Average Error: 0.2 → 0.2
Time: 28.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r8469798 = a;
        double r8469799 = r8469798 * r8469798;
        double r8469800 = b;
        double r8469801 = r8469800 * r8469800;
        double r8469802 = r8469799 + r8469801;
        double r8469803 = 2.0;
        double r8469804 = pow(r8469802, r8469803);
        double r8469805 = 4.0;
        double r8469806 = 1.0;
        double r8469807 = r8469806 + r8469798;
        double r8469808 = r8469799 * r8469807;
        double r8469809 = 3.0;
        double r8469810 = r8469809 * r8469798;
        double r8469811 = r8469806 - r8469810;
        double r8469812 = r8469801 * r8469811;
        double r8469813 = r8469808 + r8469812;
        double r8469814 = r8469805 * r8469813;
        double r8469815 = r8469804 + r8469814;
        double r8469816 = r8469815 - r8469806;
        return r8469816;
}
↓
double f(double a, double b) {
        double r8469817 = a;
        double r8469818 = r8469817 * r8469817;
        double r8469819 = b;
        double r8469820 = r8469819 * r8469819;
        double r8469821 = r8469818 + r8469820;
        double r8469822 = 2.0;
        double r8469823 = pow(r8469821, r8469822);
        double r8469824 = 1.0;
        double r8469825 = r8469817 + r8469824;
        double r8469826 = r8469818 * r8469825;
        double r8469827 = 3.0;
        double r8469828 = r8469827 * r8469817;
        double r8469829 = r8469824 - r8469828;
        double r8469830 = r8469820 * r8469829;
        double r8469831 = r8469826 + r8469830;
        double r8469832 = 4.0;
        double r8469833 = r8469831 * r8469832;
        double r8469834 = r8469823 + r8469833;
        double r8469835 = r8469834 - r8469824;
        return r8469835;
}

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

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

Reproduce

herbie shell --seed 2019169 
(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))