Average Error: 11.7 → 0.4
Time: 27.0s
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 r895248 = 3.0;
        double r895249 = 2.0;
        double r895250 = r;
        double r895251 = r895250 * r895250;
        double r895252 = r895249 / r895251;
        double r895253 = r895248 + r895252;
        double r895254 = 0.125;
        double r895255 = v;
        double r895256 = r895249 * r895255;
        double r895257 = r895248 - r895256;
        double r895258 = r895254 * r895257;
        double r895259 = w;
        double r895260 = r895259 * r895259;
        double r895261 = r895260 * r895250;
        double r895262 = r895261 * r895250;
        double r895263 = r895258 * r895262;
        double r895264 = 1.0;
        double r895265 = r895264 - r895255;
        double r895266 = r895263 / r895265;
        double r895267 = r895253 - r895266;
        double r895268 = 4.5;
        double r895269 = r895267 - r895268;
        return r895269;
}
↓
double f(double v, double w, double r) {
        double r895270 = 2.0;
        double r895271 = r;
        double r895272 = r895270 / r895271;
        double r895273 = r895272 / r895271;
        double r895274 = 3.0;
        double r895275 = 4.5;
        double r895276 = r895274 - r895275;
        double r895277 = r895273 + r895276;
        double r895278 = w;
        double r895279 = r895278 * r895271;
        double r895280 = r895279 * r895279;
        double r895281 = 1.0;
        double r895282 = v;
        double r895283 = r895281 - r895282;
        double r895284 = r895282 * r895270;
        double r895285 = r895274 - r895284;
        double r895286 = 0.125;
        double r895287 = r895285 * r895286;
        double r895288 = r895283 / r895287;
        double r895289 = r895280 / r895288;
        double r895290 = sqrt(r895289);
        double r895291 = r895290 * r895290;
        double r895292 = r895277 - r895291;
        return r895292;
}

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. Taylor expanded around inf 0.3

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

  6. Simplified0.3

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