Average Error: 13.1 → 0.3
Time: 5.9m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \left(r \cdot w\right) \cdot \left(\frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(r \cdot w\right)\right)\]
\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) - 4.5\right) - \left(r \cdot w\right) \cdot \left(\frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(r \cdot w\right)\right)
double f(double v, double w, double r) {
        double r32430341 = 3.0;
        double r32430342 = 2.0;
        double r32430343 = r;
        double r32430344 = r32430343 * r32430343;
        double r32430345 = r32430342 / r32430344;
        double r32430346 = r32430341 + r32430345;
        double r32430347 = 0.125;
        double r32430348 = v;
        double r32430349 = r32430342 * r32430348;
        double r32430350 = r32430341 - r32430349;
        double r32430351 = r32430347 * r32430350;
        double r32430352 = w;
        double r32430353 = r32430352 * r32430352;
        double r32430354 = r32430353 * r32430343;
        double r32430355 = r32430354 * r32430343;
        double r32430356 = r32430351 * r32430355;
        double r32430357 = 1.0;
        double r32430358 = r32430357 - r32430348;
        double r32430359 = r32430356 / r32430358;
        double r32430360 = r32430346 - r32430359;
        double r32430361 = 4.5;
        double r32430362 = r32430360 - r32430361;
        return r32430362;
}
↓
double f(double v, double w, double r) {
        double r32430363 = 3.0;
        double r32430364 = 2.0;
        double r32430365 = r;
        double r32430366 = r32430365 * r32430365;
        double r32430367 = r32430364 / r32430366;
        double r32430368 = r32430363 + r32430367;
        double r32430369 = 4.5;
        double r32430370 = r32430368 - r32430369;
        double r32430371 = w;
        double r32430372 = r32430365 * r32430371;
        double r32430373 = 0.125;
        double r32430374 = 1.0;
        double r32430375 = v;
        double r32430376 = r32430374 - r32430375;
        double r32430377 = r32430364 * r32430375;
        double r32430378 = r32430363 - r32430377;
        double r32430379 = r32430376 / r32430378;
        double r32430380 = r32430373 / r32430379;
        double r32430381 = r32430380 * r32430372;
        double r32430382 = r32430372 * r32430381;
        double r32430383 = r32430370 - r32430382;
        return r32430383;
}

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 13.1

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

  2. Simplified0.4

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

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

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

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

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

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

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

  7. Applied distribute-lft-out--0.4

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

  8. Applied times-frac0.4

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

  9. Applied times-frac0.4

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

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

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

  11. Applied times-frac0.4

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

  12. Simplified0.3

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

  14. Applied associate-/r/0.3

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

  15. Applied associate-*r*0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2019120 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))