Average Error: 12.6 → 12.6
Time: 2.3s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
\left(\left(3 + \frac{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{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
double code(double r, double v, double w) {
	return ((double) (((double) (((double) (3.0 + ((double) (2.0 / ((double) (r * r)))))) - ((double) (((double) (((double) (0.125 * ((double) (3.0 - ((double) (2.0 * v)))))) * ((double) (((double) (((double) (w * w)) * r)) * r)))) / ((double) (1.0 - v)))))) - 4.5));
}
↓
double code(double r, double v, double w) {
	return ((double) (((double) (((double) (3.0 + ((double) (2.0 / ((double) (r * r)))))) - ((double) (((double) (((double) (0.125 * ((double) (3.0 - ((double) (2.0 * v)))))) * ((double) (((double) (((double) (w * w)) * r)) * r)))) / ((double) (1.0 - v)))))) - 4.5));
}

Error

Bits error versus r

Bits error versus v

Bits error versus w

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. Final simplification12.6

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

Reproduce

herbie shell --seed 2020152 
(FPCore (r v w)
  :name "(- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5)"
  :precision binary64
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))