Average Error: 52.0 → 52.0
Time: 2.5s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r66048 = 9.0;
        double r66049 = x;
        double r66050 = 4.0;
        double r66051 = pow(r66049, r66050);
        double r66052 = r66048 * r66051;
        double r66053 = y;
        double r66054 = pow(r66053, r66050);
        double r66055 = r66052 - r66054;
        double r66056 = 2.0;
        double r66057 = r66053 * r66053;
        double r66058 = r66056 * r66057;
        double r66059 = r66055 + r66058;
        return r66059;
}
↓
double f(double x, double y) {
        double r66060 = 9.0;
        double r66061 = x;
        double r66062 = 4.0;
        double r66063 = pow(r66061, r66062);
        double r66064 = r66060 * r66063;
        double r66065 = y;
        double r66066 = pow(r66065, r66062);
        double r66067 = r66064 - r66066;
        double r66068 = 3.0;
        double r66069 = pow(r66067, r66068);
        double r66070 = cbrt(r66069);
        double r66071 = 2.0;
        double r66072 = r66065 * r66065;
        double r66073 = r66071 * r66072;
        double r66074 = r66070 + r66073;
        return r66074;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 52.0

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

  3. Applied add-cbrt-cube52.0

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

  4. Simplified52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))