Average Error: 0.2 → 0.2
Time: 22.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(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
double f(double a, double b) {
        double r81724 = a;
        double r81725 = r81724 * r81724;
        double r81726 = b;
        double r81727 = r81726 * r81726;
        double r81728 = r81725 + r81727;
        double r81729 = 2.0;
        double r81730 = pow(r81728, r81729);
        double r81731 = 4.0;
        double r81732 = 1.0;
        double r81733 = r81732 + r81724;
        double r81734 = r81725 * r81733;
        double r81735 = 3.0;
        double r81736 = r81735 * r81724;
        double r81737 = r81732 - r81736;
        double r81738 = r81727 * r81737;
        double r81739 = r81734 + r81738;
        double r81740 = r81731 * r81739;
        double r81741 = r81730 + r81740;
        double r81742 = r81741 - r81732;
        return r81742;
}
↓
double f(double a, double b) {
        double r81743 = a;
        double r81744 = r81743 * r81743;
        double r81745 = b;
        double r81746 = r81745 * r81745;
        double r81747 = r81744 + r81746;
        double r81748 = 2.0;
        double r81749 = pow(r81747, r81748);
        double r81750 = 4.0;
        double r81751 = 1.0;
        double r81752 = r81751 + r81743;
        double r81753 = r81744 * r81752;
        double r81754 = 3.0;
        double r81755 = r81754 * r81743;
        double r81756 = r81751 - r81755;
        double r81757 = r81746 * r81756;
        double r81758 = r81753 + r81757;
        double r81759 = r81750 * r81758;
        double r81760 = r81749 + r81759;
        double r81761 = r81760 - r81751;
        return r81761;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019208 
(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))