Average Error: 12.3 → 0.4
Time: 5.8s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{1}{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5\]
\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{2}{r \cdot 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 r16911 = 3.0;
        double r16912 = 2.0;
        double r16913 = r;
        double r16914 = r16913 * r16913;
        double r16915 = r16912 / r16914;
        double r16916 = r16911 + r16915;
        double r16917 = 0.125;
        double r16918 = v;
        double r16919 = r16912 * r16918;
        double r16920 = r16911 - r16919;
        double r16921 = r16917 * r16920;
        double r16922 = w;
        double r16923 = r16922 * r16922;
        double r16924 = r16923 * r16913;
        double r16925 = r16924 * r16913;
        double r16926 = r16921 * r16925;
        double r16927 = 1.0;
        double r16928 = r16927 - r16918;
        double r16929 = r16926 / r16928;
        double r16930 = r16916 - r16929;
        double r16931 = 4.5;
        double r16932 = r16930 - r16931;
        return r16932;
}
↓
double f(double v, double w, double r) {
        double r16933 = 3.0;
        double r16934 = 2.0;
        double r16935 = r;
        double r16936 = r16935 * r16935;
        double r16937 = r16934 / r16936;
        double r16938 = r16933 + r16937;
        double r16939 = 1.0;
        double r16940 = 1.0;
        double r16941 = v;
        double r16942 = r16940 - r16941;
        double r16943 = 0.125;
        double r16944 = r16934 * r16941;
        double r16945 = r16933 - r16944;
        double r16946 = r16943 * r16945;
        double r16947 = r16942 / r16946;
        double r16948 = w;
        double r16949 = r16948 * r16935;
        double r16950 = fabs(r16949);
        double r16951 = 2.0;
        double r16952 = pow(r16950, r16951);
        double r16953 = r16947 / r16952;
        double r16954 = r16939 / r16953;
        double r16955 = r16938 - r16954;
        double r16956 = 4.5;
        double r16957 = r16955 - r16956;
        return r16957;
}

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 12.3

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

  3. Applied add-sqr-sqrt12.4

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

  4. Simplified12.4

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

  5. Simplified6.5

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

  7. Applied clear-num6.6

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020027 
(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))