Average Error: 12.8 → 0.3
Time: 10.8s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left|r \cdot w\right| \cdot \left|r \cdot w\right|}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left|r \cdot w\right| \cdot \left|r \cdot w\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r16223 = 3.0;
        double r16224 = 2.0;
        double r16225 = r;
        double r16226 = r16225 * r16225;
        double r16227 = r16224 / r16226;
        double r16228 = r16223 + r16227;
        double r16229 = 0.125;
        double r16230 = v;
        double r16231 = r16224 * r16230;
        double r16232 = r16223 - r16231;
        double r16233 = r16229 * r16232;
        double r16234 = w;
        double r16235 = r16234 * r16234;
        double r16236 = r16235 * r16225;
        double r16237 = r16236 * r16225;
        double r16238 = r16233 * r16237;
        double r16239 = 1.0;
        double r16240 = r16239 - r16230;
        double r16241 = r16238 / r16240;
        double r16242 = r16228 - r16241;
        double r16243 = 4.5;
        double r16244 = r16242 - r16243;
        return r16244;
}
↓
double f(double v, double w, double r) {
        double r16245 = 3.0;
        double r16246 = 2.0;
        double r16247 = r;
        double r16248 = r16246 / r16247;
        double r16249 = r16248 / r16247;
        double r16250 = r16245 + r16249;
        double r16251 = 0.125;
        double r16252 = v;
        double r16253 = r16246 * r16252;
        double r16254 = r16245 - r16253;
        double r16255 = r16251 * r16254;
        double r16256 = 1.0;
        double r16257 = r16256 - r16252;
        double r16258 = w;
        double r16259 = r16247 * r16258;
        double r16260 = fabs(r16259);
        double r16261 = r16260 * r16260;
        double r16262 = r16257 / r16261;
        double r16263 = r16255 / r16262;
        double r16264 = r16250 - r16263;
        double r16265 = 4.5;
        double r16266 = r16264 - r16265;
        return r16266;
}

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 associate-*l*8.1

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

  5. Applied associate-/l*2.6

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

  7. Applied associate-/r*2.6

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

  9. Applied add-sqr-sqrt2.6

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

  10. Simplified2.6

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))