Average Error: 0.2 → 0.5
Time: 23.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} - 1
double f(double a, double b) {
        double r136474 = a;
        double r136475 = r136474 * r136474;
        double r136476 = b;
        double r136477 = r136476 * r136476;
        double r136478 = r136475 + r136477;
        double r136479 = 2.0;
        double r136480 = pow(r136478, r136479);
        double r136481 = 4.0;
        double r136482 = r136481 * r136477;
        double r136483 = r136480 + r136482;
        double r136484 = 1.0;
        double r136485 = r136483 - r136484;
        return r136485;
}
↓
double f(double a, double b) {
        double r136486 = a;
        double r136487 = r136486 * r136486;
        double r136488 = b;
        double r136489 = r136488 * r136488;
        double r136490 = r136487 + r136489;
        double r136491 = 2.0;
        double r136492 = pow(r136490, r136491);
        double r136493 = 4.0;
        double r136494 = r136493 * r136489;
        double r136495 = r136492 + r136494;
        double r136496 = cbrt(r136495);
        double r136497 = r136496 * r136496;
        double r136498 = r136497 * r136496;
        double r136499 = 1.0;
        double r136500 = r136498 - r136499;
        return r136500;
}

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

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

  3. Applied add-cube-cbrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019306 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))