Average Error: 0.2 → 0.2
Time: 17.5s
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 r183806 = a;
        double r183807 = r183806 * r183806;
        double r183808 = b;
        double r183809 = r183808 * r183808;
        double r183810 = r183807 + r183809;
        double r183811 = 2.0;
        double r183812 = pow(r183810, r183811);
        double r183813 = 4.0;
        double r183814 = 1.0;
        double r183815 = r183814 - r183806;
        double r183816 = r183807 * r183815;
        double r183817 = 3.0;
        double r183818 = r183817 + r183806;
        double r183819 = r183809 * r183818;
        double r183820 = r183816 + r183819;
        double r183821 = r183813 * r183820;
        double r183822 = r183812 + r183821;
        double r183823 = r183822 - r183814;
        return r183823;
}
↓
double f(double a, double b) {
        double r183824 = a;
        double r183825 = r183824 * r183824;
        double r183826 = b;
        double r183827 = r183826 * r183826;
        double r183828 = r183825 + r183827;
        double r183829 = 2.0;
        double r183830 = pow(r183828, r183829);
        double r183831 = 4.0;
        double r183832 = 1.0;
        double r183833 = r183832 - r183824;
        double r183834 = r183825 * r183833;
        double r183835 = 3.0;
        double r183836 = r183835 + r183824;
        double r183837 = r183827 * r183836;
        double r183838 = r183834 + r183837;
        double r183839 = r183831 * r183838;
        double r183840 = r183830 + r183839;
        double r183841 = r183840 - r183832;
        return r183841;
}

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 2019212 
(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))