Average Error: 13.1 → 0.3
Time: 5.6s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{1 - v}{\left|w \cdot r\right|}}{\left|w \cdot r\right|}}\right) - 4.5\]
\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) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{1 - v}{\left|w \cdot r\right|}}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r17248 = 3.0;
        double r17249 = 2.0;
        double r17250 = r;
        double r17251 = r17250 * r17250;
        double r17252 = r17249 / r17251;
        double r17253 = r17248 + r17252;
        double r17254 = 0.125;
        double r17255 = v;
        double r17256 = r17249 * r17255;
        double r17257 = r17248 - r17256;
        double r17258 = r17254 * r17257;
        double r17259 = w;
        double r17260 = r17259 * r17259;
        double r17261 = r17260 * r17250;
        double r17262 = r17261 * r17250;
        double r17263 = r17258 * r17262;
        double r17264 = 1.0;
        double r17265 = r17264 - r17255;
        double r17266 = r17263 / r17265;
        double r17267 = r17253 - r17266;
        double r17268 = 4.5;
        double r17269 = r17267 - r17268;
        return r17269;
}
↓
double f(double v, double w, double r) {
        double r17270 = 3.0;
        double r17271 = 2.0;
        double r17272 = r;
        double r17273 = r17271 / r17272;
        double r17274 = r17273 / r17272;
        double r17275 = r17270 + r17274;
        double r17276 = 0.125;
        double r17277 = v;
        double r17278 = r17271 * r17277;
        double r17279 = r17270 - r17278;
        double r17280 = r17276 * r17279;
        double r17281 = 1.0;
        double r17282 = r17281 - r17277;
        double r17283 = w;
        double r17284 = r17283 * r17272;
        double r17285 = fabs(r17284);
        double r17286 = r17282 / r17285;
        double r17287 = r17286 / r17285;
        double r17288 = r17280 / r17287;
        double r17289 = r17275 - r17288;
        double r17290 = 4.5;
        double r17291 = r17289 - r17290;
        return r17291;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt13.2

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

  4. Simplified13.1

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

  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 associate-/l*0.4

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

  8. Simplified0.4

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

  10. Applied associate-/r*0.4

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

  12. Applied unpow20.4

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

  13. Applied associate-/r*0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 
(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))