Average Error: 0.2 → 0.2
Time: 17.5s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r222585 = a;
        double r222586 = r222585 * r222585;
        double r222587 = b;
        double r222588 = r222587 * r222587;
        double r222589 = r222586 + r222588;
        double r222590 = 2.0;
        double r222591 = pow(r222589, r222590);
        double r222592 = 4.0;
        double r222593 = r222592 * r222588;
        double r222594 = r222591 + r222593;
        double r222595 = 1.0;
        double r222596 = r222594 - r222595;
        return r222596;
}
↓
double f(double a, double b) {
        double r222597 = b;
        double r222598 = r222597 * r222597;
        double r222599 = 4.0;
        double r222600 = r222598 * r222599;
        double r222601 = a;
        double r222602 = r222601 * r222601;
        double r222603 = r222602 + r222598;
        double r222604 = 2.0;
        double r222605 = pow(r222603, r222604);
        double r222606 = r222600 + r222605;
        double r222607 = 1.0;
        double r222608 = r222606 - r222607;
        return r222608;
}

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

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

Reproduce

herbie shell --seed 2019194 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))