Average Error: 0.2 → 0.2
Time: 16.4s
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 r211049 = a;
        double r211050 = r211049 * r211049;
        double r211051 = b;
        double r211052 = r211051 * r211051;
        double r211053 = r211050 + r211052;
        double r211054 = 2.0;
        double r211055 = pow(r211053, r211054);
        double r211056 = 4.0;
        double r211057 = r211056 * r211052;
        double r211058 = r211055 + r211057;
        double r211059 = 1.0;
        double r211060 = r211058 - r211059;
        return r211060;
}
↓
double f(double a, double b) {
        double r211061 = a;
        double r211062 = r211061 * r211061;
        double r211063 = b;
        double r211064 = r211063 * r211063;
        double r211065 = r211062 + r211064;
        double r211066 = 2.0;
        double r211067 = pow(r211065, r211066);
        double r211068 = 4.0;
        double r211069 = r211068 * r211064;
        double r211070 = r211067 + r211069;
        double r211071 = 1.0;
        double r211072 = r211070 - r211071;
        return r211072;
}

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 2020043 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))