Average Error: 0.2 → 0.2
Time: 7.6s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\frac{\left(a \cdot a\right) \cdot \left(1 \cdot 1 - a \cdot a\right)}{1 + a} + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\frac{\left(a \cdot a\right) \cdot \left(1 \cdot 1 - a \cdot a\right)}{1 + a} + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1
double f(double a, double b) {
        double r229635 = a;
        double r229636 = r229635 * r229635;
        double r229637 = b;
        double r229638 = r229637 * r229637;
        double r229639 = r229636 + r229638;
        double r229640 = 2.0;
        double r229641 = pow(r229639, r229640);
        double r229642 = 4.0;
        double r229643 = 1.0;
        double r229644 = r229643 - r229635;
        double r229645 = r229636 * r229644;
        double r229646 = 3.0;
        double r229647 = r229646 + r229635;
        double r229648 = r229638 * r229647;
        double r229649 = r229645 + r229648;
        double r229650 = r229642 * r229649;
        double r229651 = r229641 + r229650;
        double r229652 = r229651 - r229643;
        return r229652;
}
↓
double f(double a, double b) {
        double r229653 = a;
        double r229654 = r229653 * r229653;
        double r229655 = b;
        double r229656 = r229655 * r229655;
        double r229657 = r229654 + r229656;
        double r229658 = 2.0;
        double r229659 = pow(r229657, r229658);
        double r229660 = 4.0;
        double r229661 = 1.0;
        double r229662 = r229661 * r229661;
        double r229663 = r229662 - r229654;
        double r229664 = r229654 * r229663;
        double r229665 = r229661 + r229653;
        double r229666 = r229664 / r229665;
        double r229667 = 3.0;
        double r229668 = r229667 + r229653;
        double r229669 = r229656 * r229668;
        double r229670 = r229666 + r229669;
        double r229671 = r229660 * r229670;
        double r229672 = r229659 + r229671;
        double r229673 = r229672 - r229661;
        return r229673;
}

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. Using strategy rm

  3. Applied flip--0.2

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

  4. Applied associate-*r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019318 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))