Average Error: 12.9 → 0.4
Time: 18.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 - 0.25 \cdot v\right) \cdot \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}\right) - 4.5\]
\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5
↓
\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 - 0.25 \cdot v\right) \cdot \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}\right) - 4.5
double f(double v, double w, double r) {
        double r25165 = 3.0;
        double r25166 = 2.0;
        double r25167 = r;
        double r25168 = r25167 * r25167;
        double r25169 = r25166 / r25168;
        double r25170 = r25165 + r25169;
        double r25171 = 0.125;
        double r25172 = v;
        double r25173 = r25166 * r25172;
        double r25174 = r25165 - r25173;
        double r25175 = r25171 * r25174;
        double r25176 = w;
        double r25177 = r25176 * r25176;
        double r25178 = r25177 * r25167;
        double r25179 = r25178 * r25167;
        double r25180 = r25175 * r25179;
        double r25181 = 1.0;
        double r25182 = r25181 - r25172;
        double r25183 = r25180 / r25182;
        double r25184 = r25170 - r25183;
        double r25185 = 4.5;
        double r25186 = r25184 - r25185;
        return r25186;
}
↓
double f(double v, double w, double r) {
        double r25187 = 3.0;
        double r25188 = 2.0;
        double r25189 = r;
        double r25190 = r25189 * r25189;
        double r25191 = r25188 / r25190;
        double r25192 = r25187 + r25191;
        double r25193 = 0.375;
        double r25194 = 0.25;
        double r25195 = v;
        double r25196 = r25194 * r25195;
        double r25197 = r25193 - r25196;
        double r25198 = w;
        double r25199 = r25198 * r25189;
        double r25200 = r25199 * r25199;
        double r25201 = 1.0;
        double r25202 = r25201 - r25195;
        double r25203 = r25200 / r25202;
        double r25204 = r25197 * r25203;
        double r25205 = r25192 - r25204;
        double r25206 = 4.5;
        double r25207 = r25205 - r25206;
        return r25207;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.9

    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
  2. Using strategy rm

  3. Applied *-un-lft-identity12.9

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{\color{blue}{1 \cdot \left(1 - v\right)}}\right) - 4.5\]

  4. Applied times-frac8.6

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1} \cdot \frac{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}{1 - v}}\right) - 4.5\]

  5. Simplified8.6

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)} \cdot \frac{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}{1 - v}\right) - 4.5\]
  6. Using strategy rm

  7. Applied associate-*l*2.6

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{\left(w \cdot \left(w \cdot r\right)\right)} \cdot r}{1 - v}\right) - 4.5\]

  8. Taylor expanded around 0 17.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{{w}^{2} \cdot {r}^{2}}}{1 - v}\right) - 4.5\]

  9. Simplified0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}{1 - v}\right) - 4.5\]

  10. Taylor expanded around 0 0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(0.375 - 0.25 \cdot v\right)} \cdot \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}\right) - 4.5\]

  11. Final simplification0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 - 0.25 \cdot v\right) \cdot \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}\right) - 4.5\]

Reproduce

herbie shell --seed 2019235 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))