Average Error: 12.5 → 0.4
Time: 9.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - {\left(\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\left|w \cdot r\right|}\right)}^{\left(-2\right)}\right) - 4.5\]
\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{2}{r \cdot r}\right) - {\left(\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\left|w \cdot r\right|}\right)}^{\left(-2\right)}\right) - 4.5
double f(double v, double w, double r) {
        double r30240 = 3.0;
        double r30241 = 2.0;
        double r30242 = r;
        double r30243 = r30242 * r30242;
        double r30244 = r30241 / r30243;
        double r30245 = r30240 + r30244;
        double r30246 = 0.125;
        double r30247 = v;
        double r30248 = r30241 * r30247;
        double r30249 = r30240 - r30248;
        double r30250 = r30246 * r30249;
        double r30251 = w;
        double r30252 = r30251 * r30251;
        double r30253 = r30252 * r30242;
        double r30254 = r30253 * r30242;
        double r30255 = r30250 * r30254;
        double r30256 = 1.0;
        double r30257 = r30256 - r30247;
        double r30258 = r30255 / r30257;
        double r30259 = r30245 - r30258;
        double r30260 = 4.5;
        double r30261 = r30259 - r30260;
        return r30261;
}
↓
double f(double v, double w, double r) {
        double r30262 = 3.0;
        double r30263 = 2.0;
        double r30264 = r;
        double r30265 = r30264 * r30264;
        double r30266 = r30263 / r30265;
        double r30267 = r30262 + r30266;
        double r30268 = 1.0;
        double r30269 = v;
        double r30270 = r30268 - r30269;
        double r30271 = 0.125;
        double r30272 = r30263 * r30269;
        double r30273 = r30262 - r30272;
        double r30274 = r30271 * r30273;
        double r30275 = r30270 / r30274;
        double r30276 = sqrt(r30275);
        double r30277 = w;
        double r30278 = r30277 * r30264;
        double r30279 = fabs(r30278);
        double r30280 = r30276 / r30279;
        double r30281 = 2.0;
        double r30282 = -r30281;
        double r30283 = pow(r30280, r30282);
        double r30284 = r30267 - r30283;
        double r30285 = 4.5;
        double r30286 = r30284 - r30285;
        return r30286;
}

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 12.5

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

  3. Applied add-sqr-sqrt12.5

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

  4. Simplified12.5

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

  5. Simplified6.7

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

  7. Applied clear-num6.7

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

  8. Simplified0.4

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

  10. Applied add-sqr-sqrt0.5

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

  11. Applied unpow-prod-down0.5

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

  12. Applied add-sqr-sqrt0.6

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

  13. Applied times-frac0.5

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

  14. Simplified0.4

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

  15. Simplified0.4

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

  17. Applied pow10.4

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

  18. Applied pow10.4

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

  19. Applied pow-prod-up0.4

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

  20. Applied pow-flip0.4

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

  21. Simplified0.4

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

  22. Final simplification0.4

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

Reproduce

herbie shell --seed 2020081 
(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))