Details

sample677.0ms

Algorithm

intervals

Results

394.0ms	4125×	body	80	nan
66.0ms	167×	body	640	valid
15.0ms	54×	body	320	valid
3.0ms	6×	body	1280	valid
2.0ms	13×	body	160	valid
2.0ms	16×	body	80	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 6.2b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ z 1.0)) (sqrt z))
4.0b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series40.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
12.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify65.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5002	824

prune301.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 5.0b

Counts

89 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-log-exp`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
6.0ms	(+ y (- 1.0 y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series29.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ y (- 1.0 y))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify58.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	604	708
1	2432	673
2	5001	673

prune294.0ms

Filtered

86 candidates to 59 candidates (31.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 2.9b

Counts

94 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series38.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify77.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	813	1083
1	3571	1022
2	5003	1005

prune366.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	107	13	120

Merged error: 2.9b

Counts

120 → 13

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))))
1.8b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
95×	`sqrt-prod`
76×	`times-frac`
36×	`add-cube-cbrt`
33×	`associate-r` `associate-l`
27×	`distribute-lft-out`
26×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
8×	`div-exp` `prod-exp`
6×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `associate-/r/` `cbrt-unprod`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 162

Calls

4 calls:

43.0ms	(* (/ 1 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (/ 1 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify49.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1144	2512
1	5002	2218

prune564.0ms

Filtered

174 candidates to 100 candidates (42.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	173	14	187

Merged error: 2.9b

Counts

187 → 14

regimes1.7s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample77.0ms

Algorithm

intervals

Results

47.0ms	505×	body	80	nan
6.0ms	13×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	1280	valid
0.0ms	2×	body	80	valid

Details

sample677.0ms

simplify30.0ms

prune7.0ms

localize23.0ms

rewrite34.0ms

series40.0ms

simplify65.0ms

prune301.0ms

localize28.0ms

rewrite33.0ms

series29.0ms

simplify58.0ms

prune294.0ms

localize26.0ms

rewrite40.0ms

series38.0ms

simplify77.0ms

prune366.0ms

localize31.0ms

rewrite75.0ms

series37.0ms

simplify49.0ms

prune564.0ms

regimes1.7s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample77.0ms

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