Average Error: 0.2 → 0.2
Time: 17.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\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(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1
double f(double a, double b) {
        double r135905 = a;
        double r135906 = r135905 * r135905;
        double r135907 = b;
        double r135908 = r135907 * r135907;
        double r135909 = r135906 + r135908;
        double r135910 = 2.0;
        double r135911 = pow(r135909, r135910);
        double r135912 = 4.0;
        double r135913 = 1.0;
        double r135914 = r135913 - r135905;
        double r135915 = r135906 * r135914;
        double r135916 = 3.0;
        double r135917 = r135916 + r135905;
        double r135918 = r135908 * r135917;
        double r135919 = r135915 + r135918;
        double r135920 = r135912 * r135919;
        double r135921 = r135911 + r135920;
        double r135922 = r135921 - r135913;
        return r135922;
}
↓
double f(double a, double b) {
        double r135923 = a;
        double r135924 = r135923 * r135923;
        double r135925 = b;
        double r135926 = r135925 * r135925;
        double r135927 = r135924 + r135926;
        double r135928 = 2.0;
        double r135929 = pow(r135927, r135928);
        double r135930 = 4.0;
        double r135931 = 1.0;
        double r135932 = r135931 - r135923;
        double r135933 = r135924 * r135932;
        double r135934 = 3.0;
        double r135935 = r135934 + r135923;
        double r135936 = r135926 * r135935;
        double r135937 = r135933 + r135936;
        double r135938 = r135930 * r135937;
        double r135939 = r135929 + r135938;
        double r135940 = r135939 - r135931;
        return r135940;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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))