Average Error: 0.2 → 0.2
Time: 5.9s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r351285 = a;
        double r351286 = r351285 * r351285;
        double r351287 = b;
        double r351288 = r351287 * r351287;
        double r351289 = r351286 + r351288;
        double r351290 = 2.0;
        double r351291 = pow(r351289, r351290);
        double r351292 = 4.0;
        double r351293 = 1.0;
        double r351294 = r351293 + r351285;
        double r351295 = r351286 * r351294;
        double r351296 = 3.0;
        double r351297 = r351296 * r351285;
        double r351298 = r351293 - r351297;
        double r351299 = r351288 * r351298;
        double r351300 = r351295 + r351299;
        double r351301 = r351292 * r351300;
        double r351302 = r351291 + r351301;
        double r351303 = r351302 - r351293;
        return r351303;
}
↓
double f(double a, double b) {
        double r351304 = a;
        double r351305 = r351304 * r351304;
        double r351306 = b;
        double r351307 = r351306 * r351306;
        double r351308 = r351305 + r351307;
        double r351309 = 2.0;
        double r351310 = pow(r351308, r351309);
        double r351311 = 4.0;
        double r351312 = 1.0;
        double r351313 = r351312 + r351304;
        double r351314 = r351305 * r351313;
        double r351315 = 3.0;
        double r351316 = r351315 * r351304;
        double r351317 = r351312 - r351316;
        double r351318 = r351307 * r351317;
        double r351319 = r351314 + r351318;
        double r351320 = r351311 * r351319;
        double r351321 = r351310 + r351320;
        double r351322 = r351321 - r351312;
        return r351322;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

Reproduce

herbie shell --seed 2020060 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))