Average Error: 7.8 → 5.6
Time: 8.7s
Precision: 64
\[x0 = 1.854999999999999982236431605997495353222 \land x1 = 2.090000000000000115064208161541614572343 \cdot 10^{-4} \lor x0 = 2.984999999999999875655021241982467472553 \land x1 = 0.01859999999999999847899445626353553961962\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\left(x0 \cdot \frac{1}{1 - x1}\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\left(x0 \cdot \frac{1}{1 - x1}\right) \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 r6475787 = x0;
        double r6475788 = 1.0;
        double r6475789 = x1;
        double r6475790 = r6475788 - r6475789;
        double r6475791 = r6475787 / r6475790;
        double r6475792 = r6475791 - r6475787;
        return r6475792;
}
↓
double f(double x0, double x1) {
        double r6475793 = x0;
        double r6475794 = 1.0;
        double r6475795 = 1.0;
        double r6475796 = x1;
        double r6475797 = r6475795 - r6475796;
        double r6475798 = r6475794 / r6475797;
        double r6475799 = r6475793 * r6475798;
        double r6475800 = r6475793 / r6475797;
        double r6475801 = r6475799 * r6475800;
        double r6475802 = r6475793 * r6475793;
        double r6475803 = r6475801 - r6475802;
        double r6475804 = r6475793 + r6475800;
        double r6475805 = cbrt(r6475804);
        double r6475806 = r6475805 * r6475805;
        double r6475807 = r6475806 * r6475805;
        double r6475808 = r6475803 / r6475807;
        return r6475808;
}

Error

Bits error versus x0

Bits error versus x1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.8
Target0.2
Herbie5.6
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 7.8

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

  3. Applied flip--7.2

    \[\leadsto \color{blue}{\frac{\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}}\]
  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-cbrt5.6

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

  8. Final simplification5.6

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

Reproduce

herbie shell --seed 2019174 
(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))