Average Error: 12.6 → 0.3
Time: 5.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left|w \cdot r\right| \cdot \frac{\left|w \cdot r\right|}{1 - v}\right)\right) - 4.5\]
\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) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left|w \cdot r\right| \cdot \frac{\left|w \cdot r\right|}{1 - v}\right)\right) - 4.5
double f(double v, double w, double r) {
        double r17313 = 3.0;
        double r17314 = 2.0;
        double r17315 = r;
        double r17316 = r17315 * r17315;
        double r17317 = r17314 / r17316;
        double r17318 = r17313 + r17317;
        double r17319 = 0.125;
        double r17320 = v;
        double r17321 = r17314 * r17320;
        double r17322 = r17313 - r17321;
        double r17323 = r17319 * r17322;
        double r17324 = w;
        double r17325 = r17324 * r17324;
        double r17326 = r17325 * r17315;
        double r17327 = r17326 * r17315;
        double r17328 = r17323 * r17327;
        double r17329 = 1.0;
        double r17330 = r17329 - r17320;
        double r17331 = r17328 / r17330;
        double r17332 = r17318 - r17331;
        double r17333 = 4.5;
        double r17334 = r17332 - r17333;
        return r17334;
}
↓
double f(double v, double w, double r) {
        double r17335 = 3.0;
        double r17336 = 2.0;
        double r17337 = r;
        double r17338 = r17336 / r17337;
        double r17339 = r17338 / r17337;
        double r17340 = r17335 + r17339;
        double r17341 = 0.125;
        double r17342 = v;
        double r17343 = r17336 * r17342;
        double r17344 = r17335 - r17343;
        double r17345 = r17341 * r17344;
        double r17346 = w;
        double r17347 = r17346 * r17337;
        double r17348 = fabs(r17347);
        double r17349 = 1.0;
        double r17350 = r17349 - r17342;
        double r17351 = r17348 / r17350;
        double r17352 = r17348 * r17351;
        double r17353 = r17345 * r17352;
        double r17354 = r17340 - r17353;
        double r17355 = 4.5;
        double r17356 = r17354 - r17355;
        return r17356;
}

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 12.6

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

  3. Applied add-sqr-sqrt12.7

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

  4. Simplified12.6

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

  5. Simplified6.6

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

  7. Applied *-un-lft-identity6.6

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  12. Applied associate-/r*0.4

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

  14. Applied *-un-lft-identity0.4

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

  15. Applied add-sqr-sqrt0.5

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

  16. Applied unpow-prod-down0.5

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

  17. Applied times-frac0.5

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

  18. Simplified0.4

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

  19. Simplified0.3

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

  20. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(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))