Average Error: 0.2 → 0.2
Time: 5.2s
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 r290868 = a;
        double r290869 = r290868 * r290868;
        double r290870 = b;
        double r290871 = r290870 * r290870;
        double r290872 = r290869 + r290871;
        double r290873 = 2.0;
        double r290874 = pow(r290872, r290873);
        double r290875 = 4.0;
        double r290876 = r290875 * r290871;
        double r290877 = r290874 + r290876;
        double r290878 = 1.0;
        double r290879 = r290877 - r290878;
        return r290879;
}
↓
double f(double a, double b) {
        double r290880 = a;
        double r290881 = r290880 * r290880;
        double r290882 = b;
        double r290883 = r290882 * r290882;
        double r290884 = r290881 + r290883;
        double r290885 = 2.0;
        double r290886 = pow(r290884, r290885);
        double r290887 = 4.0;
        double r290888 = r290887 * r290883;
        double r290889 = r290886 + r290888;
        double r290890 = 1.0;
        double r290891 = r290889 - r290890;
        return r290891;
}

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 2020064 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))