Average Error: 0.2 → 0.2
Time: 4.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
double f(double a, double b) {
        double r257862 = a;
        double r257863 = r257862 * r257862;
        double r257864 = b;
        double r257865 = r257864 * r257864;
        double r257866 = r257863 + r257865;
        double r257867 = 2.0;
        double r257868 = pow(r257866, r257867);
        double r257869 = 4.0;
        double r257870 = r257869 * r257865;
        double r257871 = r257868 + r257870;
        double r257872 = 1.0;
        double r257873 = r257871 - r257872;
        return r257873;
}
↓
double f(double a, double b) {
        double r257874 = a;
        double r257875 = r257874 * r257874;
        double r257876 = b;
        double r257877 = r257876 * r257876;
        double r257878 = r257875 + r257877;
        double r257879 = 2.0;
        double r257880 = pow(r257878, r257879);
        double r257881 = 4.0;
        double r257882 = r257881 * r257877;
        double r257883 = r257880 + r257882;
        double r257884 = 1.0;
        double r257885 = r257883 - r257884;
        return r257885;
}

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

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))