Details

sample903.0ms

Algorithm

intervals

Results

581.0ms	3786×	body	80	nan
76.0ms	179×	body	640	valid
12.0ms	38×	body	320	valid
4.0ms	19×	body	160	valid
2.0ms	4×	body	1280	valid
2.0ms	16×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	31
1	51	31
2	155	31
3	895	31
done	5000	31

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize59.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

228×	`sqrt-prod`
200×	`*-un-lft-identity`
168×	`prod-diff`
148×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
32×	`distribute-lft-out`
28×	`fma-neg`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 280

Calls

4 calls:

76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
89.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
86.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
97.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series357.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
89.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
80.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
82.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.9s

Counts

292 → 292

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	437	7222
1	991	5127
2	3208	3879
done	5000	3639

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.4b

localize47.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (+ 1.0 x) x)
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

172×	`*-un-lft-identity`
171×	`sqrt-prod`
138×	`prod-diff`
122×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
29×	`distribute-lft-out`
25×	`fma-neg`
15×	`add-log-exp`
13×	`difference-of-squares`
11×	`distribute-lft-out--`
5×	`diff-log`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`associate--l+` `sum-log`

Counts

4 → 245

Calls

4 calls:

52.0ms	(- (+ 1.0 x) x)
108.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
97.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
85.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series308.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- (+ 1.0 x) x)
105.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
119.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
82.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.7s

Counts

257 → 257

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	389	5903
1	886	4219
2	2921	3157
done	5000	2575

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.5b	(- (+ 1.0 x) x)
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
130×	`sqrt-prod`
97×	`add-sqr-sqrt`
96×	`prod-diff`
79×	`add-cube-cbrt`
37×	`distribute-lft-out`
18×	`times-frac` `fma-neg`
13×	`add-log-exp`
9×	`difference-of-squares`
8×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `associate--l+` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

4 → 218

Calls

4 calls:

47.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
62.0ms	(- (+ 1.0 x) x)
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
82.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series403.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
2.0ms	(- (+ 1.0 x) x)
123.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
91.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.6s

Counts

230 → 230

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	385	4833
1	897	3613
2	3235	2827
done	5002	2681

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

202×	`*-un-lft-identity`
150×	`sqrt-prod`
99×	`add-sqr-sqrt`
84×	`prod-diff`
83×	`add-cube-cbrt`
59×	`distribute-lft-out`
42×	`times-frac`
14×	`fma-neg`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 235

Calls

4 calls:

67.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
83.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
77.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
86.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series573.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))
187.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
102.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
104.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.8s

Counts

247 → 247

Iterations

Useful iterations: 2 (891.0ms)

Iter	Nodes	Cost
0	428	5364
1	1034	4034
2	4043	3301
done	5000	3301

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

regimes1.4s

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	30	43
1	41	41
2	45	41
done	45	41

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.1s	21956×	body	80	nan
955.0ms	979×	body	640	valid
85.0ms	239×	body	320	valid
56.0ms	85×	body	160	valid
23.0ms	37×	body	1280	valid
9.0ms	90×	body	80	valid