Average Error: 7.9 → 5.7
Time: 3.2s
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 r156682 = x0;
        double r156683 = 1.0;
        double r156684 = x1;
        double r156685 = r156683 - r156684;
        double r156686 = r156682 / r156685;
        double r156687 = r156686 - r156682;
        return r156687;
}
↓
double f(double x0, double x1) {
        double r156688 = x0;
        double r156689 = 1.0;
        double r156690 = x1;
        double r156691 = r156689 - r156690;
        double r156692 = r156688 / r156691;
        double r156693 = sqrt(r156691);
        double r156694 = r156688 / r156693;
        double r156695 = r156694 / r156693;
        double r156696 = r156692 * r156695;
        double r156697 = r156688 * r156688;
        double r156698 = r156696 - r156697;
        double r156699 = r156692 + r156688;
        double r156700 = cbrt(r156699);
        double r156701 = r156700 * r156700;
        double r156702 = r156701 * r156700;
        double r156703 = r156698 / r156702;
        return r156703;
}

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
Target0.2
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 2020049 
(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))