Details

sample1.0s

Algorithm

intervals

Results

699.0ms	4204×	body	80	nan
73.0ms	154×	body	640	valid
20.0ms	60×	body	320	valid
3.0ms	6×	body	1280	valid
3.0ms	24×	body	80	valid
2.0ms	12×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize54.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ y 1.0)) (sqrt y))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite186.0ms

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:

48.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
46.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
41.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
40.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series391.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
105.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
102.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
84.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.6s

Counts

292 → 292

Iterations

Iter	Nodes
done	5000
2	3340
1	1010
0	443

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ y 1.0)) (sqrt y))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite535.0ms

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:

93.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
333.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
57.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series417.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
84.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
90.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
80.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify2.0s

Counts

282 → 282

Iterations

Iter	Nodes
done	5000
2	4205
1	1071
0	453

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize100.0ms

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)))
2.2b	(- (sqrt (+ y 1.0)) (sqrt y))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite294.0ms

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:

70.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
88.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
62.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
60.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series470.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
146.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify995.0ms

Counts

272 → 272

Iterations

Iter	Nodes
done	5000
1	1099
0	449

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite345.0ms

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:

100.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
75.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
101.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
58.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series708.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
215.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
187.0ms	(/ (+ 1.0 (- t t)) (+ (sqrt (+ t 1.0)) (sqrt t)))
96.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.1s

Counts

262 → 262

Iterations

Iter	Nodes
done	5001
1	1131
0	445

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.3s

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	51
1	51
0	36

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.3s	27132×	body	80	nan
810.0ms	1134×	body	640	valid
146.0ms	388×	body	320	valid
25.0ms	100×	body	160	valid
22.0ms	33×	body	1280	valid
19.0ms	141×	body	80	valid