Average Error: 0.2 → 0.2
Time: 5.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(a \cdot \left(a \cdot \left(1 + a\right)\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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(a \cdot \left(a \cdot \left(1 + a\right)\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r173206 = a;
        double r173207 = r173206 * r173206;
        double r173208 = b;
        double r173209 = r173208 * r173208;
        double r173210 = r173207 + r173209;
        double r173211 = 2.0;
        double r173212 = pow(r173210, r173211);
        double r173213 = 4.0;
        double r173214 = 1.0;
        double r173215 = r173214 + r173206;
        double r173216 = r173207 * r173215;
        double r173217 = 3.0;
        double r173218 = r173217 * r173206;
        double r173219 = r173214 - r173218;
        double r173220 = r173209 * r173219;
        double r173221 = r173216 + r173220;
        double r173222 = r173213 * r173221;
        double r173223 = r173212 + r173222;
        double r173224 = r173223 - r173214;
        return r173224;
}
↓
double f(double a, double b) {
        double r173225 = a;
        double r173226 = r173225 * r173225;
        double r173227 = b;
        double r173228 = r173227 * r173227;
        double r173229 = r173226 + r173228;
        double r173230 = 2.0;
        double r173231 = pow(r173229, r173230);
        double r173232 = 4.0;
        double r173233 = 1.0;
        double r173234 = r173233 + r173225;
        double r173235 = r173225 * r173234;
        double r173236 = r173225 * r173235;
        double r173237 = 3.0;
        double r173238 = r173237 * r173225;
        double r173239 = r173233 - r173238;
        double r173240 = r173228 * r173239;
        double r173241 = r173236 + r173240;
        double r173242 = r173232 * r173241;
        double r173243 = r173231 + r173242;
        double r173244 = r173243 - r173233;
        return r173244;
}

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. Using strategy rm

  3. Applied associate-*l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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))