Details

sample1.1s

Algorithm

intervals

Results

738.0ms	3738×	body	80	nan
102.0ms	176×	body	640	valid
20.0ms	47×	body	320	valid
3.0ms	20×	body	80	valid
3.0ms	9×	body	160	valid
2.0ms	4×	body	1280	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5010
4	4694
3	799
2	154
1	51
0	24

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize96.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite237.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

4 → 284

Calls

4 calls:

56.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
41.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
60.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series434.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
112.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
102.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
110.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.8s

Counts

296 → 296

Iterations

Iter	Nodes
done	5002
2	2352
1	1011
0	447

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.1b

localize81.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (+ 1.0 x) x)
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite246.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`sum-log` `associate--l+`

Counts

4 → 249

Calls

4 calls:

60.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
52.0ms	(- (+ 1.0 x) x)
66.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
59.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series305.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(- (+ 1.0 x) x)
87.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
122.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.1s

Counts

261 → 261

Iterations

Iter	Nodes
done	5000
2	2178
1	899
0	397

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

190×	`*-un-lft-identity`
187×	`sqrt-prod`
126×	`prod-diff`
123×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
40×	`distribute-lft-out`
21×	`fma-neg`
18×	`times-frac`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 257

Calls

4 calls:

38.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
58.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
36.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
43.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series536.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
124.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
91.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
122.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify1.9s

Counts

269 → 269

Iterations

Iter	Nodes
done	5000
2	2520
1	1021
0	443

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
1.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.2b	(- (+ 1.0 t) t)
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite133.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-exp` `associate--l+` `flip-+` `div-inv`

Counts

4 → 222

Calls

4 calls:

21.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
31.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
29.0ms	(- (+ 1.0 t) t)
48.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series389.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
80.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(- (+ 1.0 t) t)
108.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.8s

Counts

234 → 234

Iterations

Iter	Nodes
done	5002
2	2353
1	909
0	393

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.9b

regimes1.4s

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.6s	7923×	body	80	nan
164.0ms	359×	body	640	valid
33.0ms	91×	body	320	valid
5.0ms	25×	body	160	valid
4.0ms	40×	body	80	valid
3.0ms	7×	body	1280	valid