Average Error: 0.2 → 0.2
Time: 18.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r3542710 = a;
        double r3542711 = r3542710 * r3542710;
        double r3542712 = b;
        double r3542713 = r3542712 * r3542712;
        double r3542714 = r3542711 + r3542713;
        double r3542715 = 2.0;
        double r3542716 = pow(r3542714, r3542715);
        double r3542717 = 4.0;
        double r3542718 = 1.0;
        double r3542719 = r3542718 - r3542710;
        double r3542720 = r3542711 * r3542719;
        double r3542721 = 3.0;
        double r3542722 = r3542721 + r3542710;
        double r3542723 = r3542713 * r3542722;
        double r3542724 = r3542720 + r3542723;
        double r3542725 = r3542717 * r3542724;
        double r3542726 = r3542716 + r3542725;
        double r3542727 = r3542726 - r3542718;
        return r3542727;
}
↓
double f(double a, double b) {
        double r3542728 = a;
        double r3542729 = r3542728 * r3542728;
        double r3542730 = b;
        double r3542731 = r3542730 * r3542730;
        double r3542732 = r3542729 + r3542731;
        double r3542733 = 2.0;
        double r3542734 = pow(r3542732, r3542733);
        double r3542735 = 3.0;
        double r3542736 = r3542728 + r3542735;
        double r3542737 = r3542736 * r3542731;
        double r3542738 = 1.0;
        double r3542739 = r3542738 - r3542728;
        double r3542740 = r3542729 * r3542739;
        double r3542741 = r3542737 + r3542740;
        double r3542742 = 4.0;
        double r3542743 = r3542741 * r3542742;
        double r3542744 = r3542734 + r3542743;
        double r3542745 = r3542744 - r3542738;
        return r3542745;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019155 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))