Average Error: 12.8 → 0.5
Time: 6.3s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\frac{0.125 \cdot \left|\left|w \cdot r\right|\right|}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{3 - 2 \cdot v}}}{\frac{\sqrt[3]{1 - v}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5\]
\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) - \frac{\frac{0.125 \cdot \left|\left|w \cdot r\right|\right|}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{3 - 2 \cdot v}}}{\frac{\sqrt[3]{1 - v}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5
double f(double v, double w, double r) {
        double r20276 = 3.0;
        double r20277 = 2.0;
        double r20278 = r;
        double r20279 = r20278 * r20278;
        double r20280 = r20277 / r20279;
        double r20281 = r20276 + r20280;
        double r20282 = 0.125;
        double r20283 = v;
        double r20284 = r20277 * r20283;
        double r20285 = r20276 - r20284;
        double r20286 = r20282 * r20285;
        double r20287 = w;
        double r20288 = r20287 * r20287;
        double r20289 = r20288 * r20278;
        double r20290 = r20289 * r20278;
        double r20291 = r20286 * r20290;
        double r20292 = 1.0;
        double r20293 = r20292 - r20283;
        double r20294 = r20291 / r20293;
        double r20295 = r20281 - r20294;
        double r20296 = 4.5;
        double r20297 = r20295 - r20296;
        return r20297;
}
↓
double f(double v, double w, double r) {
        double r20298 = 3.0;
        double r20299 = 2.0;
        double r20300 = r;
        double r20301 = r20300 * r20300;
        double r20302 = r20299 / r20301;
        double r20303 = r20298 + r20302;
        double r20304 = 0.125;
        double r20305 = w;
        double r20306 = r20305 * r20300;
        double r20307 = fabs(r20306);
        double r20308 = fabs(r20307);
        double r20309 = r20304 * r20308;
        double r20310 = 1.0;
        double r20311 = v;
        double r20312 = r20310 - r20311;
        double r20313 = cbrt(r20312);
        double r20314 = r20313 * r20313;
        double r20315 = r20299 * r20311;
        double r20316 = r20298 - r20315;
        double r20317 = r20314 / r20316;
        double r20318 = r20309 / r20317;
        double r20319 = 2.0;
        double r20320 = pow(r20307, r20319);
        double r20321 = sqrt(r20320);
        double r20322 = r20313 / r20321;
        double r20323 = r20318 / r20322;
        double r20324 = r20303 - r20323;
        double r20325 = 4.5;
        double r20326 = r20324 - r20325;
        return r20326;
}

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 12.8

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

  3. Applied add-sqr-sqrt12.8

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

  4. Simplified12.8

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

  5. Simplified6.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left|w \cdot r\right| \cdot \color{blue}{\left|w \cdot r\right|}\right)}{1 - v}\right) - 4.5\]
  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 add-sqr-sqrt0.4

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

  11. Applied add-cube-cbrt0.5

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

  12. Applied times-frac0.5

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

  13. Applied associate-/r*0.5

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

  14. Simplified0.5

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

  15. Final simplification0.5

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

Reproduce

herbie shell --seed 2020059 
(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))