Average Error: 0.2 → 0.2
Time: 15.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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 r257906 = a;
        double r257907 = r257906 * r257906;
        double r257908 = b;
        double r257909 = r257908 * r257908;
        double r257910 = r257907 + r257909;
        double r257911 = 2.0;
        double r257912 = pow(r257910, r257911);
        double r257913 = 4.0;
        double r257914 = 1.0;
        double r257915 = r257914 + r257906;
        double r257916 = r257907 * r257915;
        double r257917 = 3.0;
        double r257918 = r257917 * r257906;
        double r257919 = r257914 - r257918;
        double r257920 = r257909 * r257919;
        double r257921 = r257916 + r257920;
        double r257922 = r257913 * r257921;
        double r257923 = r257912 + r257922;
        double r257924 = r257923 - r257914;
        return r257924;
}
↓
double f(double a, double b) {
        double r257925 = a;
        double r257926 = r257925 * r257925;
        double r257927 = b;
        double r257928 = r257927 * r257927;
        double r257929 = r257926 + r257928;
        double r257930 = 2.0;
        double r257931 = pow(r257929, r257930);
        double r257932 = 4.0;
        double r257933 = 1.0;
        double r257934 = r257933 + r257925;
        double r257935 = r257926 * r257934;
        double r257936 = 3.0;
        double r257937 = r257936 * r257925;
        double r257938 = r257933 - r257937;
        double r257939 = r257928 * r257938;
        double r257940 = r257935 + r257939;
        double r257941 = r257932 * r257940;
        double r257942 = r257931 + r257941;
        double r257943 = r257942 - r257933;
        return r257943;
}

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 2019350 
(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))