Average Error: 0.2 → 0.2
Time: 11.5s
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 r309377 = a;
        double r309378 = r309377 * r309377;
        double r309379 = b;
        double r309380 = r309379 * r309379;
        double r309381 = r309378 + r309380;
        double r309382 = 2.0;
        double r309383 = pow(r309381, r309382);
        double r309384 = 4.0;
        double r309385 = r309384 * r309380;
        double r309386 = r309383 + r309385;
        double r309387 = 1.0;
        double r309388 = r309386 - r309387;
        return r309388;
}
↓
double f(double a, double b) {
        double r309389 = a;
        double r309390 = r309389 * r309389;
        double r309391 = b;
        double r309392 = r309391 * r309391;
        double r309393 = r309390 + r309392;
        double r309394 = 2.0;
        double r309395 = pow(r309393, r309394);
        double r309396 = 4.0;
        double r309397 = r309396 * r309392;
        double r309398 = r309395 + r309397;
        double r309399 = 1.0;
        double r309400 = r309398 - r309399;
        return r309400;
}

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 2019351 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))