Average Error: 7.9 → 5.7
Time: 8.4s
Precision: 64
\[x0 = 1.854999999999999982236431605997495353222 \land x1 = 2.090000000000000115064208161541614572343 \cdot 10^{-4} \lor x0 = 2.984999999999999875655021241982467472553 \land x1 = 0.01859999999999999847899445626353553961962\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\frac{x0}{1 - x1} \cdot \left(\frac{1}{1 - x1} \cdot x0\right) - x0 \cdot x0}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\frac{x0}{1 - x1} \cdot \left(\frac{1}{1 - x1} \cdot x0\right) - x0 \cdot x0}{\left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right) \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}}
double f(double x0, double x1) {
        double r8529454 = x0;
        double r8529455 = 1.0;
        double r8529456 = x1;
        double r8529457 = r8529455 - r8529456;
        double r8529458 = r8529454 / r8529457;
        double r8529459 = r8529458 - r8529454;
        return r8529459;
}
↓
double f(double x0, double x1) {
        double r8529460 = x0;
        double r8529461 = 1.0;
        double r8529462 = x1;
        double r8529463 = r8529461 - r8529462;
        double r8529464 = r8529460 / r8529463;
        double r8529465 = 1.0;
        double r8529466 = r8529465 / r8529463;
        double r8529467 = r8529466 * r8529460;
        double r8529468 = r8529464 * r8529467;
        double r8529469 = r8529460 * r8529460;
        double r8529470 = r8529468 - r8529469;
        double r8529471 = r8529460 + r8529464;
        double r8529472 = cbrt(r8529471);
        double r8529473 = r8529472 * r8529472;
        double r8529474 = r8529473 * r8529472;
        double r8529475 = r8529470 / r8529474;
        return r8529475;
}

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
Herbie5.7
\[\frac{x0 \cdot x1}{1 - x1}\]

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

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

  7. Applied add-cube-cbrt5.7

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

  8. Final simplification5.7

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

Reproduce

herbie shell --seed 2019171 
(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) (- 1.0 x1))

  (- (/ x0 (- 1.0 x1)) x0))