Average Error: 12.1 → 0.3
Time: 3.5m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{3 + -2 \cdot v}{1 - v} \cdot \left(\left(w \cdot r\right) \cdot \left(\left(w \cdot r\right) \cdot 0.125\right)\right)\]
\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
↓
\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{3 + -2 \cdot v}{1 - v} \cdot \left(\left(w \cdot r\right) \cdot \left(\left(w \cdot r\right) \cdot 0.125\right)\right)
double f(double v, double w, double r) {
        double r18262068 = 3.0;
        double r18262069 = 2.0;
        double r18262070 = r;
        double r18262071 = r18262070 * r18262070;
        double r18262072 = r18262069 / r18262071;
        double r18262073 = r18262068 + r18262072;
        double r18262074 = 0.125;
        double r18262075 = v;
        double r18262076 = r18262069 * r18262075;
        double r18262077 = r18262068 - r18262076;
        double r18262078 = r18262074 * r18262077;
        double r18262079 = w;
        double r18262080 = r18262079 * r18262079;
        double r18262081 = r18262080 * r18262070;
        double r18262082 = r18262081 * r18262070;
        double r18262083 = r18262078 * r18262082;
        double r18262084 = 1.0;
        double r18262085 = r18262084 - r18262075;
        double r18262086 = r18262083 / r18262085;
        double r18262087 = r18262073 - r18262086;
        double r18262088 = 4.5;
        double r18262089 = r18262087 - r18262088;
        return r18262089;
}
↓
double f(double v, double w, double r) {
        double r18262090 = 3.0;
        double r18262091 = 2.0;
        double r18262092 = r;
        double r18262093 = r18262091 / r18262092;
        double r18262094 = r18262093 / r18262092;
        double r18262095 = r18262090 + r18262094;
        double r18262096 = 4.5;
        double r18262097 = r18262095 - r18262096;
        double r18262098 = -2.0;
        double r18262099 = v;
        double r18262100 = r18262098 * r18262099;
        double r18262101 = r18262090 + r18262100;
        double r18262102 = 1.0;
        double r18262103 = r18262102 - r18262099;
        double r18262104 = r18262101 / r18262103;
        double r18262105 = w;
        double r18262106 = r18262105 * r18262092;
        double r18262107 = 0.125;
        double r18262108 = r18262106 * r18262107;
        double r18262109 = r18262106 * r18262108;
        double r18262110 = r18262104 * r18262109;
        double r18262111 = r18262097 - r18262110;
        return r18262111;
}

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. Simplified0.4

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

  4. Applied div-inv0.4

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

  5. Applied *-un-lft-identity0.4

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

  6. Applied times-frac0.4

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

  7. Simplified0.4

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

  8. Simplified0.3

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

  10. Applied associate-/r*0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019119 
(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))