Average Error: 0.2 → 0.2
Time: 36.6s
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 r63635871 = a;
        double r63635872 = r63635871 * r63635871;
        double r63635873 = b;
        double r63635874 = r63635873 * r63635873;
        double r63635875 = r63635872 + r63635874;
        double r63635876 = 2.0;
        double r63635877 = pow(r63635875, r63635876);
        double r63635878 = 4.0;
        double r63635879 = 1.0;
        double r63635880 = r63635879 + r63635871;
        double r63635881 = r63635872 * r63635880;
        double r63635882 = 3.0;
        double r63635883 = r63635882 * r63635871;
        double r63635884 = r63635879 - r63635883;
        double r63635885 = r63635874 * r63635884;
        double r63635886 = r63635881 + r63635885;
        double r63635887 = r63635878 * r63635886;
        double r63635888 = r63635877 + r63635887;
        double r63635889 = r63635888 - r63635879;
        return r63635889;
}
↓
double f(double a, double b) {
        double r63635890 = a;
        double r63635891 = r63635890 * r63635890;
        double r63635892 = b;
        double r63635893 = r63635892 * r63635892;
        double r63635894 = r63635891 + r63635893;
        double r63635895 = 2.0;
        double r63635896 = pow(r63635894, r63635895);
        double r63635897 = 1.0;
        double r63635898 = r63635890 + r63635897;
        double r63635899 = r63635891 * r63635898;
        double r63635900 = 3.0;
        double r63635901 = r63635900 * r63635890;
        double r63635902 = r63635897 - r63635901;
        double r63635903 = r63635893 * r63635902;
        double r63635904 = r63635899 + r63635903;
        double r63635905 = 4.0;
        double r63635906 = r63635904 * r63635905;
        double r63635907 = r63635896 + r63635906;
        double r63635908 = r63635907 - r63635897;
        return r63635908;
}

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 2019119 
(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))