Average Error: 0.2 → 0.2
Time: 44.0s
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 r6433793 = a;
        double r6433794 = r6433793 * r6433793;
        double r6433795 = b;
        double r6433796 = r6433795 * r6433795;
        double r6433797 = r6433794 + r6433796;
        double r6433798 = 2.0;
        double r6433799 = pow(r6433797, r6433798);
        double r6433800 = 4.0;
        double r6433801 = 1.0;
        double r6433802 = r6433801 + r6433793;
        double r6433803 = r6433794 * r6433802;
        double r6433804 = 3.0;
        double r6433805 = r6433804 * r6433793;
        double r6433806 = r6433801 - r6433805;
        double r6433807 = r6433796 * r6433806;
        double r6433808 = r6433803 + r6433807;
        double r6433809 = r6433800 * r6433808;
        double r6433810 = r6433799 + r6433809;
        double r6433811 = r6433810 - r6433801;
        return r6433811;
}
↓
double f(double a, double b) {
        double r6433812 = 4.0;
        double r6433813 = 1.0;
        double r6433814 = 3.0;
        double r6433815 = a;
        double r6433816 = r6433814 * r6433815;
        double r6433817 = r6433813 - r6433816;
        double r6433818 = b;
        double r6433819 = r6433818 * r6433818;
        double r6433820 = r6433817 * r6433819;
        double r6433821 = r6433815 + r6433813;
        double r6433822 = r6433815 * r6433815;
        double r6433823 = r6433821 * r6433822;
        double r6433824 = r6433820 + r6433823;
        double r6433825 = r6433812 * r6433824;
        double r6433826 = r6433819 + r6433822;
        double r6433827 = 2.0;
        double r6433828 = pow(r6433826, r6433827);
        double r6433829 = r6433825 + r6433828;
        double r6433830 = r6433829 - r6433813;
        return r6433830;
}

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))