Average Error: 0.2 → 0.2
Time: 6.9s
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 r124756 = a;
        double r124757 = r124756 * r124756;
        double r124758 = b;
        double r124759 = r124758 * r124758;
        double r124760 = r124757 + r124759;
        double r124761 = 2.0;
        double r124762 = pow(r124760, r124761);
        double r124763 = 4.0;
        double r124764 = 1.0;
        double r124765 = r124764 + r124756;
        double r124766 = r124757 * r124765;
        double r124767 = 3.0;
        double r124768 = r124767 * r124756;
        double r124769 = r124764 - r124768;
        double r124770 = r124759 * r124769;
        double r124771 = r124766 + r124770;
        double r124772 = r124763 * r124771;
        double r124773 = r124762 + r124772;
        double r124774 = r124773 - r124764;
        return r124774;
}
↓
double f(double a, double b) {
        double r124775 = a;
        double r124776 = r124775 * r124775;
        double r124777 = b;
        double r124778 = r124777 * r124777;
        double r124779 = r124776 + r124778;
        double r124780 = 2.0;
        double r124781 = pow(r124779, r124780);
        double r124782 = 4.0;
        double r124783 = 1.0;
        double r124784 = r124783 + r124775;
        double r124785 = r124776 * r124784;
        double r124786 = 3.0;
        double r124787 = r124786 * r124775;
        double r124788 = r124783 - r124787;
        double r124789 = r124778 * r124788;
        double r124790 = r124785 + r124789;
        double r124791 = r124782 * r124790;
        double r124792 = r124781 + r124791;
        double r124793 = r124792 - r124783;
        return r124793;
}

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 2020081 
(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))