Details

sample612.0ms

Algorithm

intervals

Results

352.0ms	4093×	body	80	nan
60.0ms	169×	body	640	valid
13.0ms	49×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	16×	body	80	valid
1.0ms	3×	body	1280	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

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: 6.7b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
4.5b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite35.0ms

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify68.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5003	824

prune871.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 5.4b

Counts

89 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.9b	(+ x (- 1.0 x))
4.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite31.0ms

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	602	708
1	2429	673
2	5002	673

prune1.0s

Filtered

86 candidates to 59 candidates (31.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 4.3b

Counts

95 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
4.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite37.0ms

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:

10.0ms	(/ 1.0 (+ (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))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify80.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	816	1082
1	3586	1020
2	5002	1003

prune1.2s

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Merged error: 4.2b

Counts

121 → 13

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(+ y (- 1.0 y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
32×	`sqrt-prod`
31×	`add-sqr-sqrt`
20×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
13×	`add-log-exp`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `diff-log` `associate-/l*`
2×	`associate-+r+` `flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
6.0ms	(+ y (- 1.0 y))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	728	926
1	3069	869
2	5001	852

prune956.0ms

Filtered

108 candidates to 70 candidates (35.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 3.3b

Counts

121 → 11

regimes1.5s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	12746×	body	80	nan
191.0ms	545×	body	640	valid
41.0ms	156×	body	320	valid
8.0ms	18×	body	1280	valid
7.0ms	40×	body	160	valid
6.0ms	69×	body	80	valid

Details

sample612.0ms

simplify29.0ms

prune8.0ms

localize28.0ms

rewrite35.0ms

series39.0ms

simplify68.0ms

prune871.0ms

localize29.0ms

rewrite31.0ms

series29.0ms

simplify57.0ms

prune1.0s

localize26.0ms

rewrite37.0ms

series42.0ms

simplify80.0ms

prune1.2s

localize31.0ms

rewrite35.0ms

series29.0ms

simplify72.0ms

prune956.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.9s

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