Average Error: 12.4 → 0.4
Time: 23.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{1 - v}{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{1 - v}{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}}\right) - 4.5
double f(double v, double w, double r) {
        double r1645836 = 3.0;
        double r1645837 = 2.0;
        double r1645838 = r;
        double r1645839 = r1645838 * r1645838;
        double r1645840 = r1645837 / r1645839;
        double r1645841 = r1645836 + r1645840;
        double r1645842 = 0.125;
        double r1645843 = v;
        double r1645844 = r1645837 * r1645843;
        double r1645845 = r1645836 - r1645844;
        double r1645846 = r1645842 * r1645845;
        double r1645847 = w;
        double r1645848 = r1645847 * r1645847;
        double r1645849 = r1645848 * r1645838;
        double r1645850 = r1645849 * r1645838;
        double r1645851 = r1645846 * r1645850;
        double r1645852 = 1.0;
        double r1645853 = r1645852 - r1645843;
        double r1645854 = r1645851 / r1645853;
        double r1645855 = r1645841 - r1645854;
        double r1645856 = 4.5;
        double r1645857 = r1645855 - r1645856;
        return r1645857;
}
↓
double f(double v, double w, double r) {
        double r1645858 = 3.0;
        double r1645859 = 2.0;
        double r1645860 = r;
        double r1645861 = r1645859 / r1645860;
        double r1645862 = r1645861 / r1645860;
        double r1645863 = r1645858 + r1645862;
        double r1645864 = 0.125;
        double r1645865 = v;
        double r1645866 = r1645865 * r1645859;
        double r1645867 = r1645858 - r1645866;
        double r1645868 = r1645864 * r1645867;
        double r1645869 = 1.0;
        double r1645870 = r1645869 - r1645865;
        double r1645871 = w;
        double r1645872 = r1645860 * r1645871;
        double r1645873 = r1645872 * r1645872;
        double r1645874 = r1645870 / r1645873;
        double r1645875 = r1645868 / r1645874;
        double r1645876 = r1645863 - r1645875;
        double r1645877 = 4.5;
        double r1645878 = r1645876 - r1645877;
        return r1645878;
}

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 12.4

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

  2. Simplified0.3

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

  4. Applied div-inv0.4

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

  5. Applied associate-/l*0.4

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

  6. Simplified0.4

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

  8. Applied associate-/r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019168 
(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))