Average Error: 0.2 → 0.2
Time: 44.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(4 \cdot \left(\left(1 - 3 \cdot a\right) \cdot \left(b \cdot b\right) + \left(a + 1\right) \cdot \left(a \cdot a\right)\right) + {\left(b \cdot b + a \cdot a\right)}^{2}\right) - 1\]
\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(1 - 3 \cdot a\right) \cdot \left(b \cdot b\right) + \left(a + 1\right) \cdot \left(a \cdot a\right)\right) + {\left(b \cdot b + a \cdot a\right)}^{2}\right) - 1
double f(double a, double b) {
        double r6433820 = a;
        double r6433821 = r6433820 * r6433820;
        double r6433822 = b;
        double r6433823 = r6433822 * r6433822;
        double r6433824 = r6433821 + r6433823;
        double r6433825 = 2.0;
        double r6433826 = pow(r6433824, r6433825);
        double r6433827 = 4.0;
        double r6433828 = 1.0;
        double r6433829 = r6433828 + r6433820;
        double r6433830 = r6433821 * r6433829;
        double r6433831 = 3.0;
        double r6433832 = r6433831 * r6433820;
        double r6433833 = r6433828 - r6433832;
        double r6433834 = r6433823 * r6433833;
        double r6433835 = r6433830 + r6433834;
        double r6433836 = r6433827 * r6433835;
        double r6433837 = r6433826 + r6433836;
        double r6433838 = r6433837 - r6433828;
        return r6433838;
}
↓
double f(double a, double b) {
        double r6433839 = 4.0;
        double r6433840 = 1.0;
        double r6433841 = 3.0;
        double r6433842 = a;
        double r6433843 = r6433841 * r6433842;
        double r6433844 = r6433840 - r6433843;
        double r6433845 = b;
        double r6433846 = r6433845 * r6433845;
        double r6433847 = r6433844 * r6433846;
        double r6433848 = r6433842 + r6433840;
        double r6433849 = r6433842 * r6433842;
        double r6433850 = r6433848 * r6433849;
        double r6433851 = r6433847 + r6433850;
        double r6433852 = r6433839 * r6433851;
        double r6433853 = r6433846 + r6433849;
        double r6433854 = 2.0;
        double r6433855 = pow(r6433853, r6433854);
        double r6433856 = r6433852 + r6433855;
        double r6433857 = r6433856 - r6433840;
        return r6433857;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))