Average Error: 12.5 → 0.3
Time: 20.9s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{2}{r \cdot r} + \left(-1.5 - \frac{{\left(\left|r \cdot w\right|\right)}^{2}}{1 - v} \cdot \left(0.375 + v \cdot -0.25\right)\right)\]
\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
↓
\frac{2}{r \cdot r} + \left(-1.5 - \frac{{\left(\left|r \cdot w\right|\right)}^{2}}{1 - v} \cdot \left(0.375 + v \cdot -0.25\right)\right)
(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 (* (/ (pow (fabs (* r w)) 2.0) (- 1.0 v)) (+ 0.375 (* v -0.25))))))
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 - ((pow(fabs(r * w), 2.0) / (1.0 - v)) * (0.375 + (v * -0.25))));
}

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 12.5

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

  2. Simplified8.1

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

  4. Applied add-sqr-sqrt_binary648.2

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

  5. Simplified8.1

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

  6. Simplified0.3

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

  8. Applied pow2_binary640.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2021032 
(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))