Average Error: 52.0 → 52.0
Time: 6.1s
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 r97365 = 9.0;
        double r97366 = x;
        double r97367 = 4.0;
        double r97368 = pow(r97366, r97367);
        double r97369 = r97365 * r97368;
        double r97370 = y;
        double r97371 = pow(r97370, r97367);
        double r97372 = r97369 - r97371;
        double r97373 = 2.0;
        double r97374 = r97370 * r97370;
        double r97375 = r97373 * r97374;
        double r97376 = r97372 + r97375;
        return r97376;
}
↓
double f(double x, double y) {
        double r97377 = 9.0;
        double r97378 = x;
        double r97379 = 4.0;
        double r97380 = pow(r97378, r97379);
        double r97381 = r97377 * r97380;
        double r97382 = y;
        double r97383 = pow(r97382, r97379);
        double r97384 = r97381 - r97383;
        double r97385 = 3.0;
        double r97386 = pow(r97384, r97385);
        double r97387 = cbrt(r97386);
        double r97388 = 2.0;
        double r97389 = r97382 * r97382;
        double r97390 = r97388 * r97389;
        double r97391 = r97387 + r97390;
        return r97391;
}

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 2020047 
(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))))