Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 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} + 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
double f(double a, double b) {
        double r210856 = a;
        double r210857 = r210856 * r210856;
        double r210858 = b;
        double r210859 = r210858 * r210858;
        double r210860 = r210857 + r210859;
        double r210861 = 2.0;
        double r210862 = pow(r210860, r210861);
        double r210863 = 4.0;
        double r210864 = 1.0;
        double r210865 = r210864 + r210856;
        double r210866 = r210857 * r210865;
        double r210867 = 3.0;
        double r210868 = r210867 * r210856;
        double r210869 = r210864 - r210868;
        double r210870 = r210859 * r210869;
        double r210871 = r210866 + r210870;
        double r210872 = r210863 * r210871;
        double r210873 = r210862 + r210872;
        double r210874 = r210873 - r210864;
        return r210874;
}
↓
double f(double a, double b) {
        double r210875 = a;
        double r210876 = r210875 * r210875;
        double r210877 = b;
        double r210878 = r210877 * r210877;
        double r210879 = r210876 + r210878;
        double r210880 = 2.0;
        double r210881 = pow(r210879, r210880);
        double r210882 = 4.0;
        double r210883 = 1.0;
        double r210884 = r210883 + r210875;
        double r210885 = r210876 * r210884;
        double r210886 = 3.0;
        double r210887 = r210886 * r210875;
        double r210888 = r210883 - r210887;
        double r210889 = r210878 * r210888;
        double r210890 = r210885 + r210889;
        double r210891 = r210882 * r210890;
        double r210892 = r210881 + r210891;
        double r210893 = r210892 - r210883;
        return r210893;
}

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

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

Reproduce

herbie shell --seed 2020018 
(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))