Average Error: 12.8 → 2.9
Time: 17.1s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 - v \cdot 0.25\right) \cdot \frac{r}{\frac{\frac{1 - v}{r \cdot w}}{w}}\]
\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(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 - v \cdot 0.25\right) \cdot \frac{r}{\frac{\frac{1 - v}{r \cdot w}}{w}}
(FPCore (v w r)
 :precision binary64
 (-
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v)))
  4.5))
↓
(FPCore (v w r)
 :precision binary64
 (-
  (+ (/ 2.0 (* r r)) -1.5)
  (* (- 0.375 (* v 0.25)) (/ r (/ (/ (- 1.0 v) (* r w)) w)))))
double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}
↓
double code(double v, double w, double r) {
	return ((2.0 / (r * r)) + -1.5) - ((0.375 - (v * 0.25)) * (r / (((1.0 - v) / (r * w)) / w)));
}

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. Simplified8.7

    \[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 - v \cdot 0.25\right) \cdot \frac{r}{\frac{1 - v}{r \cdot \left(w \cdot w\right)}}}\]
  3. Using strategy rm

  4. Applied associate-*r*_binary644.0

    \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 - v \cdot 0.25\right) \cdot \frac{r}{\frac{1 - v}{\color{blue}{\left(r \cdot w\right) \cdot w}}}\]
  5. Using strategy rm

  6. Applied associate-/r*_binary642.9

    \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 - v \cdot 0.25\right) \cdot \frac{r}{\color{blue}{\frac{\frac{1 - v}{r \cdot w}}{w}}}\]

  7. Final simplification2.9

    \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 - v \cdot 0.25\right) \cdot \frac{r}{\frac{\frac{1 - v}{r \cdot w}}{w}}\]

Reproduce

herbie shell --seed 2020231 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))