Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
6.0ms	248×	body	80	nan
4.0ms	43×	body	640	valid
3.0ms	124×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	162
1	9	162
2	10	162
done	10	162

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

6.0ms	(sqrt (+ x 1.0))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series158.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(sqrt (+ x 1.0))
99.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.8s

Counts

95 → 95

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	139	40498
1	322	32284
2	785	25908
3	2271	25237
done	5003	21442

prune316.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 29.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (- (+ 1.0 x) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(- (+ 1.0 x) x)

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
46×	`distribute-lft-out`
40×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
7×	`fma-def`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `hypot-def` `div-inv`

Counts

4 → 144

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
42.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms	(- (+ 1.0 x) x)

series375.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ x 1.0))
111.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
207.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ 1.0 x) x)

simplify203.0ms

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	223	53554