Average Error: 0.2 → 0.2
Time: 21.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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 r2281464 = a;
        double r2281465 = r2281464 * r2281464;
        double r2281466 = b;
        double r2281467 = r2281466 * r2281466;
        double r2281468 = r2281465 + r2281467;
        double r2281469 = 2.0;
        double r2281470 = pow(r2281468, r2281469);
        double r2281471 = 4.0;
        double r2281472 = 1.0;
        double r2281473 = r2281472 + r2281464;
        double r2281474 = r2281465 * r2281473;
        double r2281475 = 3.0;
        double r2281476 = r2281475 * r2281464;
        double r2281477 = r2281472 - r2281476;
        double r2281478 = r2281467 * r2281477;
        double r2281479 = r2281474 + r2281478;
        double r2281480 = r2281471 * r2281479;
        double r2281481 = r2281470 + r2281480;
        double r2281482 = r2281481 - r2281472;
        return r2281482;
}
↓
double f(double a, double b) {
        double r2281483 = a;
        double r2281484 = r2281483 * r2281483;
        double r2281485 = b;
        double r2281486 = r2281485 * r2281485;
        double r2281487 = r2281484 + r2281486;
        double r2281488 = 2.0;
        double r2281489 = pow(r2281487, r2281488);
        double r2281490 = 1.0;
        double r2281491 = r2281483 + r2281490;
        double r2281492 = r2281484 * r2281491;
        double r2281493 = 3.0;
        double r2281494 = r2281493 * r2281483;
        double r2281495 = r2281490 - r2281494;
        double r2281496 = r2281486 * r2281495;
        double r2281497 = r2281492 + r2281496;
        double r2281498 = 4.0;
        double r2281499 = r2281497 * r2281498;
        double r2281500 = r2281489 + r2281499;
        double r2281501 = r2281500 - r2281490;
        return r2281501;
}

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 2019128 +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))