Average Error: 0.2 → 0.2
Time: 5.8s
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 r161881 = a;
        double r161882 = r161881 * r161881;
        double r161883 = b;
        double r161884 = r161883 * r161883;
        double r161885 = r161882 + r161884;
        double r161886 = 2.0;
        double r161887 = pow(r161885, r161886);
        double r161888 = 4.0;
        double r161889 = 1.0;
        double r161890 = r161889 + r161881;
        double r161891 = r161882 * r161890;
        double r161892 = 3.0;
        double r161893 = r161892 * r161881;
        double r161894 = r161889 - r161893;
        double r161895 = r161884 * r161894;
        double r161896 = r161891 + r161895;
        double r161897 = r161888 * r161896;
        double r161898 = r161887 + r161897;
        double r161899 = r161898 - r161889;
        return r161899;
}
↓
double f(double a, double b) {
        double r161900 = a;
        double r161901 = r161900 * r161900;
        double r161902 = b;
        double r161903 = r161902 * r161902;
        double r161904 = r161901 + r161903;
        double r161905 = 2.0;
        double r161906 = pow(r161904, r161905);
        double r161907 = 4.0;
        double r161908 = 1.0;
        double r161909 = r161908 + r161900;
        double r161910 = r161901 * r161909;
        double r161911 = 3.0;
        double r161912 = r161911 * r161900;
        double r161913 = r161908 - r161912;
        double r161914 = r161903 * r161913;
        double r161915 = r161910 + r161914;
        double r161916 = r161907 * r161915;
        double r161917 = r161906 + r161916;
        double r161918 = r161917 - r161908;
        return r161918;
}

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 2020060 
(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))