Average Error: 7.9 → 4.7
Time: 23.7s
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 r21347389 = x0;
        double r21347390 = 1.0;
        double r21347391 = x1;
        double r21347392 = r21347390 - r21347391;
        double r21347393 = r21347389 / r21347392;
        double r21347394 = r21347393 - r21347389;
        return r21347394;
}
↓
double f(double x0, double x1) {
        double r21347395 = 1.0;
        double r21347396 = x1;
        double r21347397 = r21347395 - r21347396;
        double r21347398 = r21347395 / r21347397;
        double r21347399 = x0;
        double r21347400 = r21347398 * r21347399;
        double r21347401 = r21347399 / r21347397;
        double r21347402 = r21347400 * r21347401;
        double r21347403 = r21347399 * r21347399;
        double r21347404 = r21347402 - r21347403;
        double r21347405 = exp(r21347404);
        double r21347406 = log(r21347405);
        double r21347407 = r21347399 + r21347401;
        double r21347408 = r21347406 / r21347407;
        return r21347408;
}

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
Herbie4.7
\[\frac{x0 \cdot x1}{1 - x1}\]

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-log-exp4.7

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

  8. Final simplification4.7

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

Reproduce

herbie shell --seed 2019112 
(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))