Average Error: 0.2 → 0.2
Time: 19.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r106338 = a;
        double r106339 = r106338 * r106338;
        double r106340 = b;
        double r106341 = r106340 * r106340;
        double r106342 = r106339 + r106341;
        double r106343 = 2.0;
        double r106344 = pow(r106342, r106343);
        double r106345 = 4.0;
        double r106346 = 1.0;
        double r106347 = r106346 + r106338;
        double r106348 = r106339 * r106347;
        double r106349 = 3.0;
        double r106350 = r106349 * r106338;
        double r106351 = r106346 - r106350;
        double r106352 = r106341 * r106351;
        double r106353 = r106348 + r106352;
        double r106354 = r106345 * r106353;
        double r106355 = r106344 + r106354;
        double r106356 = r106355 - r106346;
        return r106356;
}
↓
double f(double a, double b) {
        double r106357 = a;
        double r106358 = r106357 * r106357;
        double r106359 = b;
        double r106360 = r106359 * r106359;
        double r106361 = r106358 + r106360;
        double r106362 = 2.0;
        double r106363 = pow(r106361, r106362);
        double r106364 = 1.0;
        double r106365 = r106357 + r106364;
        double r106366 = r106358 * r106365;
        double r106367 = 3.0;
        double r106368 = r106367 * r106357;
        double r106369 = r106364 - r106368;
        double r106370 = r106360 * r106369;
        double r106371 = r106366 + r106370;
        double r106372 = 4.0;
        double r106373 = r106371 * r106372;
        double r106374 = r106363 + r106373;
        double r106375 = r106374 - r106364;
        return r106375;
}

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

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))