Average Error: 0.2 → 0.2
Time: 5.6s
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 r188425 = a;
        double r188426 = r188425 * r188425;
        double r188427 = b;
        double r188428 = r188427 * r188427;
        double r188429 = r188426 + r188428;
        double r188430 = 2.0;
        double r188431 = pow(r188429, r188430);
        double r188432 = 4.0;
        double r188433 = r188432 * r188428;
        double r188434 = r188431 + r188433;
        double r188435 = 1.0;
        double r188436 = r188434 - r188435;
        return r188436;
}
↓
double f(double a, double b) {
        double r188437 = a;
        double r188438 = r188437 * r188437;
        double r188439 = b;
        double r188440 = r188439 * r188439;
        double r188441 = r188438 + r188440;
        double r188442 = 2.0;
        double r188443 = pow(r188441, r188442);
        double r188444 = 4.0;
        double r188445 = r188444 * r188440;
        double r188446 = r188443 + r188445;
        double r188447 = 1.0;
        double r188448 = r188446 - r188447;
        return r188448;
}

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 2019304 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))