Average Error: 0.2 → 0.2
Time: 4.7s
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 r371390 = a;
        double r371391 = r371390 * r371390;
        double r371392 = b;
        double r371393 = r371392 * r371392;
        double r371394 = r371391 + r371393;
        double r371395 = 2.0;
        double r371396 = pow(r371394, r371395);
        double r371397 = 4.0;
        double r371398 = r371397 * r371393;
        double r371399 = r371396 + r371398;
        double r371400 = 1.0;
        double r371401 = r371399 - r371400;
        return r371401;
}
↓
double f(double a, double b) {
        double r371402 = a;
        double r371403 = r371402 * r371402;
        double r371404 = b;
        double r371405 = r371404 * r371404;
        double r371406 = r371403 + r371405;
        double r371407 = 2.0;
        double r371408 = pow(r371406, r371407);
        double r371409 = 4.0;
        double r371410 = r371409 * r371405;
        double r371411 = r371408 + r371410;
        double r371412 = 1.0;
        double r371413 = r371411 - r371412;
        return r371413;
}

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 2020056 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))