Average Error: 7.9 → 4.6
Time: 30.2s
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 r3909724 = x0;
        double r3909725 = 1.0;
        double r3909726 = x1;
        double r3909727 = r3909725 - r3909726;
        double r3909728 = r3909724 / r3909727;
        double r3909729 = r3909728 - r3909724;
        return r3909729;
}
↓
double f(double x0, double x1) {
        double r3909730 = 1.0;
        double r3909731 = x1;
        double r3909732 = r3909730 - r3909731;
        double r3909733 = r3909730 / r3909732;
        double r3909734 = x0;
        double r3909735 = r3909733 * r3909734;
        double r3909736 = r3909734 / r3909732;
        double r3909737 = r3909735 * r3909736;
        double r3909738 = r3909734 * r3909734;
        double r3909739 = r3909737 - r3909738;
        double r3909740 = exp(r3909739);
        double r3909741 = log(r3909740);
        double r3909742 = r3909734 + r3909736;
        double r3909743 = r3909741 / r3909742;
        return r3909743;
}

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
Target0.2
Herbie4.6
\[\frac{x0 \cdot x1}{1 - x1}\]

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

    \[\leadsto \frac{\color{blue}{\left(x0 \cdot \frac{1}{1 - x1}\right)} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
  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 2019124 
(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))