Average Error: 0.2 → 0.2
Time: 19.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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 r128860 = a;
        double r128861 = r128860 * r128860;
        double r128862 = b;
        double r128863 = r128862 * r128862;
        double r128864 = r128861 + r128863;
        double r128865 = 2.0;
        double r128866 = pow(r128864, r128865);
        double r128867 = 4.0;
        double r128868 = 1.0;
        double r128869 = r128868 + r128860;
        double r128870 = r128861 * r128869;
        double r128871 = 3.0;
        double r128872 = r128871 * r128860;
        double r128873 = r128868 - r128872;
        double r128874 = r128863 * r128873;
        double r128875 = r128870 + r128874;
        double r128876 = r128867 * r128875;
        double r128877 = r128866 + r128876;
        double r128878 = r128877 - r128868;
        return r128878;
}
↓
double f(double a, double b) {
        double r128879 = a;
        double r128880 = r128879 * r128879;
        double r128881 = b;
        double r128882 = r128881 * r128881;
        double r128883 = r128880 + r128882;
        double r128884 = 2.0;
        double r128885 = pow(r128883, r128884);
        double r128886 = 4.0;
        double r128887 = 1.0;
        double r128888 = r128887 + r128879;
        double r128889 = r128880 * r128888;
        double r128890 = 3.0;
        double r128891 = r128890 * r128879;
        double r128892 = r128887 - r128891;
        double r128893 = r128882 * r128892;
        double r128894 = r128889 + r128893;
        double r128895 = r128886 * r128894;
        double r128896 = r128885 + r128895;
        double r128897 = r128896 - r128887;
        return r128897;
}

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 2019298 
(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))