Average Error: 7.8 → 5.7
Time: 3.2s
Precision: 64
\[x0 = 1.854999999999999982236431605997495353222 \land x1 = 2.090000000000000115064208161541614572343 \cdot 10^{-4} \lor x0 = 2.984999999999999875655021241982467472553 \land x1 = 0.01859999999999999847899445626353553961962\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{e^{\log \left(\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0\right)}}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{e^{\log \left(\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0\right)}}{\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 r181064 = x0;
        double r181065 = 1.0;
        double r181066 = x1;
        double r181067 = r181065 - r181066;
        double r181068 = r181064 / r181067;
        double r181069 = r181068 - r181064;
        return r181069;
}
↓
double f(double x0, double x1) {
        double r181070 = x0;
        double r181071 = 1.0;
        double r181072 = x1;
        double r181073 = r181071 - r181072;
        double r181074 = r181070 / r181073;
        double r181075 = 1.0;
        double r181076 = r181075 / r181073;
        double r181077 = r181070 * r181076;
        double r181078 = r181074 * r181077;
        double r181079 = r181070 * r181070;
        double r181080 = r181078 - r181079;
        double r181081 = log(r181080);
        double r181082 = exp(r181081);
        double r181083 = r181074 + r181070;
        double r181084 = cbrt(r181083);
        double r181085 = r181084 * r181084;
        double r181086 = r181085 * r181084;
        double r181087 = r181082 / r181086;
        return r181087;
}

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

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-cbrt5.7

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

  9. Applied add-exp-log5.7

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

  10. Final simplification5.7

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :precision binary64
  :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))