Average Error: 62.0 → 52.0
Time: 10.0s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]
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(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r37935 = 9.0;
        double r37936 = x;
        double r37937 = 4.0;
        double r37938 = pow(r37936, r37937);
        double r37939 = r37935 * r37938;
        double r37940 = y;
        double r37941 = r37940 * r37940;
        double r37942 = 2.0;
        double r37943 = r37941 - r37942;
        double r37944 = r37941 * r37943;
        double r37945 = r37939 - r37944;
        return r37945;
}
↓
double f(double x, double y) {
        double r37946 = 9.0;
        double r37947 = x;
        double r37948 = 4.0;
        double r37949 = pow(r37947, r37948);
        double r37950 = r37946 * r37949;
        double r37951 = y;
        double r37952 = 4.0;
        double r37953 = pow(r37951, r37952);
        double r37954 = r37950 - r37953;
        double r37955 = 3.0;
        double r37956 = pow(r37954, r37955);
        double r37957 = cbrt(r37956);
        double r37958 = 2.0;
        double r37959 = -r37958;
        double r37960 = r37951 * r37951;
        double r37961 = r37959 * r37960;
        double r37962 = r37957 - r37961;
        return r37962;
}

Error

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Your Program's Arguments

Results

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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-rgt-in62.0

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

  5. Applied associate--r+52.0

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

  6. Simplified52.0

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

  8. Applied add-cbrt-cube52.0

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

  9. Simplified52.0

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

  10. Final simplification52.0

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

Reproduce

herbie shell --seed 2020042 
(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))))