Average Error: 12.6 → 0.3
Time: 5.1m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} - 1.5\right) - \frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\]
\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(\frac{\frac{2}{r}}{r} - 1.5\right) - \frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)
double f(double v, double w, double r) {
        double r31747360 = 3.0;
        double r31747361 = 2.0;
        double r31747362 = r;
        double r31747363 = r31747362 * r31747362;
        double r31747364 = r31747361 / r31747363;
        double r31747365 = r31747360 + r31747364;
        double r31747366 = 0.125;
        double r31747367 = v;
        double r31747368 = r31747361 * r31747367;
        double r31747369 = r31747360 - r31747368;
        double r31747370 = r31747366 * r31747369;
        double r31747371 = w;
        double r31747372 = r31747371 * r31747371;
        double r31747373 = r31747372 * r31747362;
        double r31747374 = r31747373 * r31747362;
        double r31747375 = r31747370 * r31747374;
        double r31747376 = 1.0;
        double r31747377 = r31747376 - r31747367;
        double r31747378 = r31747375 / r31747377;
        double r31747379 = r31747365 - r31747378;
        double r31747380 = 4.5;
        double r31747381 = r31747379 - r31747380;
        return r31747381;
}
↓
double f(double v, double w, double r) {
        double r31747382 = 2.0;
        double r31747383 = r;
        double r31747384 = r31747382 / r31747383;
        double r31747385 = r31747384 / r31747383;
        double r31747386 = 1.5;
        double r31747387 = r31747385 - r31747386;
        double r31747388 = 0.125;
        double r31747389 = 1.0;
        double r31747390 = v;
        double r31747391 = r31747389 - r31747390;
        double r31747392 = 3.0;
        double r31747393 = r31747382 * r31747390;
        double r31747394 = r31747392 - r31747393;
        double r31747395 = r31747391 / r31747394;
        double r31747396 = r31747388 / r31747395;
        double r31747397 = w;
        double r31747398 = r31747397 * r31747383;
        double r31747399 = r31747398 * r31747398;
        double r31747400 = r31747396 * r31747399;
        double r31747401 = r31747387 - r31747400;
        return r31747401;
}

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. 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 associate-/r/0.4

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

  5. Taylor expanded around inf 0.3

    \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{{r}^{2}} - 1.5\right)} - \frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\]

  6. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} - 1.5\right)} - \frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\]
  7. Using strategy rm

  8. Applied associate-/r*0.3

    \[\leadsto \left(\color{blue}{\frac{\frac{2}{r}}{r}} - 1.5\right) - \frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\]

  9. Final simplification0.3

    \[\leadsto \left(\frac{\frac{2}{r}}{r} - 1.5\right) - \frac{0.125}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\]

Reproduce

herbie shell --seed 2019128 
(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))