Average Error: 0.2 → 0.2
Time: 5.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
double f(double a, double b) {
        double r349184 = a;
        double r349185 = r349184 * r349184;
        double r349186 = b;
        double r349187 = r349186 * r349186;
        double r349188 = r349185 + r349187;
        double r349189 = 2.0;
        double r349190 = pow(r349188, r349189);
        double r349191 = 4.0;
        double r349192 = r349191 * r349187;
        double r349193 = r349190 + r349192;
        double r349194 = 1.0;
        double r349195 = r349193 - r349194;
        return r349195;
}
↓
double f(double a, double b) {
        double r349196 = a;
        double r349197 = r349196 * r349196;
        double r349198 = b;
        double r349199 = r349198 * r349198;
        double r349200 = r349197 + r349199;
        double r349201 = 2.0;
        double r349202 = pow(r349200, r349201);
        double r349203 = 4.0;
        double r349204 = r349203 * r349199;
        double r349205 = r349202 + r349204;
        double r349206 = 1.0;
        double r349207 = r349205 - r349206;
        return r349207;
}

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

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))