Average Error: 0.2 → 0.2
Time: 34.6s
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 r98642297 = a;
        double r98642298 = r98642297 * r98642297;
        double r98642299 = b;
        double r98642300 = r98642299 * r98642299;
        double r98642301 = r98642298 + r98642300;
        double r98642302 = 2.0;
        double r98642303 = pow(r98642301, r98642302);
        double r98642304 = 4.0;
        double r98642305 = r98642304 * r98642300;
        double r98642306 = r98642303 + r98642305;
        double r98642307 = 1.0;
        double r98642308 = r98642306 - r98642307;
        return r98642308;
}
↓
double f(double a, double b) {
        double r98642309 = b;
        double r98642310 = r98642309 * r98642309;
        double r98642311 = 4.0;
        double r98642312 = r98642310 * r98642311;
        double r98642313 = a;
        double r98642314 = r98642313 * r98642313;
        double r98642315 = r98642314 + r98642310;
        double r98642316 = 2.0;
        double r98642317 = pow(r98642315, r98642316);
        double r98642318 = r98642312 + r98642317;
        double r98642319 = 1.0;
        double r98642320 = r98642318 - r98642319;
        return r98642320;
}

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 2019128 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))