Average Error: 0.2 → 0.2
Time: 3.0s
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 r161437 = a;
        double r161438 = r161437 * r161437;
        double r161439 = b;
        double r161440 = r161439 * r161439;
        double r161441 = r161438 + r161440;
        double r161442 = 2.0;
        double r161443 = pow(r161441, r161442);
        double r161444 = 4.0;
        double r161445 = r161444 * r161440;
        double r161446 = r161443 + r161445;
        double r161447 = 1.0;
        double r161448 = r161446 - r161447;
        return r161448;
}
↓
double f(double a, double b) {
        double r161449 = a;
        double r161450 = r161449 * r161449;
        double r161451 = b;
        double r161452 = r161451 * r161451;
        double r161453 = r161450 + r161452;
        double r161454 = 2.0;
        double r161455 = pow(r161453, r161454);
        double r161456 = 4.0;
        double r161457 = r161456 * r161452;
        double r161458 = r161455 + r161457;
        double r161459 = 1.0;
        double r161460 = r161458 - r161459;
        return r161460;
}

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 2020057 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))