Average Error: 12.1 → 0.5
Time: 24.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \sqrt{\frac{\frac{2}{r}}{r}} \cdot \sqrt{\frac{\frac{2}{r}}{r}}\right) - \frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{\frac{\frac{1 - v}{w \cdot r}}{w \cdot r}}\right) - 4.5\]
\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 + \sqrt{\frac{\frac{2}{r}}{r}} \cdot \sqrt{\frac{\frac{2}{r}}{r}}\right) - \frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{\frac{\frac{1 - v}{w \cdot r}}{w \cdot r}}\right) - 4.5
double f(double v, double w, double r) {
        double r1539937 = 3.0;
        double r1539938 = 2.0;
        double r1539939 = r;
        double r1539940 = r1539939 * r1539939;
        double r1539941 = r1539938 / r1539940;
        double r1539942 = r1539937 + r1539941;
        double r1539943 = 0.125;
        double r1539944 = v;
        double r1539945 = r1539938 * r1539944;
        double r1539946 = r1539937 - r1539945;
        double r1539947 = r1539943 * r1539946;
        double r1539948 = w;
        double r1539949 = r1539948 * r1539948;
        double r1539950 = r1539949 * r1539939;
        double r1539951 = r1539950 * r1539939;
        double r1539952 = r1539947 * r1539951;
        double r1539953 = 1.0;
        double r1539954 = r1539953 - r1539944;
        double r1539955 = r1539952 / r1539954;
        double r1539956 = r1539942 - r1539955;
        double r1539957 = 4.5;
        double r1539958 = r1539956 - r1539957;
        return r1539958;
}
↓
double f(double v, double w, double r) {
        double r1539959 = 3.0;
        double r1539960 = 2.0;
        double r1539961 = r;
        double r1539962 = r1539960 / r1539961;
        double r1539963 = r1539962 / r1539961;
        double r1539964 = sqrt(r1539963);
        double r1539965 = r1539964 * r1539964;
        double r1539966 = r1539959 + r1539965;
        double r1539967 = v;
        double r1539968 = r1539960 * r1539967;
        double r1539969 = r1539959 - r1539968;
        double r1539970 = 0.125;
        double r1539971 = r1539969 * r1539970;
        double r1539972 = 1.0;
        double r1539973 = r1539972 - r1539967;
        double r1539974 = w;
        double r1539975 = r1539974 * r1539961;
        double r1539976 = r1539973 / r1539975;
        double r1539977 = r1539976 / r1539975;
        double r1539978 = r1539971 / r1539977;
        double r1539979 = r1539966 - r1539978;
        double r1539980 = 4.5;
        double r1539981 = r1539979 - r1539980;
        return r1539981;
}

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 12.1

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

  3. Applied associate-/l*8.5

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

  4. Simplified0.4

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

  6. Applied associate-/r*0.3

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

  8. Applied associate-/r*0.3

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

  10. Applied add-sqr-sqrt0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2019163 
(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))