Average Error: 12.6 → 0.2
Time: 7.6s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
↓
\[\left(\left(3 + 2 \cdot {r}^{-2}\right) - \frac{3 - 2 \cdot v}{\frac{\left(1 - v\right) \cdot {\left(r \cdot w\right)}^{-2}}{0.125}}\right) - 4.5 \]
\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 + 2 \cdot {r}^{-2}\right) - \frac{3 - 2 \cdot v}{\frac{\left(1 - v\right) \cdot {\left(r \cdot w\right)}^{-2}}{0.125}}\right) - 4.5

(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
 (-
  (-
   (+ 3.0 (* 2.0 (pow r -2.0)))
   (/ (- 3.0 (* 2.0 v)) (/ (* (- 1.0 v) (pow (* r w) -2.0)) 0.125)))
  4.5))
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 ((3.0 + (2.0 * pow(r, -2.0))) - ((3.0 - (2.0 * v)) / (((1.0 - v) * pow((r * w), -2.0)) / 0.125))) - 4.5;
}

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 12.6

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

  2. Applied egg-rr0.4

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

  3. Applied egg-rr0.3

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

  4. Applied egg-rr0.3

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

  5. Applied egg-rr0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2022129 
(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))