Average Error: 0.2 → 0.2
Time: 26.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4}\right) \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left(\left(\sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4}\right) \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r7783491 = a;
        double r7783492 = r7783491 * r7783491;
        double r7783493 = b;
        double r7783494 = r7783493 * r7783493;
        double r7783495 = r7783492 + r7783494;
        double r7783496 = 2.0;
        double r7783497 = pow(r7783495, r7783496);
        double r7783498 = 4.0;
        double r7783499 = 1.0;
        double r7783500 = r7783499 + r7783491;
        double r7783501 = r7783492 * r7783500;
        double r7783502 = 3.0;
        double r7783503 = r7783502 * r7783491;
        double r7783504 = r7783499 - r7783503;
        double r7783505 = r7783494 * r7783504;
        double r7783506 = r7783501 + r7783505;
        double r7783507 = r7783498 * r7783506;
        double r7783508 = r7783497 + r7783507;
        double r7783509 = r7783508 - r7783499;
        return r7783509;
}
↓
double f(double a, double b) {
        double r7783510 = a;
        double r7783511 = r7783510 * r7783510;
        double r7783512 = 1.0;
        double r7783513 = r7783510 + r7783512;
        double r7783514 = r7783511 * r7783513;
        double r7783515 = b;
        double r7783516 = r7783515 * r7783515;
        double r7783517 = 3.0;
        double r7783518 = r7783517 * r7783510;
        double r7783519 = r7783512 - r7783518;
        double r7783520 = r7783516 * r7783519;
        double r7783521 = r7783514 + r7783520;
        double r7783522 = 4.0;
        double r7783523 = r7783521 * r7783522;
        double r7783524 = cbrt(r7783523);
        double r7783525 = r7783524 * r7783524;
        double r7783526 = r7783525 * r7783524;
        double r7783527 = r7783511 + r7783516;
        double r7783528 = 2.0;
        double r7783529 = pow(r7783527, r7783528);
        double r7783530 = r7783526 + r7783529;
        double r7783531 = r7783530 - r7783512;
        return r7783531;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + \color{blue}{\left(\sqrt[3]{4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)} \cdot \sqrt[3]{4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)}\right) \cdot \sqrt[3]{4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)}}\right) - 1\]

  4. Final simplification0.2

    \[\leadsto \left(\left(\sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4}\right) \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]

Reproduce

herbie shell --seed 2019172 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))