Average Error: 0.2 → 0.2
Time: 17.0s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r185912 = a;
        double r185913 = r185912 * r185912;
        double r185914 = b;
        double r185915 = r185914 * r185914;
        double r185916 = r185913 + r185915;
        double r185917 = 2.0;
        double r185918 = pow(r185916, r185917);
        double r185919 = 4.0;
        double r185920 = 1.0;
        double r185921 = r185920 - r185912;
        double r185922 = r185913 * r185921;
        double r185923 = 3.0;
        double r185924 = r185923 + r185912;
        double r185925 = r185915 * r185924;
        double r185926 = r185922 + r185925;
        double r185927 = r185919 * r185926;
        double r185928 = r185918 + r185927;
        double r185929 = r185928 - r185920;
        return r185929;
}
↓
double f(double a, double b) {
        double r185930 = a;
        double r185931 = r185930 * r185930;
        double r185932 = b;
        double r185933 = r185932 * r185932;
        double r185934 = r185931 + r185933;
        double r185935 = 2.0;
        double r185936 = pow(r185934, r185935);
        double r185937 = 3.0;
        double r185938 = r185930 + r185937;
        double r185939 = r185938 * r185933;
        double r185940 = 1.0;
        double r185941 = r185940 - r185930;
        double r185942 = r185931 * r185941;
        double r185943 = r185939 + r185942;
        double r185944 = 4.0;
        double r185945 = r185943 * r185944;
        double r185946 = r185936 + r185945;
        double r185947 = r185946 - r185940;
        return r185947;
}

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

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

Reproduce

herbie shell --seed 2019174 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))