Details

sample1.4s

Algorithm

intervals

Results

853.0ms	3602×	body	80	nan
172.0ms	154×	body	640	valid
47.0ms	19×	body	80	valid
30.0ms	64×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	5×	body	1280	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	897
2	155
1	51
0	24

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize61.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ y 1.0)) (sqrt y))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite276.0ms

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` `log1p-expm1-u` `flip--`

Counts

4 → 280

Calls

4 calls:

64.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
41.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
76.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
80.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
83.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
80.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
93.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.6s

Counts

292 → 292

Iterations

Iter	Nodes
done	5000
2	3339
1	1010
0	443

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(- (sqrt (+ y 1.0)) (sqrt y))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

241×	`*-un-lft-identity`
195×	`sqrt-prod`
126×	`prod-diff`
125×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
62×	`distribute-lft-out`
30×	`times-frac`
21×	`fma-neg`
16×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 270

Calls

4 calls:

77.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
50.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series494.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
97.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
98.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
113.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.2s

Counts

282 → 282

Iterations

Iter	Nodes
done	5000
2	4211
1	1071
0	453

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.7b	(- (sqrt (+ y 1.0)) (sqrt y))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

282×	`*-un-lft-identity`
162×	`sqrt-prod`
102×	`add-sqr-sqrt`
92×	`distribute-lft-out`
86×	`add-cube-cbrt`
84×	`prod-diff`
60×	`times-frac`
20×	`distribute-lft-out--`
14×	`fma-neg`
12×	`associate-/r*`
10×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `associate-+r-` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 260

Calls

4 calls:

111.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
93.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
46.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
64.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series647.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
222.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
124.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
113.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.0s

Counts

272 → 272

Iterations

Iter	Nodes
done	5000
1	1099
0	449

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize116.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

323×	`*-un-lft-identity`
129×	`sqrt-prod`
122×	`distribute-lft-out`
90×	`times-frac`
79×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
42×	`prod-diff`
24×	`distribute-lft-out--`
18×	`associate-/r*`
15×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
7×	`fma-neg`
6×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp` `associate-/l/`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `div-sub` `div-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 250

Calls

4 calls:

78.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
116.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
115.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
66.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series676.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
188.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
190.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
99.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.1s

Counts

262 → 262

Iterations

Iter	Nodes
done	5001
1	1131
0	445

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.5s

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	51
1	51
0	36

end0.0ms

sample1.6s

Algorithm

intervals

Results

953.0ms	6236×	body	80	nan
185.0ms	293×	body	640	valid
78.0ms	107×	body	320	valid
8.0ms	25×	body	160	valid
6.0ms	10×	body	1280	valid
4.0ms	33×	body	80	valid