Average Error: 7.9 → 5.7
Time: 8.2s
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 r3291124 = x0;
        double r3291125 = 1.0;
        double r3291126 = x1;
        double r3291127 = r3291125 - r3291126;
        double r3291128 = r3291124 / r3291127;
        double r3291129 = r3291128 - r3291124;
        return r3291129;
}
↓
double f(double x0, double x1) {
        double r3291130 = 1.0;
        double r3291131 = x1;
        double r3291132 = r3291130 - r3291131;
        double r3291133 = r3291130 / r3291132;
        double r3291134 = x0;
        double r3291135 = r3291133 * r3291134;
        double r3291136 = r3291134 / r3291132;
        double r3291137 = r3291135 * r3291136;
        double r3291138 = r3291134 * r3291134;
        double r3291139 = r3291137 - r3291138;
        double r3291140 = r3291134 + r3291136;
        double r3291141 = cbrt(r3291140);
        double r3291142 = r3291141 * r3291141;
        double r3291143 = r3291141 * r3291142;
        double r3291144 = r3291139 / r3291143;
        return r3291144;
}

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
Herbie5.7
\[\frac{x0 \cdot x1}{1 - x1}\]

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 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-cbrt5.7

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

  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 2019151 
(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))