Details

sample1.2s

Algorithm

intervals

Results

906.0ms	3622×	body	80	nan
61.0ms	156×	body	640	valid
25.0ms	49×	body	320	valid
4.0ms	9×	body	1280	valid
3.0ms	30×	body	80	valid
2.0ms	12×	body	160	valid

simplify1.3s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize50.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.4b	(- (sqrt (+ z 1.0)) (sqrt z))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite234.0ms

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:

54.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
55.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
57.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
53.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series336.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
97.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
86.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.6s

Counts

292 → 292

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	437	7222
1	991	5127
2	3215	3879
done	5000	3639

prune1.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 4.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.4b	(- (+ x 1.0) x)
2.4b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite229.0ms

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:

54.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
55.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
47.0ms	(- (+ x 1.0) x)
60.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series212.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
1.0ms	(- (+ x 1.0) x)
72.0ms	(- (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	4221
2	2916	3205
done	5000	2650

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.4b	(- (+ x 1.0) x)

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity`
134×	`sqrt-prod`
98×	`add-sqr-sqrt`
96×	`prod-diff`
80×	`add-cube-cbrt`
48×	`distribute-lft-out`
24×	`times-frac`
18×	`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` `associate-/l*`
3×	`sub-neg` `flip3--` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate--l+` `clear-num` `sum-log` `div-inv`

Counts

4 → 227

Calls

4 calls:

98.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
78.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
82.0ms	(- (+ x 1.0) x)

series302.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
87.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
2.0ms	(- (+ x 1.0) x)

simplify1.6s

Counts

239 → 239

Iterations

Useful iterations: 2 (625.0ms)

Iter	Nodes	Cost
0	394	5113
1	933	3734
2	3408	2976
done	5000	2976

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite309.0ms

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:

53.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
84.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
85.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series649.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
219.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
95.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
116.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.1s

Counts

247 → 247

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	426	5362
1	1022	4034
2	3961	3302
done	5001	3302

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

regimes964.0ms

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.3s	22276×	body	80	nan
729.0ms	946×	body	640	valid
188.0ms	286×	body	320	valid
26.0ms	38×	body	1280	valid
23.0ms	85×	body	160	valid
16.0ms	120×	body	80	valid