Average Error: 0.2 → 0.2
Time: 23.5s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \sqrt[3]{\left(b \cdot b\right) \cdot 4} \cdot \left(\sqrt[3]{\left(b \cdot b\right) \cdot 4} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot 4}\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \sqrt[3]{\left(b \cdot b\right) \cdot 4} \cdot \left(\sqrt[3]{\left(b \cdot b\right) \cdot 4} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot 4}\right)\right) - 1
double f(double a, double b) {
        double r8795441 = a;
        double r8795442 = r8795441 * r8795441;
        double r8795443 = b;
        double r8795444 = r8795443 * r8795443;
        double r8795445 = r8795442 + r8795444;
        double r8795446 = 2.0;
        double r8795447 = pow(r8795445, r8795446);
        double r8795448 = 4.0;
        double r8795449 = r8795448 * r8795444;
        double r8795450 = r8795447 + r8795449;
        double r8795451 = 1.0;
        double r8795452 = r8795450 - r8795451;
        return r8795452;
}
↓
double f(double a, double b) {
        double r8795453 = a;
        double r8795454 = r8795453 * r8795453;
        double r8795455 = b;
        double r8795456 = r8795455 * r8795455;
        double r8795457 = r8795454 + r8795456;
        double r8795458 = 2.0;
        double r8795459 = pow(r8795457, r8795458);
        double r8795460 = 4.0;
        double r8795461 = r8795456 * r8795460;
        double r8795462 = cbrt(r8795461);
        double r8795463 = r8795462 * r8795462;
        double r8795464 = r8795462 * r8795463;
        double r8795465 = r8795459 + r8795464;
        double r8795466 = 1.0;
        double r8795467 = r8795465 - r8795466;
        return r8795467;
}

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-cbrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))