Average Error: 0.2 → 0.2
Time: 24.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r6219257 = a;
        double r6219258 = r6219257 * r6219257;
        double r6219259 = b;
        double r6219260 = r6219259 * r6219259;
        double r6219261 = r6219258 + r6219260;
        double r6219262 = 2.0;
        double r6219263 = pow(r6219261, r6219262);
        double r6219264 = 4.0;
        double r6219265 = 1.0;
        double r6219266 = r6219265 - r6219257;
        double r6219267 = r6219258 * r6219266;
        double r6219268 = 3.0;
        double r6219269 = r6219268 + r6219257;
        double r6219270 = r6219260 * r6219269;
        double r6219271 = r6219267 + r6219270;
        double r6219272 = r6219264 * r6219271;
        double r6219273 = r6219263 + r6219272;
        double r6219274 = r6219273 - r6219265;
        return r6219274;
}
↓
double f(double a, double b) {
        double r6219275 = a;
        double r6219276 = r6219275 * r6219275;
        double r6219277 = b;
        double r6219278 = r6219277 * r6219277;
        double r6219279 = r6219276 + r6219278;
        double r6219280 = 2.0;
        double r6219281 = pow(r6219279, r6219280);
        double r6219282 = 3.0;
        double r6219283 = r6219275 + r6219282;
        double r6219284 = r6219283 * r6219278;
        double r6219285 = 1.0;
        double r6219286 = r6219285 - r6219275;
        double r6219287 = r6219276 * r6219286;
        double r6219288 = r6219284 + r6219287;
        double r6219289 = 4.0;
        double r6219290 = r6219288 * r6219289;
        double r6219291 = r6219281 + r6219290;
        double r6219292 = r6219291 - r6219285;
        return r6219292;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))