Average Error: 12.9 → 0.5
Time: 7.6s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\frac{1}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \frac{\left|w \cdot r\right|}{\sqrt[3]{1}}\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{1}}{\sqrt[3]{1 - v}}\right) - 4.5\]
\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(\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\frac{1}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \frac{\left|w \cdot r\right|}{\sqrt[3]{1}}\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{1}}{\sqrt[3]{1 - v}}\right) - 4.5
double f(double v, double w, double r) {
        double r26287 = 3.0;
        double r26288 = 2.0;
        double r26289 = r;
        double r26290 = r26289 * r26289;
        double r26291 = r26288 / r26290;
        double r26292 = r26287 + r26291;
        double r26293 = 0.125;
        double r26294 = v;
        double r26295 = r26288 * r26294;
        double r26296 = r26287 - r26295;
        double r26297 = r26293 * r26296;
        double r26298 = w;
        double r26299 = r26298 * r26298;
        double r26300 = r26299 * r26289;
        double r26301 = r26300 * r26289;
        double r26302 = r26297 * r26301;
        double r26303 = 1.0;
        double r26304 = r26303 - r26294;
        double r26305 = r26302 / r26304;
        double r26306 = r26292 - r26305;
        double r26307 = 4.5;
        double r26308 = r26306 - r26307;
        return r26308;
}
↓
double f(double v, double w, double r) {
        double r26309 = 3.0;
        double r26310 = 2.0;
        double r26311 = r;
        double r26312 = r26311 * r26311;
        double r26313 = r26310 / r26312;
        double r26314 = r26309 + r26313;
        double r26315 = 0.125;
        double r26316 = v;
        double r26317 = r26310 * r26316;
        double r26318 = r26309 - r26317;
        double r26319 = r26315 * r26318;
        double r26320 = 1.0;
        double r26321 = 1.0;
        double r26322 = r26321 - r26316;
        double r26323 = cbrt(r26322);
        double r26324 = r26323 * r26323;
        double r26325 = r26320 / r26324;
        double r26326 = w;
        double r26327 = r26326 * r26311;
        double r26328 = fabs(r26327);
        double r26329 = cbrt(r26320);
        double r26330 = r26328 / r26329;
        double r26331 = r26325 * r26330;
        double r26332 = r26319 * r26331;
        double r26333 = pow(r26328, r26320);
        double r26334 = r26333 / r26323;
        double r26335 = r26332 * r26334;
        double r26336 = r26314 - r26335;
        double r26337 = 4.5;
        double r26338 = r26336 - r26337;
        return r26338;
}

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 12.9

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

  3. Applied add-sqr-sqrt13.0

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

  4. Simplified13.0

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

  5. Simplified6.8

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

  7. Applied add-cube-cbrt6.9

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

  8. Applied times-frac0.5

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

  9. Simplified0.5

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

  11. Applied *-un-lft-identity0.5

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

  12. Applied cbrt-prod0.5

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

  13. Applied sqr-pow0.5

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

  14. Applied times-frac0.5

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

  15. Applied associate-*r*0.5

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

  16. Simplified0.5

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

  18. Applied div-inv0.5

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

  19. Applied associate-*l*0.5

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

  20. Final simplification0.5

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

Reproduce

herbie shell --seed 2020046 
(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))