Average Error: 0.2 → 0.2
Time: 5.5s
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 r144965 = a;
        double r144966 = r144965 * r144965;
        double r144967 = b;
        double r144968 = r144967 * r144967;
        double r144969 = r144966 + r144968;
        double r144970 = 2.0;
        double r144971 = pow(r144969, r144970);
        double r144972 = 4.0;
        double r144973 = 1.0;
        double r144974 = r144973 + r144965;
        double r144975 = r144966 * r144974;
        double r144976 = 3.0;
        double r144977 = r144976 * r144965;
        double r144978 = r144973 - r144977;
        double r144979 = r144968 * r144978;
        double r144980 = r144975 + r144979;
        double r144981 = r144972 * r144980;
        double r144982 = r144971 + r144981;
        double r144983 = r144982 - r144973;
        return r144983;
}
↓
double f(double a, double b) {
        double r144984 = a;
        double r144985 = r144984 * r144984;
        double r144986 = b;
        double r144987 = r144986 * r144986;
        double r144988 = r144985 + r144987;
        double r144989 = 2.0;
        double r144990 = pow(r144988, r144989);
        double r144991 = 4.0;
        double r144992 = 1.0;
        double r144993 = r144992 + r144984;
        double r144994 = r144985 * r144993;
        double r144995 = 3.0;
        double r144996 = r144995 * r144984;
        double r144997 = r144992 - r144996;
        double r144998 = r144987 * r144997;
        double r144999 = r144994 + r144998;
        double r145000 = r144991 * r144999;
        double r145001 = r144990 + r145000;
        double r145002 = r145001 - r144992;
        return r145002;
}

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 2020018 
(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))