Average Error: 12.5 → 0.4
Time: 6.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r14817 = 3.0;
        double r14818 = 2.0;
        double r14819 = r;
        double r14820 = r14819 * r14819;
        double r14821 = r14818 / r14820;
        double r14822 = r14817 + r14821;
        double r14823 = 0.125;
        double r14824 = v;
        double r14825 = r14818 * r14824;
        double r14826 = r14817 - r14825;
        double r14827 = r14823 * r14826;
        double r14828 = w;
        double r14829 = r14828 * r14828;
        double r14830 = r14829 * r14819;
        double r14831 = r14830 * r14819;
        double r14832 = r14827 * r14831;
        double r14833 = 1.0;
        double r14834 = r14833 - r14824;
        double r14835 = r14832 / r14834;
        double r14836 = r14822 - r14835;
        double r14837 = 4.5;
        double r14838 = r14836 - r14837;
        return r14838;
}
↓
double f(double v, double w, double r) {
        double r14839 = 3.0;
        double r14840 = 2.0;
        double r14841 = r;
        double r14842 = r14840 / r14841;
        double r14843 = r14842 / r14841;
        double r14844 = r14839 + r14843;
        double r14845 = 0.125;
        double r14846 = v;
        double r14847 = r14840 * r14846;
        double r14848 = r14839 - r14847;
        double r14849 = r14845 * r14848;
        double r14850 = w;
        double r14851 = r14850 * r14841;
        double r14852 = fabs(r14851);
        double r14853 = 1.0;
        double r14854 = r14853 - r14846;
        double r14855 = r14854 / r14852;
        double r14856 = r14852 / r14855;
        double r14857 = r14849 * r14856;
        double r14858 = r14844 - r14857;
        double r14859 = 4.5;
        double r14860 = r14858 - r14859;
        return r14860;
}

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 12.5

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

  3. Applied *-un-lft-identity12.5

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

  4. Applied times-frac8.1

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

  5. Simplified8.1

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

  7. Applied add-sqr-sqrt8.1

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

  8. Simplified8.1

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

  9. Simplified0.4

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

  11. Applied associate-/r*0.4

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

  13. Applied associate-/l*0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2020100 
(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))