\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 r164594 = x0;
        double r164595 = 1.0;
        double r164596 = x1;
        double r164597 = r164595 - r164596;
        double r164598 = r164594 / r164597;
        double r164599 = r164598 - r164594;
        return r164599;
}
↓
double f(double x0, double x1) {
        double r164600 = x0;
        double r164601 = 1.0;
        double r164602 = x1;
        double r164603 = r164601 - r164602;
        double r164604 = r164600 / r164603;
        double r164605 = sqrt(r164603);
        double r164606 = r164600 / r164605;
        double r164607 = r164606 / r164605;
        double r164608 = r164604 * r164607;
        double r164609 = r164600 * r164600;
        double r164610 = r164608 - r164609;
        double r164611 = r164604 + r164600;
        double r164612 = cbrt(r164611);
        double r164613 = r164612 * r164612;
        double r164614 = r164613 * r164612;
        double r164615 = r164610 / r164614;
        return r164615;
}

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 add-sqr-sqrt5.6

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

  6. Applied associate-/r*5.6

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

  8. Applied add-cube-cbrt5.7

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

  9. Final simplification5.7

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :precision binary64
  :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))