Average Error: 7.9 → 4.7
Time: 17.6s
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 r18896383 = x0;
        double r18896384 = 1.0;
        double r18896385 = x1;
        double r18896386 = r18896384 - r18896385;
        double r18896387 = r18896383 / r18896386;
        double r18896388 = r18896387 - r18896383;
        return r18896388;
}
↓
double f(double x0, double x1) {
        double r18896389 = 1.0;
        double r18896390 = x1;
        double r18896391 = r18896389 - r18896390;
        double r18896392 = r18896389 / r18896391;
        double r18896393 = x0;
        double r18896394 = r18896392 * r18896393;
        double r18896395 = r18896393 / r18896391;
        double r18896396 = r18896394 * r18896395;
        double r18896397 = r18896393 * r18896393;
        double r18896398 = r18896396 - r18896397;
        double r18896399 = exp(r18896398);
        double r18896400 = log(r18896399);
        double r18896401 = r18896393 + r18896395;
        double r18896402 = r18896400 / r18896401;
        return r18896402;
}

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 2019104 
(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))