Average Error: 12.8 → 0.4
Time: 21.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({\left(\left|w \cdot r\right|\right)}^{2} \cdot \frac{1}{1 - v}\right)\right) - 4.5\]
\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) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({\left(\left|w \cdot r\right|\right)}^{2} \cdot \frac{1}{1 - v}\right)\right) - 4.5
double f(double v, double w, double r) {
        double r24004 = 3.0;
        double r24005 = 2.0;
        double r24006 = r;
        double r24007 = r24006 * r24006;
        double r24008 = r24005 / r24007;
        double r24009 = r24004 + r24008;
        double r24010 = 0.125;
        double r24011 = v;
        double r24012 = r24005 * r24011;
        double r24013 = r24004 - r24012;
        double r24014 = r24010 * r24013;
        double r24015 = w;
        double r24016 = r24015 * r24015;
        double r24017 = r24016 * r24006;
        double r24018 = r24017 * r24006;
        double r24019 = r24014 * r24018;
        double r24020 = 1.0;
        double r24021 = r24020 - r24011;
        double r24022 = r24019 / r24021;
        double r24023 = r24009 - r24022;
        double r24024 = 4.5;
        double r24025 = r24023 - r24024;
        return r24025;
}
↓
double f(double v, double w, double r) {
        double r24026 = 3.0;
        double r24027 = 2.0;
        double r24028 = r;
        double r24029 = r24028 * r24028;
        double r24030 = r24027 / r24029;
        double r24031 = r24026 + r24030;
        double r24032 = 0.125;
        double r24033 = v;
        double r24034 = r24027 * r24033;
        double r24035 = r24026 - r24034;
        double r24036 = r24032 * r24035;
        double r24037 = w;
        double r24038 = r24037 * r24028;
        double r24039 = fabs(r24038);
        double r24040 = 2.0;
        double r24041 = pow(r24039, r24040);
        double r24042 = 1.0;
        double r24043 = 1.0;
        double r24044 = r24043 - r24033;
        double r24045 = r24042 / r24044;
        double r24046 = r24041 * r24045;
        double r24047 = r24036 * r24046;
        double r24048 = r24031 - r24047;
        double r24049 = 4.5;
        double r24050 = r24048 - r24049;
        return r24050;
}

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 12.8

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

  3. Applied add-sqr-sqrt12.9

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

  4. Simplified12.8

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

  5. Simplified6.9

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

  7. Applied *-un-lft-identity6.9

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  12. Applied div-inv0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019326 
(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))