Average Error: 0.2 → 0.2
Time: 45.5s
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 r6341472 = a;
        double r6341473 = r6341472 * r6341472;
        double r6341474 = b;
        double r6341475 = r6341474 * r6341474;
        double r6341476 = r6341473 + r6341475;
        double r6341477 = 2.0;
        double r6341478 = pow(r6341476, r6341477);
        double r6341479 = 4.0;
        double r6341480 = 1.0;
        double r6341481 = r6341480 + r6341472;
        double r6341482 = r6341473 * r6341481;
        double r6341483 = 3.0;
        double r6341484 = r6341483 * r6341472;
        double r6341485 = r6341480 - r6341484;
        double r6341486 = r6341475 * r6341485;
        double r6341487 = r6341482 + r6341486;
        double r6341488 = r6341479 * r6341487;
        double r6341489 = r6341478 + r6341488;
        double r6341490 = r6341489 - r6341480;
        return r6341490;
}
↓
double f(double a, double b) {
        double r6341491 = a;
        double r6341492 = r6341491 * r6341491;
        double r6341493 = b;
        double r6341494 = r6341493 * r6341493;
        double r6341495 = r6341492 + r6341494;
        double r6341496 = 2.0;
        double r6341497 = pow(r6341495, r6341496);
        double r6341498 = 1.0;
        double r6341499 = r6341491 + r6341498;
        double r6341500 = r6341492 * r6341499;
        double r6341501 = 3.0;
        double r6341502 = r6341501 * r6341491;
        double r6341503 = r6341498 - r6341502;
        double r6341504 = r6341494 * r6341503;
        double r6341505 = r6341500 + r6341504;
        double r6341506 = 4.0;
        double r6341507 = r6341505 * r6341506;
        double r6341508 = r6341497 + r6341507;
        double r6341509 = r6341508 - r6341498;
        return r6341509;
}

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 2019149 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))