Average Error: 11.9 → 0.3
Time: 25.3s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(r \cdot w\right) \cdot \frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{1 - v}{r \cdot w}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \left(r \cdot w\right) \cdot \frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{1 - v}{r \cdot w}}\right) - 4.5
double f(double v, double w, double r) {
        double r1593137 = 3.0;
        double r1593138 = 2.0;
        double r1593139 = r;
        double r1593140 = r1593139 * r1593139;
        double r1593141 = r1593138 / r1593140;
        double r1593142 = r1593137 + r1593141;
        double r1593143 = 0.125;
        double r1593144 = v;
        double r1593145 = r1593138 * r1593144;
        double r1593146 = r1593137 - r1593145;
        double r1593147 = r1593143 * r1593146;
        double r1593148 = w;
        double r1593149 = r1593148 * r1593148;
        double r1593150 = r1593149 * r1593139;
        double r1593151 = r1593150 * r1593139;
        double r1593152 = r1593147 * r1593151;
        double r1593153 = 1.0;
        double r1593154 = r1593153 - r1593144;
        double r1593155 = r1593152 / r1593154;
        double r1593156 = r1593142 - r1593155;
        double r1593157 = 4.5;
        double r1593158 = r1593156 - r1593157;
        return r1593158;
}
↓
double f(double v, double w, double r) {
        double r1593159 = 3.0;
        double r1593160 = 2.0;
        double r1593161 = r;
        double r1593162 = r1593160 / r1593161;
        double r1593163 = r1593162 / r1593161;
        double r1593164 = r1593159 + r1593163;
        double r1593165 = w;
        double r1593166 = r1593161 * r1593165;
        double r1593167 = 0.125;
        double r1593168 = v;
        double r1593169 = r1593168 * r1593160;
        double r1593170 = r1593159 - r1593169;
        double r1593171 = r1593167 * r1593170;
        double r1593172 = 1.0;
        double r1593173 = r1593172 - r1593168;
        double r1593174 = r1593173 / r1593166;
        double r1593175 = r1593171 / r1593174;
        double r1593176 = r1593166 * r1593175;
        double r1593177 = r1593164 - r1593176;
        double r1593178 = 4.5;
        double r1593179 = r1593177 - r1593178;
        return r1593179;
}

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 11.9

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

  2. Simplified0.3

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

  4. Applied associate-/r/0.3

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

  6. Applied associate-/r*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(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))