Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 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} + 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
double f(double a, double b) {
        double r123554 = a;
        double r123555 = r123554 * r123554;
        double r123556 = b;
        double r123557 = r123556 * r123556;
        double r123558 = r123555 + r123557;
        double r123559 = 2.0;
        double r123560 = pow(r123558, r123559);
        double r123561 = 4.0;
        double r123562 = 1.0;
        double r123563 = r123562 + r123554;
        double r123564 = r123555 * r123563;
        double r123565 = 3.0;
        double r123566 = r123565 * r123554;
        double r123567 = r123562 - r123566;
        double r123568 = r123557 * r123567;
        double r123569 = r123564 + r123568;
        double r123570 = r123561 * r123569;
        double r123571 = r123560 + r123570;
        double r123572 = r123571 - r123562;
        return r123572;
}
↓
double f(double a, double b) {
        double r123573 = a;
        double r123574 = r123573 * r123573;
        double r123575 = b;
        double r123576 = r123575 * r123575;
        double r123577 = r123574 + r123576;
        double r123578 = 2.0;
        double r123579 = pow(r123577, r123578);
        double r123580 = 4.0;
        double r123581 = 1.0;
        double r123582 = r123581 + r123573;
        double r123583 = r123574 * r123582;
        double r123584 = 3.0;
        double r123585 = r123584 * r123573;
        double r123586 = r123581 - r123585;
        double r123587 = r123576 * r123586;
        double r123588 = r123583 + r123587;
        double r123589 = r123580 * r123588;
        double r123590 = r123579 + r123589;
        double r123591 = r123590 - r123581;
        return r123591;
}

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

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))