Average Error: 12.7 → 0.3
Time: 23.7s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(\frac{1}{8} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{2}}{1 - v} + \frac{9}{2}\right)\]
\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
↓
\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(\frac{1}{8} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{2}}{1 - v} + \frac{9}{2}\right)
double f(double v, double w, double r) {
        double r31968 = 3.0;
        double r31969 = 2.0;
        double r31970 = r;
        double r31971 = r31970 * r31970;
        double r31972 = r31969 / r31971;
        double r31973 = r31968 + r31972;
        double r31974 = 0.125;
        double r31975 = v;
        double r31976 = r31969 * r31975;
        double r31977 = r31968 - r31976;
        double r31978 = r31974 * r31977;
        double r31979 = w;
        double r31980 = r31979 * r31979;
        double r31981 = r31980 * r31970;
        double r31982 = r31981 * r31970;
        double r31983 = r31978 * r31982;
        double r31984 = 1.0;
        double r31985 = r31984 - r31975;
        double r31986 = r31983 / r31985;
        double r31987 = r31973 - r31986;
        double r31988 = 4.5;
        double r31989 = r31987 - r31988;
        return r31989;
}
↓
double f(double v, double w, double r) {
        double r31990 = 3.0;
        double r31991 = 2.0;
        double r31992 = r;
        double r31993 = r31992 * r31992;
        double r31994 = r31991 / r31993;
        double r31995 = r31990 + r31994;
        double r31996 = 1.0;
        double r31997 = 8.0;
        double r31998 = r31996 / r31997;
        double r31999 = v;
        double r32000 = r31991 * r31999;
        double r32001 = r31990 - r32000;
        double r32002 = r31998 * r32001;
        double r32003 = w;
        double r32004 = r32003 * r31992;
        double r32005 = fabs(r32004);
        double r32006 = 2.0;
        double r32007 = pow(r32005, r32006);
        double r32008 = r31996 - r31999;
        double r32009 = r32007 / r32008;
        double r32010 = r32002 * r32009;
        double r32011 = 9.0;
        double r32012 = r32011 / r31991;
        double r32013 = r32010 + r32012;
        double r32014 = r31995 - r32013;
        return r32014;
}

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 12.7

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

  3. Applied add-sqr-sqrt12.8

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

  4. Simplified12.7

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

  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 *-un-lft-identity6.5

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

  8. Applied times-frac0.3

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

  9. Simplified0.3

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(\frac{1}{8} \cdot \left(3 - 2 \cdot v\right)\right)} \cdot \frac{\left|w \cdot r\right| \cdot \left|w \cdot r\right|}{1 - v}\right) - 4.5\]

  10. Simplified0.3

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

  12. Applied add-sqr-sqrt0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\sqrt{\left(\frac{1}{8} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{2}}{1 - v}} \cdot \sqrt{\left(\frac{1}{8} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{2}}{1 - v}}}\right) - 4.5\]

  13. Final simplification0.3

    \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - \left(\left(\frac{1}{8} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\left|w \cdot r\right|\right)}^{2}}{1 - v} + \frac{9}{2}\right)\]

Reproduce

herbie shell --seed 2019303 
(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))