Average Error: 0.2 → 0.2
Time: 1.0m
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r37909866 = a;
        double r37909867 = r37909866 * r37909866;
        double r37909868 = b;
        double r37909869 = r37909868 * r37909868;
        double r37909870 = r37909867 + r37909869;
        double r37909871 = 2.0;
        double r37909872 = pow(r37909870, r37909871);
        double r37909873 = 4.0;
        double r37909874 = 1.0;
        double r37909875 = r37909874 + r37909866;
        double r37909876 = r37909867 * r37909875;
        double r37909877 = 3.0;
        double r37909878 = r37909877 * r37909866;
        double r37909879 = r37909874 - r37909878;
        double r37909880 = r37909869 * r37909879;
        double r37909881 = r37909876 + r37909880;
        double r37909882 = r37909873 * r37909881;
        double r37909883 = r37909872 + r37909882;
        double r37909884 = r37909883 - r37909874;
        return r37909884;
}
↓
double f(double a, double b) {
        double r37909885 = a;
        double r37909886 = r37909885 * r37909885;
        double r37909887 = b;
        double r37909888 = r37909887 * r37909887;
        double r37909889 = r37909886 + r37909888;
        double r37909890 = 2.0;
        double r37909891 = pow(r37909889, r37909890);
        double r37909892 = 1.0;
        double r37909893 = r37909885 + r37909892;
        double r37909894 = r37909886 * r37909893;
        double r37909895 = 3.0;
        double r37909896 = r37909895 * r37909885;
        double r37909897 = r37909892 - r37909896;
        double r37909898 = r37909888 * r37909897;
        double r37909899 = r37909894 + r37909898;
        double r37909900 = 4.0;
        double r37909901 = r37909899 * r37909900;
        double r37909902 = r37909891 + r37909901;
        double r37909903 = r37909902 - r37909892;
        return r37909903;
}

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

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))