Average Error: 11.6 → 0.4
Time: 34.2s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}} + \left(3 - 4.5\right)\right) - \left(w \cdot r\right) \cdot \frac{w \cdot r}{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}\]
\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(\sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}} + \left(3 - 4.5\right)\right) - \left(w \cdot r\right) \cdot \frac{w \cdot r}{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}
double f(double v, double w, double r) {
        double r1649810 = 3.0;
        double r1649811 = 2.0;
        double r1649812 = r;
        double r1649813 = r1649812 * r1649812;
        double r1649814 = r1649811 / r1649813;
        double r1649815 = r1649810 + r1649814;
        double r1649816 = 0.125;
        double r1649817 = v;
        double r1649818 = r1649811 * r1649817;
        double r1649819 = r1649810 - r1649818;
        double r1649820 = r1649816 * r1649819;
        double r1649821 = w;
        double r1649822 = r1649821 * r1649821;
        double r1649823 = r1649822 * r1649812;
        double r1649824 = r1649823 * r1649812;
        double r1649825 = r1649820 * r1649824;
        double r1649826 = 1.0;
        double r1649827 = r1649826 - r1649817;
        double r1649828 = r1649825 / r1649827;
        double r1649829 = r1649815 - r1649828;
        double r1649830 = 4.5;
        double r1649831 = r1649829 - r1649830;
        return r1649831;
}
↓
double f(double v, double w, double r) {
        double r1649832 = 2.0;
        double r1649833 = r;
        double r1649834 = r1649833 * r1649833;
        double r1649835 = r1649832 / r1649834;
        double r1649836 = sqrt(r1649835);
        double r1649837 = r1649836 * r1649836;
        double r1649838 = 3.0;
        double r1649839 = 4.5;
        double r1649840 = r1649838 - r1649839;
        double r1649841 = r1649837 + r1649840;
        double r1649842 = w;
        double r1649843 = r1649842 * r1649833;
        double r1649844 = 1.0;
        double r1649845 = v;
        double r1649846 = r1649844 - r1649845;
        double r1649847 = r1649845 * r1649832;
        double r1649848 = r1649838 - r1649847;
        double r1649849 = 0.125;
        double r1649850 = r1649848 * r1649849;
        double r1649851 = r1649846 / r1649850;
        double r1649852 = r1649843 / r1649851;
        double r1649853 = r1649843 * r1649852;
        double r1649854 = r1649841 - r1649853;
        return r1649854;
}

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 11.6

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

  2. Simplified0.3

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

  4. Applied associate-/r/0.3

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

  6. Applied associate-/l/0.3

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

  8. Applied add-sqr-sqrt0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019151 
(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))