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 r65250 = 9.0;
        double r65251 = x;
        double r65252 = 4.0;
        double r65253 = pow(r65251, r65252);
        double r65254 = r65250 * r65253;
        double r65255 = y;
        double r65256 = pow(r65255, r65252);
        double r65257 = r65254 - r65256;
        double r65258 = 2.0;
        double r65259 = r65255 * r65255;
        double r65260 = r65258 * r65259;
        double r65261 = r65257 + r65260;
        return r65261;
}
↓
double f(double x, double y) {
        double r65262 = 9.0;
        double r65263 = x;
        double r65264 = 4.0;
        double r65265 = pow(r65263, r65264);
        double r65266 = r65262 * r65265;
        double r65267 = y;
        double r65268 = pow(r65267, r65264);
        double r65269 = r65266 - r65268;
        double r65270 = 3.0;
        double r65271 = pow(r65269, r65270);
        double r65272 = cbrt(r65271);
        double r65273 = 2.0;
        double r65274 = r65267 * r65267;
        double r65275 = r65273 * r65274;
        double r65276 = r65272 + r65275;
        return r65276;
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019353 +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))))