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 r54390 = 9.0;
        double r54391 = x;
        double r54392 = 4.0;
        double r54393 = pow(r54391, r54392);
        double r54394 = r54390 * r54393;
        double r54395 = y;
        double r54396 = pow(r54395, r54392);
        double r54397 = r54394 - r54396;
        double r54398 = 2.0;
        double r54399 = r54395 * r54395;
        double r54400 = r54398 * r54399;
        double r54401 = r54397 + r54400;
        return r54401;
}
↓
double f(double x, double y) {
        double r54402 = 9.0;
        double r54403 = x;
        double r54404 = 4.0;
        double r54405 = pow(r54403, r54404);
        double r54406 = r54402 * r54405;
        double r54407 = y;
        double r54408 = pow(r54407, r54404);
        double r54409 = r54406 - r54408;
        double r54410 = 3.0;
        double r54411 = pow(r54409, r54410);
        double r54412 = cbrt(r54411);
        double r54413 = 2.0;
        double r54414 = r54407 * r54407;
        double r54415 = r54413 * r54414;
        double r54416 = r54412 + r54415;
        return r54416;
}

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 2020001 
(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))))