Average Error: 62.0 → 52.0
Time: 2.9s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)
double f(double x, double y) {
        double r61567 = 9.0;
        double r61568 = x;
        double r61569 = 4.0;
        double r61570 = pow(r61568, r61569);
        double r61571 = r61567 * r61570;
        double r61572 = y;
        double r61573 = r61572 * r61572;
        double r61574 = 2.0;
        double r61575 = r61573 - r61574;
        double r61576 = r61573 * r61575;
        double r61577 = r61571 - r61576;
        return r61577;
}
↓
double f(double x, double y) {
        double r61578 = 9.0;
        double r61579 = x;
        double r61580 = 4.0;
        double r61581 = pow(r61579, r61580);
        double r61582 = r61578 * r61581;
        double r61583 = y;
        double r61584 = 4.0;
        double r61585 = pow(r61583, r61584);
        double r61586 = r61582 - r61585;
        double r61587 = 3.0;
        double r61588 = pow(r61586, r61587);
        double r61589 = cbrt(r61588);
        double r61590 = r61583 * r61583;
        double r61591 = 2.0;
        double r61592 = -r61591;
        double r61593 = r61590 * r61592;
        double r61594 = r61589 - r61593;
        return r61594;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg62.0

    \[\leadsto 9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot y + \left(-2\right)\right)}\]

  4. Applied distribute-lft-in62.0

    \[\leadsto 9 \cdot {x}^{4} - \color{blue}{\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right) + \left(y \cdot y\right) \cdot \left(-2\right)\right)}\]

  5. Applied associate--r+52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) - \left(y \cdot y\right) \cdot \left(-2\right)}\]

  6. Simplified52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)} - \left(y \cdot y\right) \cdot \left(-2\right)\]
  7. Using strategy rm

  8. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  9. Simplified52.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  10. Final simplification52.0

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (- (* 9 (pow x 4)) (* (* y y) (- (* y y) 2))))