Average Error: 12.9 → 6.9
Time: 12.6s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(3 + \left(\frac{2}{r \cdot r} - 4.5\right)\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(\sqrt{\left|w \cdot r\right|}\right)}^{4}}{1 - v}\]
\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(3 + \left(\frac{2}{r \cdot r} - 4.5\right)\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(\sqrt{\left|w \cdot r\right|}\right)}^{4}}{1 - v}
double f(double v, double w, double r) {
        double r28254 = 3.0;
        double r28255 = 2.0;
        double r28256 = r;
        double r28257 = r28256 * r28256;
        double r28258 = r28255 / r28257;
        double r28259 = r28254 + r28258;
        double r28260 = 0.125;
        double r28261 = v;
        double r28262 = r28255 * r28261;
        double r28263 = r28254 - r28262;
        double r28264 = r28260 * r28263;
        double r28265 = w;
        double r28266 = r28265 * r28265;
        double r28267 = r28266 * r28256;
        double r28268 = r28267 * r28256;
        double r28269 = r28264 * r28268;
        double r28270 = 1.0;
        double r28271 = r28270 - r28261;
        double r28272 = r28269 / r28271;
        double r28273 = r28259 - r28272;
        double r28274 = 4.5;
        double r28275 = r28273 - r28274;
        return r28275;
}
↓
double f(double v, double w, double r) {
        double r28276 = 3.0;
        double r28277 = 2.0;
        double r28278 = r;
        double r28279 = r28278 * r28278;
        double r28280 = r28277 / r28279;
        double r28281 = 4.5;
        double r28282 = r28280 - r28281;
        double r28283 = r28276 + r28282;
        double r28284 = 0.125;
        double r28285 = v;
        double r28286 = r28277 * r28285;
        double r28287 = r28276 - r28286;
        double r28288 = r28284 * r28287;
        double r28289 = w;
        double r28290 = r28289 * r28278;
        double r28291 = fabs(r28290);
        double r28292 = sqrt(r28291);
        double r28293 = 4.0;
        double r28294 = pow(r28292, r28293);
        double r28295 = r28288 * r28294;
        double r28296 = 1.0;
        double r28297 = r28296 - r28285;
        double r28298 = r28295 / r28297;
        double r28299 = r28283 - r28298;
        return r28299;
}

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-sqrt12.9

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

  4. Simplified12.9

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

  5. Simplified6.8

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left|w \cdot r\right| \cdot \color{blue}{\left|w \cdot r\right|}\right)}{1 - v}\right) - 4.5\]
  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 add-sqr-sqrt0.5

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

  11. Applied unpow-prod-down0.5

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

  12. Applied associate-/r*0.5

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

  13. Simplified0.4

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

  14. Final simplification6.9

    \[\leadsto \left(3 + \left(\frac{2}{r \cdot r} - 4.5\right)\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(\sqrt{\left|w \cdot r\right|}\right)}^{4}}{1 - v}\]

Reproduce

herbie shell --seed 2019308 
(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))