Average Error: 12.8 → 0.3
Time: 12.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \le -6.832602897595849 \cdot 10^{-9} \lor \neg \left(r \le 3.482628925649384 \cdot 10^{139}\right):\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}\right) - 4.5\\ \end{array}\]
\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
↓
\begin{array}{l}
\mathbf{if}\;r \le -6.832602897595849 \cdot 10^{-9} \lor \neg \left(r \le 3.482628925649384 \cdot 10^{139}\right):\\
\;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)\right) - 4.5\\

\mathbf{else}:\\
\;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}\right) - 4.5\\

\end{array}
double f(double v, double w, double r) {
        double r16961 = 3.0;
        double r16962 = 2.0;
        double r16963 = r;
        double r16964 = r16963 * r16963;
        double r16965 = r16962 / r16964;
        double r16966 = r16961 + r16965;
        double r16967 = 0.125;
        double r16968 = v;
        double r16969 = r16962 * r16968;
        double r16970 = r16961 - r16969;
        double r16971 = r16967 * r16970;
        double r16972 = w;
        double r16973 = r16972 * r16972;
        double r16974 = r16973 * r16963;
        double r16975 = r16974 * r16963;
        double r16976 = r16971 * r16975;
        double r16977 = 1.0;
        double r16978 = r16977 - r16968;
        double r16979 = r16976 / r16978;
        double r16980 = r16966 - r16979;
        double r16981 = 4.5;
        double r16982 = r16980 - r16981;
        return r16982;
}
↓
double f(double v, double w, double r) {
        double r16983 = r;
        double r16984 = -6.832602897595849e-09;
        bool r16985 = r16983 <= r16984;
        double r16986 = 3.482628925649384e+139;
        bool r16987 = r16983 <= r16986;
        double r16988 = !r16987;
        bool r16989 = r16985 || r16988;
        double r16990 = 3.0;
        double r16991 = 2.0;
        double r16992 = r16991 / r16983;
        double r16993 = r16992 / r16983;
        double r16994 = r16990 + r16993;
        double r16995 = 0.125;
        double r16996 = v;
        double r16997 = r16991 * r16996;
        double r16998 = r16990 - r16997;
        double r16999 = r16995 * r16998;
        double r17000 = 1.0;
        double r17001 = r17000 - r16996;
        double r17002 = r16999 / r17001;
        double r17003 = w;
        double r17004 = r17003 * r16983;
        double r17005 = r17003 * r17004;
        double r17006 = r17005 * r16983;
        double r17007 = r17002 * r17006;
        double r17008 = r16994 - r17007;
        double r17009 = 4.5;
        double r17010 = r17008 - r17009;
        double r17011 = r17004 * r16983;
        double r17012 = r17003 * r17011;
        double r17013 = r17001 / r17012;
        double r17014 = r16999 / r17013;
        double r17015 = r16994 - r17014;
        double r17016 = r17015 - r17009;
        double r17017 = r16989 ? r17010 : r17016;
        return r17017;
}

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. Split input into 2 regimes

  2. if r < -6.832602897595849e-09 or 3.482628925649384e+139 < r

    1. Initial program 17.3

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

    3. Applied associate-*l*9.0

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

    5. Applied associate-/l*0.3

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

    7. Applied associate-/r*0.3

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

    9. Applied associate-/r/0.2

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

    if -6.832602897595849e-09 < r < 3.482628925649384e+139

    1. Initial program 10.1

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

    3. Applied associate-*l*7.7

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

    5. Applied associate-/l*4.0

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

    7. Applied associate-/r*4.0

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

    9. Applied associate-*l*0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \le -6.832602897595849 \cdot 10^{-9} \lor \neg \left(r \le 3.482628925649384 \cdot 10^{139}\right):\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}\right) - 4.5\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))