Average Error: 0.2 → 0.2
Time: 11.4s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\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(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) + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r209607 = a;
        double r209608 = r209607 * r209607;
        double r209609 = b;
        double r209610 = r209609 * r209609;
        double r209611 = r209608 + r209610;
        double r209612 = 2.0;
        double r209613 = pow(r209611, r209612);
        double r209614 = 4.0;
        double r209615 = 1.0;
        double r209616 = r209615 + r209607;
        double r209617 = r209608 * r209616;
        double r209618 = 3.0;
        double r209619 = r209618 * r209607;
        double r209620 = r209615 - r209619;
        double r209621 = r209610 * r209620;
        double r209622 = r209617 + r209621;
        double r209623 = r209614 * r209622;
        double r209624 = r209613 + r209623;
        double r209625 = r209624 - r209615;
        return r209625;
}
↓
double f(double a, double b) {
        double r209626 = 4.0;
        double r209627 = a;
        double r209628 = r209627 * r209627;
        double r209629 = 1.0;
        double r209630 = r209629 + r209627;
        double r209631 = r209628 * r209630;
        double r209632 = b;
        double r209633 = r209632 * r209632;
        double r209634 = 3.0;
        double r209635 = r209634 * r209627;
        double r209636 = r209629 - r209635;
        double r209637 = r209633 * r209636;
        double r209638 = r209631 + r209637;
        double r209639 = r209626 * r209638;
        double r209640 = r209628 + r209633;
        double r209641 = 2.0;
        double r209642 = pow(r209640, r209641);
        double r209643 = r209639 + r209642;
        double r209644 = r209643 - r209629;
        return r209644;
}

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. Using strategy rm

  3. Applied +-commutative0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 
(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))