Details

sample1.1s

Algorithm

intervals

Results

690.0ms	3685×	body	80	nan
133.0ms	171×	body	640	valid
65.0ms	47×	body	320	valid
4.0ms	14×	body	160	valid
3.0ms	22×	body	80	valid
2.0ms	2×	body	1280	valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize74.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.9b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite271.0ms

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:

78.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
64.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
43.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series392.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
97.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
99.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
100.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.1s

Counts

292 → 292

Iterations

Iter	Nodes
done	5000
2	3335
1	1010
0	443

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.4b

localize106.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.9b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite306.0ms

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 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
41.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
81.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series529.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
102.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
116.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
86.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.2s

Counts

282 → 282

Iterations

Iter	Nodes
done	5000
2	4184
1	1066
0	451

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.3b

localize102.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.2b	(+ t (- 1.0 t))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

204×	`*-un-lft-identity`
138×	`sqrt-prod`
96×	`add-sqr-sqrt`
93×	`prod-diff`
80×	`add-cube-cbrt`
56×	`distribute-lft-out`
30×	`times-frac`
14×	`fma-neg` `distribute-lft-out--`
13×	`add-log-exp`
11×	`associate-+r+`
8×	`difference-of-squares`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`sub-neg` `fma-def` `flip3-+` `diff-log` `flip-+`
2×	`associate-+r-` `sum-log` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 231

Calls

4 calls:

117.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
57.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
55.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
22.0ms	(+ t (- 1.0 t))

series375.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
81.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
98.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
2.0ms	(+ t (- 1.0 t))

simplify2.0s

Counts

243 → 243

Iterations

Iter	Nodes
done	5000
2	3896
1	964
0	401

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize103.0ms

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)))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.2b	(+ t (- 1.0 t))

rewrite361.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
105×	`sqrt-prod`
86×	`distribute-lft-out`
73×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
60×	`times-frac`
51×	`prod-diff`
18×	`distribute-lft-out--`
12×	`associate-/r*`
11×	`associate-+r+` `add-log-exp`
10×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`fma-neg`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `difference-of-squares` `associate-/l/`
3×	`associate-+r-` `fma-def`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`
1×	`+-commutative` `flip3--` `flip--`

Counts

4 → 221

Calls

4 calls:

113.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
141.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
83.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
15.0ms	(+ t (- 1.0 t))

series529.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
243.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
120.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ t (- 1.0 t))

simplify2.4s

Counts

233 → 233

Iterations

Iter	Nodes
done	5000
2	4709
1	992
0	399

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

regimes1.2s

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	43
1	43
0	31

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s	7184×	body	80	nan
141.0ms	323×	body	640	valid
71.0ms	97×	body	320	valid
7.0ms	30×	body	160	valid
5.0ms	10×	body	1280	valid
4.0ms	39×	body	80	valid