Details

sample1.1s

Algorithm

intervals

Results

737.0ms	3915×	body	80	nan
130.0ms	167×	body	640	valid
15.0ms	50×	body	320	valid
4.0ms	21×	body	160	valid
2.0ms	4×	body	1280	valid
1.0ms	14×	body	80	valid

simplify1.7s

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: 6.0b

localize78.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.9b	(- (sqrt (+ y 1.0)) (sqrt y))
4.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite193.0ms

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:

40.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
40.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
41.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
60.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series308.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
79.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
85.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts

292 → 292

Iterations

Iter	Nodes
done	5000
2	3337
1	1010
0	443

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.8b

localize63.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.4b	(+ x (- 1.0 x))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

171×	`sqrt-prod`
163×	`*-un-lft-identity`
135×	`prod-diff`
119×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
26×	`distribute-lft-out`
21×	`fma-neg`
15×	`add-log-exp`
12×	`difference-of-squares`
11×	`associate-+r+`
10×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `sub-neg` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u`
3×	`fma-def` `flip3--` `flip--`
2×	`sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 241

Calls

4 calls:

41.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
40.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
43.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
13.0ms	(+ x (- 1.0 x))

series226.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
78.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(+ x (- 1.0 x))

simplify1.4s

Counts

253 → 253

Iterations

Iter	Nodes
done	5002
2	3044
1	909
0	393

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(+ x (- 1.0 x))

rewrite287.0ms

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:

112.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
60.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
40.0ms	(+ x (- 1.0 x))

series440.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
89.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
100.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ x (- 1.0 x))

simplify2.2s

Counts

243 → 243

Iterations

Iter	Nodes
done	5000
2	3897
1	965
0	401

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.9b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
154×	`sqrt-prod`
100×	`add-sqr-sqrt`
84×	`prod-diff` `add-cube-cbrt`
70×	`distribute-lft-out`
48×	`times-frac`
14×	`fma-neg`
13×	`distribute-lft-out--`
12×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `associate-/l/`
1×	`associate-+r-` `div-sub`

Counts

4 → 243

Calls

4 calls:

43.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
108.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series691.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
244.0ms	(/ (+ 1.0 (- y y)) (+ (sqrt (+ y 1.0)) (sqrt y)))
118.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
103.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify2.1s

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
2	4365
1	1051
0	435

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.9b

regimes1.8s

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	43
1	43
0	31

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.6s	15165×	body	80	nan
417.0ms	675×	body	640	valid
78.0ms	197×	body	320	valid
46.0ms	76×	body	80	valid
17.0ms	62×	body	160	valid
14.0ms	21×	body	1280	valid