Average Error: 0.2 → 0.2
Time: 13.9s
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 r337120 = a;
        double r337121 = r337120 * r337120;
        double r337122 = b;
        double r337123 = r337122 * r337122;
        double r337124 = r337121 + r337123;
        double r337125 = 2.0;
        double r337126 = pow(r337124, r337125);
        double r337127 = 4.0;
        double r337128 = r337127 * r337123;
        double r337129 = r337126 + r337128;
        double r337130 = 1.0;
        double r337131 = r337129 - r337130;
        return r337131;
}
↓
double f(double a, double b) {
        double r337132 = a;
        double r337133 = r337132 * r337132;
        double r337134 = b;
        double r337135 = r337134 * r337134;
        double r337136 = r337133 + r337135;
        double r337137 = 2.0;
        double r337138 = pow(r337136, r337137);
        double r337139 = 4.0;
        double r337140 = r337139 * r337135;
        double r337141 = r337138 + r337140;
        double r337142 = 1.0;
        double r337143 = r337141 - r337142;
        return r337143;
}

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))