Average Error: 0.2 → 0.2
Time: 23.2s
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 r7924347 = a;
        double r7924348 = r7924347 * r7924347;
        double r7924349 = b;
        double r7924350 = r7924349 * r7924349;
        double r7924351 = r7924348 + r7924350;
        double r7924352 = 2.0;
        double r7924353 = pow(r7924351, r7924352);
        double r7924354 = 4.0;
        double r7924355 = 1.0;
        double r7924356 = r7924355 + r7924347;
        double r7924357 = r7924348 * r7924356;
        double r7924358 = 3.0;
        double r7924359 = r7924358 * r7924347;
        double r7924360 = r7924355 - r7924359;
        double r7924361 = r7924350 * r7924360;
        double r7924362 = r7924357 + r7924361;
        double r7924363 = r7924354 * r7924362;
        double r7924364 = r7924353 + r7924363;
        double r7924365 = r7924364 - r7924355;
        return r7924365;
}
↓
double f(double a, double b) {
        double r7924366 = a;
        double r7924367 = r7924366 * r7924366;
        double r7924368 = b;
        double r7924369 = r7924368 * r7924368;
        double r7924370 = r7924367 + r7924369;
        double r7924371 = 2.0;
        double r7924372 = pow(r7924370, r7924371);
        double r7924373 = 1.0;
        double r7924374 = r7924366 + r7924373;
        double r7924375 = r7924367 * r7924374;
        double r7924376 = 3.0;
        double r7924377 = r7924376 * r7924366;
        double r7924378 = r7924373 - r7924377;
        double r7924379 = r7924369 * r7924378;
        double r7924380 = r7924375 + r7924379;
        double r7924381 = 4.0;
        double r7924382 = r7924380 * r7924381;
        double r7924383 = r7924372 + r7924382;
        double r7924384 = r7924383 - r7924373;
        return r7924384;
}

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 2019171 
(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))