Average Error: 0.2 → 0.2
Time: 22.6s
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 r88755 = a;
        double r88756 = r88755 * r88755;
        double r88757 = b;
        double r88758 = r88757 * r88757;
        double r88759 = r88756 + r88758;
        double r88760 = 2.0;
        double r88761 = pow(r88759, r88760);
        double r88762 = 4.0;
        double r88763 = 1.0;
        double r88764 = r88763 + r88755;
        double r88765 = r88756 * r88764;
        double r88766 = 3.0;
        double r88767 = r88766 * r88755;
        double r88768 = r88763 - r88767;
        double r88769 = r88758 * r88768;
        double r88770 = r88765 + r88769;
        double r88771 = r88762 * r88770;
        double r88772 = r88761 + r88771;
        double r88773 = r88772 - r88763;
        return r88773;
}
↓
double f(double a, double b) {
        double r88774 = a;
        double r88775 = r88774 * r88774;
        double r88776 = b;
        double r88777 = r88776 * r88776;
        double r88778 = r88775 + r88777;
        double r88779 = 2.0;
        double r88780 = pow(r88778, r88779);
        double r88781 = 4.0;
        double r88782 = 1.0;
        double r88783 = r88782 + r88774;
        double r88784 = r88775 * r88783;
        double r88785 = 3.0;
        double r88786 = r88785 * r88774;
        double r88787 = r88782 - r88786;
        double r88788 = r88777 * r88787;
        double r88789 = r88784 + r88788;
        double r88790 = r88781 * r88789;
        double r88791 = r88780 + r88790;
        double r88792 = r88791 - r88782;
        return r88792;
}

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 2019323 
(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))