Average Error: 7.8 → 4.6
Time: 20.7s
Precision: 64
\[x0 = 1.855 \land x1 = 0.000209 \lor x0 = 2.985 \land x1 = 0.0186\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\log \left(e^{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}\right)}{x0 + \frac{x0}{1 - x1}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\log \left(e^{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}\right)}{x0 + \frac{x0}{1 - x1}}
double f(double x0, double x1) {
        double r62011677 = x0;
        double r62011678 = 1.0;
        double r62011679 = x1;
        double r62011680 = r62011678 - r62011679;
        double r62011681 = r62011677 / r62011680;
        double r62011682 = r62011681 - r62011677;
        return r62011682;
}
↓
double f(double x0, double x1) {
        double r62011683 = 1.0;
        double r62011684 = x1;
        double r62011685 = r62011683 - r62011684;
        double r62011686 = r62011683 / r62011685;
        double r62011687 = x0;
        double r62011688 = r62011686 * r62011687;
        double r62011689 = r62011687 / r62011685;
        double r62011690 = r62011688 * r62011689;
        double r62011691 = r62011687 * r62011687;
        double r62011692 = r62011690 - r62011691;
        double r62011693 = exp(r62011692);
        double r62011694 = log(r62011693);
        double r62011695 = r62011687 + r62011689;
        double r62011696 = r62011694 / r62011695;
        return r62011696;
}

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
Herbie4.6
\[\frac{x0 \cdot x1}{1 - x1}\]

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

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

  7. Applied add-log-exp4.6

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

  8. Final simplification4.6

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

Reproduce

herbie shell --seed 2019120 
(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))