Average Error: 8.0 → 5.7
Time: 12.1s
Precision: 64
\[x0 = 1.854999999999999982236431605997495353222 \land x1 = 2.090000000000000115064208161541614572343 \cdot 10^{-4} \lor x0 = 2.984999999999999875655021241982467472553 \land x1 = 0.01859999999999999847899445626353553961962\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0}{\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}}
double f(double x0, double x1) {
        double r10614173 = x0;
        double r10614174 = 1.0;
        double r10614175 = x1;
        double r10614176 = r10614174 - r10614175;
        double r10614177 = r10614173 / r10614176;
        double r10614178 = r10614177 - r10614173;
        return r10614178;
}
↓
double f(double x0, double x1) {
        double r10614179 = x0;
        double r10614180 = 1.0;
        double r10614181 = x1;
        double r10614182 = r10614180 - r10614181;
        double r10614183 = r10614179 / r10614182;
        double r10614184 = 1.0;
        double r10614185 = r10614184 / r10614182;
        double r10614186 = r10614179 * r10614185;
        double r10614187 = r10614183 * r10614186;
        double r10614188 = r10614179 * r10614179;
        double r10614189 = r10614187 - r10614188;
        double r10614190 = r10614183 + r10614179;
        double r10614191 = cbrt(r10614190);
        double r10614192 = r10614191 * r10614191;
        double r10614193 = r10614192 * r10614191;
        double r10614194 = r10614189 / r10614193;
        return r10614194;
}

Error

Bits error versus x0

Bits error versus x1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.0
Target0.2
Herbie5.7
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 8.0

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

  3. Applied flip--7.4

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

  5. Applied div-inv5.7

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

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

Reproduce

herbie shell --seed 2019173 
(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))