Average Error: 7.9 → 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 r7058183 = x0;
        double r7058184 = 1.0;
        double r7058185 = x1;
        double r7058186 = r7058184 - r7058185;
        double r7058187 = r7058183 / r7058186;
        double r7058188 = r7058187 - r7058183;
        return r7058188;
}
↓
double f(double x0, double x1) {
        double r7058189 = 1.0;
        double r7058190 = x1;
        double r7058191 = r7058189 - r7058190;
        double r7058192 = r7058189 / r7058191;
        double r7058193 = x0;
        double r7058194 = r7058192 * r7058193;
        double r7058195 = r7058193 / r7058191;
        double r7058196 = r7058194 * r7058195;
        double r7058197 = r7058193 * r7058193;
        double r7058198 = r7058196 - r7058197;
        double r7058199 = r7058193 + r7058195;
        double r7058200 = cbrt(r7058199);
        double r7058201 = r7058200 * r7058200;
        double r7058202 = r7058200 * r7058201;
        double r7058203 = r7058198 / r7058202;
        return r7058203;
}

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

    \[\leadsto \frac{\color{blue}{\left(x0 \cdot \frac{1}{1 - x1}\right)} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt5.7

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

  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 2019139 
(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))