Average Error: 0.2 → 0.2
Time: 18.7s
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 r202218 = a;
        double r202219 = r202218 * r202218;
        double r202220 = b;
        double r202221 = r202220 * r202220;
        double r202222 = r202219 + r202221;
        double r202223 = 2.0;
        double r202224 = pow(r202222, r202223);
        double r202225 = 4.0;
        double r202226 = r202225 * r202221;
        double r202227 = r202224 + r202226;
        double r202228 = 1.0;
        double r202229 = r202227 - r202228;
        return r202229;
}
↓
double f(double a, double b) {
        double r202230 = b;
        double r202231 = r202230 * r202230;
        double r202232 = 4.0;
        double r202233 = r202231 * r202232;
        double r202234 = a;
        double r202235 = r202234 * r202234;
        double r202236 = r202235 + r202231;
        double r202237 = 2.0;
        double r202238 = pow(r202236, r202237);
        double r202239 = r202233 + r202238;
        double r202240 = 1.0;
        double r202241 = r202239 - r202240;
        return r202241;
}

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 2019194 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))