Average Error: 14.7 → 12.2
Time: 1.8s
Precision: binary64
\[\left(6 \cdot v - \frac{\left(0.5 \cdot v\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 2.5\]
↓
\[v \cdot \left(6 - \frac{0.5}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) - 2.5\]
\left(6 \cdot v - \frac{\left(0.5 \cdot v\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 2.5
↓
v \cdot \left(6 - \frac{0.5}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) - 2.5
double code(double v, double w, double r) {
	return ((double) (((double) (((double) (6.0 * v)) - ((double) (((double) (((double) (0.5 * v)) * ((double) (((double) (((double) (w * w)) * r)) * r)))) / ((double) (1.0 - v)))))) - 2.5));
}
↓
double code(double v, double w, double r) {
	return ((double) (((double) (v * ((double) (6.0 - ((double) (0.5 / ((double) (((double) (1.0 - v)) / ((double) (((double) (((double) (w * w)) * r)) * r)))))))))) - 2.5));
}

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 14.7

    \[\left(6 \cdot v - \frac{\left(0.5 \cdot v\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 2.5\]

  2. Simplified12.2

    \[\leadsto \color{blue}{v \cdot \left(6 - \frac{0.5}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) - 2.5}\]

  3. Final simplification12.2

    \[\leadsto v \cdot \left(6 - \frac{0.5}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) - 2.5\]

Reproduce

herbie shell --seed 2020152 
(FPCore (v w r)
  :name "(- (- (* 6 v) (/ (* (* 0.5 v) (* (* (* w w) r) r)) (- 1 v))) 2.5)"
  :precision binary64
  (- (- (* 6.0 v) (/ (* (* 0.5 v) (* (* (* w w) r) r)) (- 1.0 v))) 2.5))