Average Error: 13.0 → 0.4
Time: 30.1s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{\frac{2}{r}}{r} - \left(\left(\sqrt{\frac{1}{\frac{1}{\sqrt{0.125}}}} \cdot \left(\left(\sqrt{\frac{3 - v \cdot 2}{\frac{1 - v}{0.125}}} \cdot \left(r \cdot w\right)\right) \cdot \sqrt{\frac{3 - v \cdot 2}{\frac{1 - v}{\sqrt{0.125}}}}\right)\right) \cdot \left(r \cdot w\right) - \left(3 - 4.5\right)\right)\]
\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
↓
\frac{\frac{2}{r}}{r} - \left(\left(\sqrt{\frac{1}{\frac{1}{\sqrt{0.125}}}} \cdot \left(\left(\sqrt{\frac{3 - v \cdot 2}{\frac{1 - v}{0.125}}} \cdot \left(r \cdot w\right)\right) \cdot \sqrt{\frac{3 - v \cdot 2}{\frac{1 - v}{\sqrt{0.125}}}}\right)\right) \cdot \left(r \cdot w\right) - \left(3 - 4.5\right)\right)
double f(double v, double w, double r) {
        double r2191958 = 3.0;
        double r2191959 = 2.0;
        double r2191960 = r;
        double r2191961 = r2191960 * r2191960;
        double r2191962 = r2191959 / r2191961;
        double r2191963 = r2191958 + r2191962;
        double r2191964 = 0.125;
        double r2191965 = v;
        double r2191966 = r2191959 * r2191965;
        double r2191967 = r2191958 - r2191966;
        double r2191968 = r2191964 * r2191967;
        double r2191969 = w;
        double r2191970 = r2191969 * r2191969;
        double r2191971 = r2191970 * r2191960;
        double r2191972 = r2191971 * r2191960;
        double r2191973 = r2191968 * r2191972;
        double r2191974 = 1.0;
        double r2191975 = r2191974 - r2191965;
        double r2191976 = r2191973 / r2191975;
        double r2191977 = r2191963 - r2191976;
        double r2191978 = 4.5;
        double r2191979 = r2191977 - r2191978;
        return r2191979;
}
↓
double f(double v, double w, double r) {
        double r2191980 = 2.0;
        double r2191981 = r;
        double r2191982 = r2191980 / r2191981;
        double r2191983 = r2191982 / r2191981;
        double r2191984 = 1.0;
        double r2191985 = 0.125;
        double r2191986 = sqrt(r2191985);
        double r2191987 = r2191984 / r2191986;
        double r2191988 = r2191984 / r2191987;
        double r2191989 = sqrt(r2191988);
        double r2191990 = 3.0;
        double r2191991 = v;
        double r2191992 = r2191991 * r2191980;
        double r2191993 = r2191990 - r2191992;
        double r2191994 = 1.0;
        double r2191995 = r2191994 - r2191991;
        double r2191996 = r2191995 / r2191985;
        double r2191997 = r2191993 / r2191996;
        double r2191998 = sqrt(r2191997);
        double r2191999 = w;
        double r2192000 = r2191981 * r2191999;
        double r2192001 = r2191998 * r2192000;
        double r2192002 = r2191995 / r2191986;
        double r2192003 = r2191993 / r2192002;
        double r2192004 = sqrt(r2192003);
        double r2192005 = r2192001 * r2192004;
        double r2192006 = r2191989 * r2192005;
        double r2192007 = r2192006 * r2192000;
        double r2192008 = 4.5;
        double r2192009 = r2191990 - r2192008;
        double r2192010 = r2192007 - r2192009;
        double r2192011 = r2191983 - r2192010;
        return r2192011;
}

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 13.0

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

  2. Simplified0.3

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

  4. Applied associate-/r*0.3

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

  6. Applied add-sqr-sqrt0.4

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

  7. Applied associate-*l*0.4

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

  9. Applied add-sqr-sqrt0.3

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

  10. Applied *-un-lft-identity0.3

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

  11. Applied times-frac0.3

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

  12. Applied *-un-lft-identity0.3

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

  13. Applied times-frac0.3

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

  14. Applied sqrt-prod0.4

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

  15. Applied associate-*l*0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))