Average Error: 12.9 → 0.4
Time: 22.1s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\left(1 - v\right) \cdot \frac{1}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\left(1 - v\right) \cdot \frac{1}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5
double f(double v, double w, double r) {
        double r27232 = 3.0;
        double r27233 = 2.0;
        double r27234 = r;
        double r27235 = r27234 * r27234;
        double r27236 = r27233 / r27235;
        double r27237 = r27232 + r27236;
        double r27238 = 0.125;
        double r27239 = v;
        double r27240 = r27233 * r27239;
        double r27241 = r27232 - r27240;
        double r27242 = r27238 * r27241;
        double r27243 = w;
        double r27244 = r27243 * r27243;
        double r27245 = r27244 * r27234;
        double r27246 = r27245 * r27234;
        double r27247 = r27242 * r27246;
        double r27248 = 1.0;
        double r27249 = r27248 - r27239;
        double r27250 = r27247 / r27249;
        double r27251 = r27237 - r27250;
        double r27252 = 4.5;
        double r27253 = r27251 - r27252;
        return r27253;
}
↓
double f(double v, double w, double r) {
        double r27254 = 3.0;
        double r27255 = 2.0;
        double r27256 = r;
        double r27257 = r27255 / r27256;
        double r27258 = r27257 / r27256;
        double r27259 = r27254 + r27258;
        double r27260 = 0.125;
        double r27261 = v;
        double r27262 = r27255 * r27261;
        double r27263 = r27254 - r27262;
        double r27264 = r27260 * r27263;
        double r27265 = 1.0;
        double r27266 = r27265 - r27261;
        double r27267 = 1.0;
        double r27268 = w;
        double r27269 = r27268 * r27256;
        double r27270 = fabs(r27269);
        double r27271 = 2.0;
        double r27272 = pow(r27270, r27271);
        double r27273 = r27267 / r27272;
        double r27274 = r27266 * r27273;
        double r27275 = r27264 / r27274;
        double r27276 = r27259 - r27275;
        double r27277 = 4.5;
        double r27278 = r27276 - r27277;
        return r27278;
}

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 add-sqr-sqrt13.0

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

  4. Simplified13.0

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

  5. Simplified7.0

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

  7. Applied associate-/l*0.4

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

  8. Simplified0.4

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

  10. Applied associate-/r*0.4

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

  12. Applied div-inv0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019304 
(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))