Average Error: 12.6 → 0.4
Time: 11.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{1}{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5\]
\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{1}{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5
double f(double v, double w, double r) {
        double r41891 = 3.0;
        double r41892 = 2.0;
        double r41893 = r;
        double r41894 = r41893 * r41893;
        double r41895 = r41892 / r41894;
        double r41896 = r41891 + r41895;
        double r41897 = 0.125;
        double r41898 = v;
        double r41899 = r41892 * r41898;
        double r41900 = r41891 - r41899;
        double r41901 = r41897 * r41900;
        double r41902 = w;
        double r41903 = r41902 * r41902;
        double r41904 = r41903 * r41893;
        double r41905 = r41904 * r41893;
        double r41906 = r41901 * r41905;
        double r41907 = 1.0;
        double r41908 = r41907 - r41898;
        double r41909 = r41906 / r41908;
        double r41910 = r41896 - r41909;
        double r41911 = 4.5;
        double r41912 = r41910 - r41911;
        return r41912;
}
↓
double f(double v, double w, double r) {
        double r41913 = 3.0;
        double r41914 = 2.0;
        double r41915 = r;
        double r41916 = r41914 / r41915;
        double r41917 = r41916 / r41915;
        double r41918 = r41913 + r41917;
        double r41919 = 1.0;
        double r41920 = 1.0;
        double r41921 = v;
        double r41922 = r41920 - r41921;
        double r41923 = 0.125;
        double r41924 = r41914 * r41921;
        double r41925 = r41913 - r41924;
        double r41926 = r41923 * r41925;
        double r41927 = r41922 / r41926;
        double r41928 = w;
        double r41929 = r41928 * r41915;
        double r41930 = fabs(r41929);
        double r41931 = 2.0;
        double r41932 = pow(r41930, r41931);
        double r41933 = r41927 / r41932;
        double r41934 = r41919 / r41933;
        double r41935 = r41918 - r41934;
        double r41936 = 4.5;
        double r41937 = r41935 - r41936;
        return r41937;
}

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 12.6

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

  3. Applied add-sqr-sqrt12.7

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

  4. Simplified12.6

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

  5. Simplified6.6

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

  7. Applied clear-num6.7

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

  8. Simplified0.4

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

  10. Applied associate-/r*0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020003 
(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))