Average Error: 0.2 → 0.2
Time: 2.6s
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 r222915 = a;
        double r222916 = r222915 * r222915;
        double r222917 = b;
        double r222918 = r222917 * r222917;
        double r222919 = r222916 + r222918;
        double r222920 = 2.0;
        double r222921 = pow(r222919, r222920);
        double r222922 = 4.0;
        double r222923 = r222922 * r222918;
        double r222924 = r222921 + r222923;
        double r222925 = 1.0;
        double r222926 = r222924 - r222925;
        return r222926;
}
↓
double f(double a, double b) {
        double r222927 = a;
        double r222928 = r222927 * r222927;
        double r222929 = b;
        double r222930 = r222929 * r222929;
        double r222931 = r222928 + r222930;
        double r222932 = 2.0;
        double r222933 = pow(r222931, r222932);
        double r222934 = 4.0;
        double r222935 = r222934 * r222930;
        double r222936 = r222933 + r222935;
        double r222937 = 1.0;
        double r222938 = r222936 - r222937;
        return r222938;
}

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 2020024 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))