Average Error: 0.2 → 0.2
Time: 16.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r3646383 = a;
        double r3646384 = r3646383 * r3646383;
        double r3646385 = b;
        double r3646386 = r3646385 * r3646385;
        double r3646387 = r3646384 + r3646386;
        double r3646388 = 2.0;
        double r3646389 = pow(r3646387, r3646388);
        double r3646390 = 4.0;
        double r3646391 = r3646390 * r3646386;
        double r3646392 = r3646389 + r3646391;
        double r3646393 = 1.0;
        double r3646394 = r3646392 - r3646393;
        return r3646394;
}
↓
double f(double a, double b) {
        double r3646395 = b;
        double r3646396 = r3646395 * r3646395;
        double r3646397 = 4.0;
        double r3646398 = r3646396 * r3646397;
        double r3646399 = a;
        double r3646400 = r3646399 * r3646399;
        double r3646401 = r3646400 + r3646396;
        double r3646402 = 2.0;
        double r3646403 = pow(r3646401, r3646402);
        double r3646404 = r3646398 + r3646403;
        double r3646405 = 1.0;
        double r3646406 = r3646404 - r3646405;
        return r3646406;
}

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

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

Reproduce

herbie shell --seed 2019155 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))