Average Error: 0.2 → 0.2
Time: 4.2s
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 r351444 = a;
        double r351445 = r351444 * r351444;
        double r351446 = b;
        double r351447 = r351446 * r351446;
        double r351448 = r351445 + r351447;
        double r351449 = 2.0;
        double r351450 = pow(r351448, r351449);
        double r351451 = 4.0;
        double r351452 = r351451 * r351447;
        double r351453 = r351450 + r351452;
        double r351454 = 1.0;
        double r351455 = r351453 - r351454;
        return r351455;
}
↓
double f(double a, double b) {
        double r351456 = a;
        double r351457 = r351456 * r351456;
        double r351458 = b;
        double r351459 = r351458 * r351458;
        double r351460 = r351457 + r351459;
        double r351461 = 2.0;
        double r351462 = pow(r351460, r351461);
        double r351463 = 4.0;
        double r351464 = r351463 * r351459;
        double r351465 = r351462 + r351464;
        double r351466 = 1.0;
        double r351467 = r351465 - r351466;
        return r351467;
}

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 2019353 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))