Average Error: 12.1 → 0.4
Time: 4.8m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{\frac{1 - v}{r \cdot w}}{r \cdot w}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{\frac{1 - v}{r \cdot w}}{r \cdot w}}\right) - 4.5
double f(double v, double w, double r) {
        double r12068875 = 3.0;
        double r12068876 = 2.0;
        double r12068877 = r;
        double r12068878 = r12068877 * r12068877;
        double r12068879 = r12068876 / r12068878;
        double r12068880 = r12068875 + r12068879;
        double r12068881 = 0.125;
        double r12068882 = v;
        double r12068883 = r12068876 * r12068882;
        double r12068884 = r12068875 - r12068883;
        double r12068885 = r12068881 * r12068884;
        double r12068886 = w;
        double r12068887 = r12068886 * r12068886;
        double r12068888 = r12068887 * r12068877;
        double r12068889 = r12068888 * r12068877;
        double r12068890 = r12068885 * r12068889;
        double r12068891 = 1.0;
        double r12068892 = r12068891 - r12068882;
        double r12068893 = r12068890 / r12068892;
        double r12068894 = r12068880 - r12068893;
        double r12068895 = 4.5;
        double r12068896 = r12068894 - r12068895;
        return r12068896;
}
↓
double f(double v, double w, double r) {
        double r12068897 = 3.0;
        double r12068898 = 2.0;
        double r12068899 = r;
        double r12068900 = r12068898 / r12068899;
        double r12068901 = r12068900 / r12068899;
        double r12068902 = r12068897 + r12068901;
        double r12068903 = 0.125;
        double r12068904 = v;
        double r12068905 = r12068904 * r12068898;
        double r12068906 = r12068897 - r12068905;
        double r12068907 = r12068903 * r12068906;
        double r12068908 = 1.0;
        double r12068909 = r12068908 - r12068904;
        double r12068910 = w;
        double r12068911 = r12068899 * r12068910;
        double r12068912 = r12068909 / r12068911;
        double r12068913 = r12068912 / r12068911;
        double r12068914 = r12068907 / r12068913;
        double r12068915 = r12068902 - r12068914;
        double r12068916 = 4.5;
        double r12068917 = r12068915 - r12068916;
        return r12068917;
}

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 12.1

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

  2. Simplified0.4

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

  4. Applied associate-/r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019158 
(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))