Average Error: 12.9 → 0.3
Time: 29.3s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{2}{r \cdot r} - \left(\left(r \cdot w\right) \cdot \left(\left(\frac{1}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)\right) \cdot \left(r \cdot w\right)\right) - \left(3 - 4.5\right)\right)\]
\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{2}{r \cdot r} - \left(\left(r \cdot w\right) \cdot \left(\left(\frac{1}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)\right) \cdot \left(r \cdot w\right)\right) - \left(3 - 4.5\right)\right)
double f(double v, double w, double r) {
        double r1566987 = 3.0;
        double r1566988 = 2.0;
        double r1566989 = r;
        double r1566990 = r1566989 * r1566989;
        double r1566991 = r1566988 / r1566990;
        double r1566992 = r1566987 + r1566991;
        double r1566993 = 0.125;
        double r1566994 = v;
        double r1566995 = r1566988 * r1566994;
        double r1566996 = r1566987 - r1566995;
        double r1566997 = r1566993 * r1566996;
        double r1566998 = w;
        double r1566999 = r1566998 * r1566998;
        double r1567000 = r1566999 * r1566989;
        double r1567001 = r1567000 * r1566989;
        double r1567002 = r1566997 * r1567001;
        double r1567003 = 1.0;
        double r1567004 = r1567003 - r1566994;
        double r1567005 = r1567002 / r1567004;
        double r1567006 = r1566992 - r1567005;
        double r1567007 = 4.5;
        double r1567008 = r1567006 - r1567007;
        return r1567008;
}
↓
double f(double v, double w, double r) {
        double r1567009 = 2.0;
        double r1567010 = r;
        double r1567011 = r1567010 * r1567010;
        double r1567012 = r1567009 / r1567011;
        double r1567013 = w;
        double r1567014 = r1567010 * r1567013;
        double r1567015 = 1.0;
        double r1567016 = 1.0;
        double r1567017 = v;
        double r1567018 = r1567016 - r1567017;
        double r1567019 = r1567015 / r1567018;
        double r1567020 = 0.125;
        double r1567021 = 3.0;
        double r1567022 = r1567009 * r1567017;
        double r1567023 = r1567021 - r1567022;
        double r1567024 = r1567020 * r1567023;
        double r1567025 = r1567019 * r1567024;
        double r1567026 = r1567025 * r1567014;
        double r1567027 = r1567014 * r1567026;
        double r1567028 = 4.5;
        double r1567029 = r1567021 - r1567028;
        double r1567030 = r1567027 - r1567029;
        double r1567031 = r1567012 - r1567030;
        return r1567031;
}

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 12.9

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

  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 div-inv0.3

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

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

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(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))