Average Error: 0.2 → 0.2
Time: 6.1s
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 r307127 = a;
        double r307128 = r307127 * r307127;
        double r307129 = b;
        double r307130 = r307129 * r307129;
        double r307131 = r307128 + r307130;
        double r307132 = 2.0;
        double r307133 = pow(r307131, r307132);
        double r307134 = 4.0;
        double r307135 = r307134 * r307130;
        double r307136 = r307133 + r307135;
        double r307137 = 1.0;
        double r307138 = r307136 - r307137;
        return r307138;
}
↓
double f(double a, double b) {
        double r307139 = a;
        double r307140 = r307139 * r307139;
        double r307141 = b;
        double r307142 = r307141 * r307141;
        double r307143 = r307140 + r307142;
        double r307144 = 2.0;
        double r307145 = pow(r307143, r307144);
        double r307146 = 4.0;
        double r307147 = r307146 * r307142;
        double r307148 = r307145 + r307147;
        double r307149 = 1.0;
        double r307150 = r307148 - r307149;
        return r307150;
}

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 2019354 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))