Average Error: 8.0 → 5.7
Time: 9.3s
Precision: 64
\[x0 = 1.855 \land x1 = 0.000209 \lor x0 = 2.985 \land x1 = 0.0186\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right)}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right)}
double f(double x0, double x1) {
        double r6625698 = x0;
        double r6625699 = 1.0;
        double r6625700 = x1;
        double r6625701 = r6625699 - r6625700;
        double r6625702 = r6625698 / r6625701;
        double r6625703 = r6625702 - r6625698;
        return r6625703;
}
↓
double f(double x0, double x1) {
        double r6625704 = 1.0;
        double r6625705 = x1;
        double r6625706 = r6625704 - r6625705;
        double r6625707 = r6625704 / r6625706;
        double r6625708 = x0;
        double r6625709 = r6625707 * r6625708;
        double r6625710 = r6625708 / r6625706;
        double r6625711 = r6625709 * r6625710;
        double r6625712 = r6625708 * r6625708;
        double r6625713 = r6625711 - r6625712;
        double r6625714 = r6625708 + r6625710;
        double r6625715 = cbrt(r6625714);
        double r6625716 = r6625715 * r6625715;
        double r6625717 = r6625715 * r6625716;
        double r6625718 = r6625713 / r6625717;
        return r6625718;
}

Error

Bits error versus x0

Bits error versus x1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.0
Target0.2
Herbie5.7
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 8.0

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

  3. Applied flip--7.4

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

  5. Applied div-inv5.7

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \color{blue}{\left(x0 \cdot \frac{1}{1 - x1}\right)} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
  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. Final simplification5.7

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

Reproduce

herbie shell --seed 2019135 
(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))