(+ (+ (/ (* x (+ j 1)) n) (/ (* y (+ j 2)) (- n 1))) (/ (* z (+ j 3)) (- n 2)))

Average Error: 7.6 → 7.6

Time: 1.9s

Precision: binary64

Math

\[\left(\frac{x \cdot \left(j + 1\right)}{n} + \frac{y \cdot \left(j + 2\right)}{n - 1}\right) + \frac{z \cdot \left(j + 3\right)}{n - 2}\]

↓

\[\left(\frac{x \cdot \left(j + 1\right)}{n} + \frac{y \cdot \left(j + 2\right)}{n - 1}\right) + \frac{z \cdot \left(j + 3\right)}{n - 2}\]

C

double code(double x, double j, double n, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * ((double) (j + 1.0)))) / n)) + ((double) (((double) (y * ((double) (j + 2.0)))) / ((double) (n - 1.0)))))) + ((double) (((double) (z * ((double) (j + 3.0)))) / ((double) (n - 2.0))))));
}

↓

double code(double x, double j, double n, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * ((double) (j + 1.0)))) / n)) + ((double) (((double) (y * ((double) (j + 2.0)))) / ((double) (n - 1.0)))))) + ((double) (((double) (z * ((double) (j + 3.0)))) / ((double) (n - 2.0))))));
}

Error

Bits error versus x

Bits error versus j

Bits error versus n

Bits error versus y

Bits error versus z

Derivation

1. Initial program 7.6

   \[\left(\frac{x \cdot \left(j + 1\right)}{n} + \frac{y \cdot \left(j + 2\right)}{n - 1}\right) + \frac{z \cdot \left(j + 3\right)}{n - 2}\]

2. Final simplification 7.6

   \[\leadsto \left(\frac{x \cdot \left(j + 1\right)}{n} + \frac{y \cdot \left(j + 2\right)}{n - 1}\right) + \frac{z \cdot \left(j + 3\right)}{n - 2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x j n y z)
  :name "(+ (+ (/ (* x (+ j 1)) n) (/ (* y (+ j 2)) (- n 1))) (/ (* z (+ j 3)) (- n 2)))"
  :precision binary64
  (+ (+ (/ (* x (+ j 1.0)) n) (/ (* y (+ j 2.0)) (- n 1.0))) (/ (* z (+ j 3.0)) (- n 2.0))))