Average Error: 12.2 → 0.3
Time: 28.1s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{\frac{2}{r}}{r} - \left(\left(4.5 + \left(\frac{\left(3 - v \cdot 2\right) \cdot 0.125}{1 - v} \cdot \left(r \cdot w\right)\right) \cdot \left(r \cdot w\right)\right) - 3\right)\]
\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
↓
\frac{\frac{2}{r}}{r} - \left(\left(4.5 + \left(\frac{\left(3 - v \cdot 2\right) \cdot 0.125}{1 - v} \cdot \left(r \cdot w\right)\right) \cdot \left(r \cdot w\right)\right) - 3\right)
double f(double v, double w, double r) {
        double r1025867 = 3.0;
        double r1025868 = 2.0;
        double r1025869 = r;
        double r1025870 = r1025869 * r1025869;
        double r1025871 = r1025868 / r1025870;
        double r1025872 = r1025867 + r1025871;
        double r1025873 = 0.125;
        double r1025874 = v;
        double r1025875 = r1025868 * r1025874;
        double r1025876 = r1025867 - r1025875;
        double r1025877 = r1025873 * r1025876;
        double r1025878 = w;
        double r1025879 = r1025878 * r1025878;
        double r1025880 = r1025879 * r1025869;
        double r1025881 = r1025880 * r1025869;
        double r1025882 = r1025877 * r1025881;
        double r1025883 = 1.0;
        double r1025884 = r1025883 - r1025874;
        double r1025885 = r1025882 / r1025884;
        double r1025886 = r1025872 - r1025885;
        double r1025887 = 4.5;
        double r1025888 = r1025886 - r1025887;
        return r1025888;
}
↓
double f(double v, double w, double r) {
        double r1025889 = 2.0;
        double r1025890 = r;
        double r1025891 = r1025889 / r1025890;
        double r1025892 = r1025891 / r1025890;
        double r1025893 = 4.5;
        double r1025894 = 3.0;
        double r1025895 = v;
        double r1025896 = r1025895 * r1025889;
        double r1025897 = r1025894 - r1025896;
        double r1025898 = 0.125;
        double r1025899 = r1025897 * r1025898;
        double r1025900 = 1.0;
        double r1025901 = r1025900 - r1025895;
        double r1025902 = r1025899 / r1025901;
        double r1025903 = w;
        double r1025904 = r1025890 * r1025903;
        double r1025905 = r1025902 * r1025904;
        double r1025906 = r1025905 * r1025904;
        double r1025907 = r1025893 + r1025906;
        double r1025908 = r1025907 - r1025894;
        double r1025909 = r1025892 - r1025908;
        return r1025909;
}

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 12.2

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

  2. Simplified0.3

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

  4. Applied clear-num0.3

    \[\leadsto \frac{2}{r \cdot r} - \left(\mathsf{fma}\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right), \color{blue}{\frac{1}{\frac{1 - v}{\left(3 - 2 \cdot v\right) \cdot 0.125}}}, 4.5\right) - 3\right)\]
  5. Using strategy rm

  6. Applied associate-/r*0.3

    \[\leadsto \color{blue}{\frac{\frac{2}{r}}{r}} - \left(\mathsf{fma}\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right), \frac{1}{\frac{1 - v}{\left(3 - 2 \cdot v\right) \cdot 0.125}}, 4.5\right) - 3\right)\]
  7. Using strategy rm

  8. Applied fma-udef0.3

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

  9. Simplified0.3

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

  11. Applied associate-*l*0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))