Average Error: 7.9 → 5.9
Time: 10.9s
Precision: 64
\[x0 = 1.855 \land x1 = 0.000209 \lor x0 = 2.985 \land x1 = 0.0186\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\log \left(\sqrt{e^{\frac{\left(\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1}\right) \cdot x0}{1 - x1} - x0 \cdot \left(x0 \cdot x0\right)}}\right) + \log \left(\sqrt{e^{\frac{\left(\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1}\right) \cdot x0}{1 - x1} - x0 \cdot \left(x0 \cdot x0\right)}}\right)}{\left(\frac{x0}{1 - x1} \cdot x0 + x0 \cdot x0\right) + \frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\log \left(\sqrt{e^{\frac{\left(\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1}\right) \cdot x0}{1 - x1} - x0 \cdot \left(x0 \cdot x0\right)}}\right) + \log \left(\sqrt{e^{\frac{\left(\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1}\right) \cdot x0}{1 - x1} - x0 \cdot \left(x0 \cdot x0\right)}}\right)}{\left(\frac{x0}{1 - x1} \cdot x0 + x0 \cdot x0\right) + \frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1}}
double f(double x0, double x1) {
        double r3596465 = x0;
        double r3596466 = 1.0;
        double r3596467 = x1;
        double r3596468 = r3596466 - r3596467;
        double r3596469 = r3596465 / r3596468;
        double r3596470 = r3596469 - r3596465;
        return r3596470;
}
↓
double f(double x0, double x1) {
        double r3596471 = x0;
        double r3596472 = 1.0;
        double r3596473 = x1;
        double r3596474 = r3596472 - r3596473;
        double r3596475 = r3596471 / r3596474;
        double r3596476 = r3596475 * r3596475;
        double r3596477 = r3596476 * r3596471;
        double r3596478 = r3596477 / r3596474;
        double r3596479 = r3596471 * r3596471;
        double r3596480 = r3596471 * r3596479;
        double r3596481 = r3596478 - r3596480;
        double r3596482 = exp(r3596481);
        double r3596483 = sqrt(r3596482);
        double r3596484 = log(r3596483);
        double r3596485 = r3596484 + r3596484;
        double r3596486 = r3596475 * r3596471;
        double r3596487 = r3596486 + r3596479;
        double r3596488 = r3596487 + r3596476;
        double r3596489 = r3596485 / r3596488;
        return r3596489;
}

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
Herbie5.9
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 7.9

    \[\frac{x0}{1 - x1} - x0\]
  2. Using strategy rm

  3. Applied flip3--7.7

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

  4. Simplified7.3

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

  6. Applied associate-*l/6.1

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

  8. Applied add-log-exp6.0

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

  10. Applied add-sqr-sqrt6.1

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

  11. Applied log-prod5.9

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

  12. Final simplification5.9

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

Reproduce

herbie shell --seed 2019152 
(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))