Average Error: 0.2 → 0.2
Time: 23.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(\sqrt[3]{\left(a + 3\right) \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{\left(a + 3\right) \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{\left(a + 3\right) \cdot \left(b \cdot b\right)}\right) \cdot 4\right) - 1\]
\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(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(\sqrt[3]{\left(a + 3\right) \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{\left(a + 3\right) \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{\left(a + 3\right) \cdot \left(b \cdot b\right)}\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r9150704 = a;
        double r9150705 = r9150704 * r9150704;
        double r9150706 = b;
        double r9150707 = r9150706 * r9150706;
        double r9150708 = r9150705 + r9150707;
        double r9150709 = 2.0;
        double r9150710 = pow(r9150708, r9150709);
        double r9150711 = 4.0;
        double r9150712 = 1.0;
        double r9150713 = r9150712 - r9150704;
        double r9150714 = r9150705 * r9150713;
        double r9150715 = 3.0;
        double r9150716 = r9150715 + r9150704;
        double r9150717 = r9150707 * r9150716;
        double r9150718 = r9150714 + r9150717;
        double r9150719 = r9150711 * r9150718;
        double r9150720 = r9150710 + r9150719;
        double r9150721 = r9150720 - r9150712;
        return r9150721;
}
↓
double f(double a, double b) {
        double r9150722 = a;
        double r9150723 = r9150722 * r9150722;
        double r9150724 = b;
        double r9150725 = r9150724 * r9150724;
        double r9150726 = r9150723 + r9150725;
        double r9150727 = 2.0;
        double r9150728 = pow(r9150726, r9150727);
        double r9150729 = 1.0;
        double r9150730 = r9150729 - r9150722;
        double r9150731 = r9150723 * r9150730;
        double r9150732 = 3.0;
        double r9150733 = r9150722 + r9150732;
        double r9150734 = r9150733 * r9150725;
        double r9150735 = cbrt(r9150734);
        double r9150736 = r9150735 * r9150735;
        double r9150737 = r9150736 * r9150735;
        double r9150738 = r9150731 + r9150737;
        double r9150739 = 4.0;
        double r9150740 = r9150738 * r9150739;
        double r9150741 = r9150728 + r9150740;
        double r9150742 = r9150741 - r9150729;
        return r9150742;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(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))