Average Error: 12.9 → 0.3
Time: 20.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(0.125 \cdot \left|w \cdot r\right|\right) \cdot \frac{3 - 2 \cdot v}{1 - v}\right) \cdot \left|w \cdot r\right|\right) - 4.5\]
\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{2}{r \cdot r}\right) - \left(\left(0.125 \cdot \left|w \cdot r\right|\right) \cdot \frac{3 - 2 \cdot v}{1 - v}\right) \cdot \left|w \cdot r\right|\right) - 4.5
double f(double v, double w, double r) {
        double r27057 = 3.0;
        double r27058 = 2.0;
        double r27059 = r;
        double r27060 = r27059 * r27059;
        double r27061 = r27058 / r27060;
        double r27062 = r27057 + r27061;
        double r27063 = 0.125;
        double r27064 = v;
        double r27065 = r27058 * r27064;
        double r27066 = r27057 - r27065;
        double r27067 = r27063 * r27066;
        double r27068 = w;
        double r27069 = r27068 * r27068;
        double r27070 = r27069 * r27059;
        double r27071 = r27070 * r27059;
        double r27072 = r27067 * r27071;
        double r27073 = 1.0;
        double r27074 = r27073 - r27064;
        double r27075 = r27072 / r27074;
        double r27076 = r27062 - r27075;
        double r27077 = 4.5;
        double r27078 = r27076 - r27077;
        return r27078;
}
↓
double f(double v, double w, double r) {
        double r27079 = 3.0;
        double r27080 = 2.0;
        double r27081 = r;
        double r27082 = r27081 * r27081;
        double r27083 = r27080 / r27082;
        double r27084 = r27079 + r27083;
        double r27085 = 0.125;
        double r27086 = w;
        double r27087 = r27086 * r27081;
        double r27088 = fabs(r27087);
        double r27089 = r27085 * r27088;
        double r27090 = v;
        double r27091 = r27080 * r27090;
        double r27092 = r27079 - r27091;
        double r27093 = 1.0;
        double r27094 = r27093 - r27090;
        double r27095 = r27092 / r27094;
        double r27096 = r27089 * r27095;
        double r27097 = r27096 * r27088;
        double r27098 = r27084 - r27097;
        double r27099 = 4.5;
        double r27100 = r27098 - r27099;
        return r27100;
}

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-sqrt12.9

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

  4. Simplified12.9

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

  5. Simplified6.9

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left|w \cdot r\right| \cdot \color{blue}{\left|w \cdot r\right|}\right)}{1 - v}\right) - 4.5\]
  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-sqrt0.6

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

  11. Applied unpow-prod-down0.6

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

  12. Applied *-un-lft-identity0.6

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

  13. Applied times-frac0.5

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

  14. Applied times-frac0.5

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

  15. Simplified0.4

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

  16. Simplified0.3

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

  18. Applied associate-/r/0.3

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

  19. Applied associate-*r*0.3

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

  20. Final simplification0.3

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

Reproduce

herbie shell --seed 2019298 
(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))