Average Error: 0.2 → 0.2
Time: 16.6s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + b \cdot \left(4 \cdot b\right)\right) - 1\]
\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} + b \cdot \left(4 \cdot b\right)\right) - 1
double f(double a, double b) {
        double r209481 = a;
        double r209482 = r209481 * r209481;
        double r209483 = b;
        double r209484 = r209483 * r209483;
        double r209485 = r209482 + r209484;
        double r209486 = 2.0;
        double r209487 = pow(r209485, r209486);
        double r209488 = 4.0;
        double r209489 = r209488 * r209484;
        double r209490 = r209487 + r209489;
        double r209491 = 1.0;
        double r209492 = r209490 - r209491;
        return r209492;
}
↓
double f(double a, double b) {
        double r209493 = a;
        double r209494 = r209493 * r209493;
        double r209495 = b;
        double r209496 = r209495 * r209495;
        double r209497 = r209494 + r209496;
        double r209498 = 2.0;
        double r209499 = pow(r209497, r209498);
        double r209500 = 4.0;
        double r209501 = r209500 * r209495;
        double r209502 = r209495 * r209501;
        double r209503 = r209499 + r209502;
        double r209504 = 1.0;
        double r209505 = r209503 - r209504;
        return r209505;
}

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. Taylor expanded around 0 0.2

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))