Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	242×	body	80	valid
2.0ms	7×	body	1280	valid
1.0ms	3×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	10	8
2	11	8
done	11	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 12

Calls

1 calls:

11.0ms

(+ x (/ (fabs (- y x)) 2.0))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(+ x (/ (fabs (- y x)) 2.0))

simplify2.9s

Counts

15 → 15

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	31	195
1	84	187
2	209	171
3	459	171
4	1200	171
5	2875	171
done	5001	171

prune73.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
30×	`sqrt-prod`
26×	`add-sqr-sqrt`
20×	`pow1`
14×	`sqrt-div`
13×	`add-cube-cbrt`
11×	`swap-sqr`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`
8×	`add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-r/` `associate-l/` `sum-log`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 102

Calls

4 calls:

34.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
15.0ms	(+ x (/ (fabs (- y x)) 2.0))
11.0ms	(+ x (/ (fabs (- y x)) 2.0))
135.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series140.0ms

Calls

3 calls:

32.0ms	(+ x (/ (fabs (- y x)) 2.0))
31.0ms	(+ x (/ (fabs (- y x)) 2.0))
33.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))