Average Error: 7.9 → 5.6
Time: 11.7s
Precision: 64
\[x0 = 1.855 \land x1 = 2.09000000000000012 \cdot 10^{-4} \lor x0 = 2.98499999999999988 \land x1 = 0.018599999999999998\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\frac{\frac{x0}{\sqrt{1 - x1}}}{\sqrt{1 - x1}} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\frac{\frac{x0}{\sqrt{1 - x1}}}{\sqrt{1 - x1}} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}
double f(double x0, double x1) {
        double r128044 = x0;
        double r128045 = 1.0;
        double r128046 = x1;
        double r128047 = r128045 - r128046;
        double r128048 = r128044 / r128047;
        double r128049 = r128048 - r128044;
        return r128049;
}
↓
double f(double x0, double x1) {
        double r128050 = x0;
        double r128051 = 1.0;
        double r128052 = x1;
        double r128053 = r128051 - r128052;
        double r128054 = sqrt(r128053);
        double r128055 = r128050 / r128054;
        double r128056 = r128055 / r128054;
        double r128057 = r128050 / r128053;
        double r128058 = r128056 * r128057;
        double r128059 = r128050 * r128050;
        double r128060 = r128058 - r128059;
        double r128061 = r128050 + r128057;
        double r128062 = cbrt(r128061);
        double r128063 = r128062 * r128062;
        double r128064 = r128063 * r128062;
        double r128065 = r128060 / r128064;
        return r128065;
}

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
Herbie5.6
\[\frac{x0 \cdot x1}{1 - x1}\]

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. Simplified7.3

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

  6. Applied add-sqr-sqrt5.6

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

  7. Applied associate-/r*5.6

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

  9. Applied add-cube-cbrt5.6

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

  10. Final simplification5.6

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

Reproduce

herbie shell --seed 2019199 
(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) (- 1.0 x1))

  (- (/ x0 (- 1.0 x1)) x0))