Average Error: 0.2 → 0.2
Time: 22.5s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(b \cdot b\right) \cdot \left(\left(12 + 4 \cdot a\right) + \left(b \cdot b + a \cdot a\right)\right) + \left(a \cdot \left(a \cdot \left(\left(b \cdot b + a \cdot a\right) + \left(4 - 4 \cdot a\right)\right)\right) + -1\right)\]
\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(b \cdot b\right) \cdot \left(\left(12 + 4 \cdot a\right) + \left(b \cdot b + a \cdot a\right)\right) + \left(a \cdot \left(a \cdot \left(\left(b \cdot b + a \cdot a\right) + \left(4 - 4 \cdot a\right)\right)\right) + -1\right)
double f(double a, double b) {
        double r6626462 = a;
        double r6626463 = r6626462 * r6626462;
        double r6626464 = b;
        double r6626465 = r6626464 * r6626464;
        double r6626466 = r6626463 + r6626465;
        double r6626467 = 2.0;
        double r6626468 = pow(r6626466, r6626467);
        double r6626469 = 4.0;
        double r6626470 = 1.0;
        double r6626471 = r6626470 - r6626462;
        double r6626472 = r6626463 * r6626471;
        double r6626473 = 3.0;
        double r6626474 = r6626473 + r6626462;
        double r6626475 = r6626465 * r6626474;
        double r6626476 = r6626472 + r6626475;
        double r6626477 = r6626469 * r6626476;
        double r6626478 = r6626468 + r6626477;
        double r6626479 = r6626478 - r6626470;
        return r6626479;
}
↓
double f(double a, double b) {
        double r6626480 = b;
        double r6626481 = r6626480 * r6626480;
        double r6626482 = 12.0;
        double r6626483 = 4.0;
        double r6626484 = a;
        double r6626485 = r6626483 * r6626484;
        double r6626486 = r6626482 + r6626485;
        double r6626487 = r6626484 * r6626484;
        double r6626488 = r6626481 + r6626487;
        double r6626489 = r6626486 + r6626488;
        double r6626490 = r6626481 * r6626489;
        double r6626491 = r6626483 - r6626485;
        double r6626492 = r6626488 + r6626491;
        double r6626493 = r6626484 * r6626492;
        double r6626494 = r6626484 * r6626493;
        double r6626495 = -1.0;
        double r6626496 = r6626494 + r6626495;
        double r6626497 = r6626490 + r6626496;
        return r6626497;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\left(b \cdot b\right) \cdot \left(\left(a \cdot a + b \cdot b\right) + \left(12 + 4 \cdot a\right)\right) + \left(\left(a \cdot a\right) \cdot \left(\left(a \cdot a + b \cdot b\right) + \left(4 - 4 \cdot a\right)\right) + -1\right)}\]
  3. Using strategy rm

  4. Applied associate-*l*0.2

    \[\leadsto \left(b \cdot b\right) \cdot \left(\left(a \cdot a + b \cdot b\right) + \left(12 + 4 \cdot a\right)\right) + \left(\color{blue}{a \cdot \left(a \cdot \left(\left(a \cdot a + b \cdot b\right) + \left(4 - 4 \cdot a\right)\right)\right)} + -1\right)\]

  5. Final simplification0.2

    \[\leadsto \left(b \cdot b\right) \cdot \left(\left(12 + 4 \cdot a\right) + \left(b \cdot b + a \cdot a\right)\right) + \left(a \cdot \left(a \cdot \left(\left(b \cdot b + a \cdot a\right) + \left(4 - 4 \cdot a\right)\right)\right) + -1\right)\]

Reproduce

herbie shell --seed 2019144 
(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))