Average Error: 0.2 → 0.2
Time: 26.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r5956870 = a;
        double r5956871 = r5956870 * r5956870;
        double r5956872 = b;
        double r5956873 = r5956872 * r5956872;
        double r5956874 = r5956871 + r5956873;
        double r5956875 = 2.0;
        double r5956876 = pow(r5956874, r5956875);
        double r5956877 = 4.0;
        double r5956878 = r5956877 * r5956873;
        double r5956879 = r5956876 + r5956878;
        double r5956880 = 1.0;
        double r5956881 = r5956879 - r5956880;
        return r5956881;
}
↓
double f(double a, double b) {
        double r5956882 = b;
        double r5956883 = r5956882 * r5956882;
        double r5956884 = 4.0;
        double r5956885 = r5956883 * r5956884;
        double r5956886 = a;
        double r5956887 = r5956886 * r5956886;
        double r5956888 = r5956887 + r5956883;
        double r5956889 = 2.0;
        double r5956890 = pow(r5956888, r5956889);
        double r5956891 = r5956885 + r5956890;
        double r5956892 = 1.0;
        double r5956893 = r5956891 - r5956892;
        return r5956893;
}

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

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))