Average Error: 7.8 → 5.6
Time: 40.6s
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 r25797867 = x0;
        double r25797868 = 1.0;
        double r25797869 = x1;
        double r25797870 = r25797868 - r25797869;
        double r25797871 = r25797867 / r25797870;
        double r25797872 = r25797871 - r25797867;
        return r25797872;
}
↓
double f(double x0, double x1) {
        double r25797873 = 1.0;
        double r25797874 = x1;
        double r25797875 = r25797873 - r25797874;
        double r25797876 = r25797873 / r25797875;
        double r25797877 = x0;
        double r25797878 = r25797876 * r25797877;
        double r25797879 = r25797877 / r25797875;
        double r25797880 = r25797878 * r25797879;
        double r25797881 = r25797877 * r25797877;
        double r25797882 = r25797880 - r25797881;
        double r25797883 = r25797877 + r25797879;
        double r25797884 = cbrt(r25797883);
        double r25797885 = r25797884 * r25797884;
        double r25797886 = r25797884 * r25797885;
        double r25797887 = r25797882 / r25797886;
        return r25797887;
}

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
Target0.3
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-inv5.5

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

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

Reproduce

herbie shell --seed 2019128 
(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))