Average Error: 0.2 → 0.2
Time: 21.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r155681 = a;
        double r155682 = r155681 * r155681;
        double r155683 = b;
        double r155684 = r155683 * r155683;
        double r155685 = r155682 + r155684;
        double r155686 = 2.0;
        double r155687 = pow(r155685, r155686);
        double r155688 = 4.0;
        double r155689 = 1.0;
        double r155690 = r155689 + r155681;
        double r155691 = r155682 * r155690;
        double r155692 = 3.0;
        double r155693 = r155692 * r155681;
        double r155694 = r155689 - r155693;
        double r155695 = r155684 * r155694;
        double r155696 = r155691 + r155695;
        double r155697 = r155688 * r155696;
        double r155698 = r155687 + r155697;
        double r155699 = r155698 - r155689;
        return r155699;
}
↓
double f(double a, double b) {
        double r155700 = a;
        double r155701 = r155700 * r155700;
        double r155702 = b;
        double r155703 = r155702 * r155702;
        double r155704 = r155701 + r155703;
        double r155705 = 2.0;
        double r155706 = pow(r155704, r155705);
        double r155707 = 1.0;
        double r155708 = r155700 + r155707;
        double r155709 = r155701 * r155708;
        double r155710 = 3.0;
        double r155711 = r155710 * r155700;
        double r155712 = r155707 - r155711;
        double r155713 = r155703 * r155712;
        double r155714 = r155709 + r155713;
        double r155715 = 4.0;
        double r155716 = r155714 * r155715;
        double r155717 = r155706 + r155716;
        double r155718 = r155717 - r155707;
        return r155718;
}

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

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))