Average Error: 11.7 → 0.4
Time: 21.1s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} + \left(3 - 4.5\right)\right) - \sqrt{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}} \cdot \sqrt{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}}\]
\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} + \left(3 - 4.5\right)\right) - \sqrt{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}} \cdot \sqrt{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}}
double f(double v, double w, double r) {
        double r866390 = 3.0;
        double r866391 = 2.0;
        double r866392 = r;
        double r866393 = r866392 * r866392;
        double r866394 = r866391 / r866393;
        double r866395 = r866390 + r866394;
        double r866396 = 0.125;
        double r866397 = v;
        double r866398 = r866391 * r866397;
        double r866399 = r866390 - r866398;
        double r866400 = r866396 * r866399;
        double r866401 = w;
        double r866402 = r866401 * r866401;
        double r866403 = r866402 * r866392;
        double r866404 = r866403 * r866392;
        double r866405 = r866400 * r866404;
        double r866406 = 1.0;
        double r866407 = r866406 - r866397;
        double r866408 = r866405 / r866407;
        double r866409 = r866395 - r866408;
        double r866410 = 4.5;
        double r866411 = r866409 - r866410;
        return r866411;
}
↓
double f(double v, double w, double r) {
        double r866412 = 2.0;
        double r866413 = r;
        double r866414 = r866412 / r866413;
        double r866415 = r866414 / r866413;
        double r866416 = 3.0;
        double r866417 = 4.5;
        double r866418 = r866416 - r866417;
        double r866419 = r866415 + r866418;
        double r866420 = w;
        double r866421 = r866420 * r866413;
        double r866422 = r866421 * r866421;
        double r866423 = 1.0;
        double r866424 = v;
        double r866425 = r866423 - r866424;
        double r866426 = r866424 * r866412;
        double r866427 = r866416 - r866426;
        double r866428 = 0.125;
        double r866429 = r866427 * r866428;
        double r866430 = r866425 / r866429;
        double r866431 = r866422 / r866430;
        double r866432 = sqrt(r866431);
        double r866433 = r866432 * r866432;
        double r866434 = r866419 - r866433;
        return r866434;
}

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 11.7

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

  2. Simplified5.9

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

  4. Applied associate-/l*0.3

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

  6. Applied associate-/r*0.3

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

  8. Applied add-sqr-sqrt0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019153 
(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))