Average Error: 0.2 → 0.2
Time: 7.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right)\right) - 1\]
\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(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right)\right) - 1
double f(double a, double b) {
        double r341772 = a;
        double r341773 = r341772 * r341772;
        double r341774 = b;
        double r341775 = r341774 * r341774;
        double r341776 = r341773 + r341775;
        double r341777 = 2.0;
        double r341778 = pow(r341776, r341777);
        double r341779 = 4.0;
        double r341780 = 1.0;
        double r341781 = r341780 + r341772;
        double r341782 = r341773 * r341781;
        double r341783 = 3.0;
        double r341784 = r341783 * r341772;
        double r341785 = r341780 - r341784;
        double r341786 = r341775 * r341785;
        double r341787 = r341782 + r341786;
        double r341788 = r341779 * r341787;
        double r341789 = r341778 + r341788;
        double r341790 = r341789 - r341780;
        return r341790;
}
↓
double f(double a, double b) {
        double r341791 = a;
        double r341792 = r341791 * r341791;
        double r341793 = b;
        double r341794 = r341793 * r341793;
        double r341795 = r341792 + r341794;
        double r341796 = 2.0;
        double r341797 = pow(r341795, r341796);
        double r341798 = 4.0;
        double r341799 = 1.0;
        double r341800 = r341799 + r341791;
        double r341801 = r341792 * r341800;
        double r341802 = 3.0;
        double r341803 = r341802 * r341791;
        double r341804 = r341799 - r341803;
        double r341805 = r341794 * r341804;
        double r341806 = cbrt(r341805);
        double r341807 = r341806 * r341806;
        double r341808 = r341807 * r341806;
        double r341809 = r341801 + r341808;
        double r341810 = r341798 * r341809;
        double r341811 = r341797 + r341810;
        double r341812 = r341811 - r341799;
        return r341812;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))