Average Error: 0.2 → 0.2
Time: 16.5s
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 r147265 = a;
        double r147266 = r147265 * r147265;
        double r147267 = b;
        double r147268 = r147267 * r147267;
        double r147269 = r147266 + r147268;
        double r147270 = 2.0;
        double r147271 = pow(r147269, r147270);
        double r147272 = 4.0;
        double r147273 = r147272 * r147268;
        double r147274 = r147271 + r147273;
        double r147275 = 1.0;
        double r147276 = r147274 - r147275;
        return r147276;
}
↓
double f(double a, double b) {
        double r147277 = b;
        double r147278 = r147277 * r147277;
        double r147279 = 4.0;
        double r147280 = r147278 * r147279;
        double r147281 = a;
        double r147282 = r147281 * r147281;
        double r147283 = r147282 + r147278;
        double r147284 = 2.0;
        double r147285 = pow(r147283, r147284);
        double r147286 = r147280 + r147285;
        double r147287 = 1.0;
        double r147288 = r147286 - r147287;
        return r147288;
}

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