Average Error: 0.2 → 0.2
Time: 38.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)}\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left(\left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)}\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}\right) - 1
double f(double a, double b) {
        double r9506484 = a;
        double r9506485 = r9506484 * r9506484;
        double r9506486 = b;
        double r9506487 = r9506486 * r9506486;
        double r9506488 = r9506485 + r9506487;
        double r9506489 = 2.0;
        double r9506490 = pow(r9506488, r9506489);
        double r9506491 = 4.0;
        double r9506492 = 1.0;
        double r9506493 = r9506492 - r9506484;
        double r9506494 = r9506485 * r9506493;
        double r9506495 = 3.0;
        double r9506496 = r9506495 + r9506484;
        double r9506497 = r9506487 * r9506496;
        double r9506498 = r9506494 + r9506497;
        double r9506499 = r9506491 * r9506498;
        double r9506500 = r9506490 + r9506499;
        double r9506501 = r9506500 - r9506492;
        return r9506501;
}
↓
double f(double a, double b) {
        double r9506502 = 1.0;
        double r9506503 = a;
        double r9506504 = r9506502 - r9506503;
        double r9506505 = r9506503 * r9506503;
        double r9506506 = r9506504 * r9506505;
        double r9506507 = cbrt(r9506506);
        double r9506508 = r9506507 * r9506507;
        double r9506509 = r9506507 * r9506508;
        double r9506510 = b;
        double r9506511 = r9506510 * r9506510;
        double r9506512 = 3.0;
        double r9506513 = r9506512 + r9506503;
        double r9506514 = r9506511 * r9506513;
        double r9506515 = r9506509 + r9506514;
        double r9506516 = 4.0;
        double r9506517 = r9506515 * r9506516;
        double r9506518 = r9506511 + r9506505;
        double r9506519 = 2.0;
        double r9506520 = pow(r9506518, r9506519);
        double r9506521 = r9506517 + r9506520;
        double r9506522 = r9506521 - r9506502;
        return r9506522;
}

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

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

  3. Applied add-cube-cbrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))