Average Error: 0.2 → 0.2
Time: 20.3s
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 r2262502 = a;
        double r2262503 = r2262502 * r2262502;
        double r2262504 = b;
        double r2262505 = r2262504 * r2262504;
        double r2262506 = r2262503 + r2262505;
        double r2262507 = 2.0;
        double r2262508 = pow(r2262506, r2262507);
        double r2262509 = 4.0;
        double r2262510 = 1.0;
        double r2262511 = r2262510 + r2262502;
        double r2262512 = r2262503 * r2262511;
        double r2262513 = 3.0;
        double r2262514 = r2262513 * r2262502;
        double r2262515 = r2262510 - r2262514;
        double r2262516 = r2262505 * r2262515;
        double r2262517 = r2262512 + r2262516;
        double r2262518 = r2262509 * r2262517;
        double r2262519 = r2262508 + r2262518;
        double r2262520 = r2262519 - r2262510;
        return r2262520;
}
↓
double f(double a, double b) {
        double r2262521 = a;
        double r2262522 = r2262521 * r2262521;
        double r2262523 = 1.0;
        double r2262524 = r2262521 + r2262523;
        double r2262525 = r2262522 * r2262524;
        double r2262526 = b;
        double r2262527 = r2262526 * r2262526;
        double r2262528 = 3.0;
        double r2262529 = r2262528 * r2262521;
        double r2262530 = r2262523 - r2262529;
        double r2262531 = r2262527 * r2262530;
        double r2262532 = r2262525 + r2262531;
        double r2262533 = 4.0;
        double r2262534 = r2262532 * r2262533;
        double r2262535 = cbrt(r2262534);
        double r2262536 = r2262535 * r2262535;
        double r2262537 = r2262536 * r2262535;
        double r2262538 = r2262522 + r2262527;
        double r2262539 = 2.0;
        double r2262540 = pow(r2262538, r2262539);
        double r2262541 = r2262537 + r2262540;
        double r2262542 = r2262541 - r2262523;
        return r2262542;
}

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 2019154 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))