Details

sample596.0ms

Algorithm

intervals

Results

393.0ms	4339×	body	80	nan
58.0ms	160×	body	640	valid
14.0ms	53×	body	320	valid
3.0ms	19×	body	160	valid
2.0ms	5×	body	1280	valid
2.0ms	19×	body	80	valid

simplify28.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 4.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite36.0ms

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:

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

series732.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
184.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
180.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
183.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify69.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5001	824

prune468.0ms

Filtered

88 candidates to 60 candidates (68.2%)

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: 3.3b

Counts

89 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.9b	(+ t (- 1.0 t))

rewrite35.0ms

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:

11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
6.0ms	(+ t (- 1.0 t))

series551.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
183.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
186.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ t (- 1.0 t))

simplify59.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	601	708
1	2432	673
2	5001	673

prune453.0ms

Filtered

86 candidates to 59 candidates (68.6%)

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: 2.5b

Counts

95 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))

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:

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

series756.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
188.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
184.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
182.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify81.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	814	1082
1	3594	1022
2	5002	1005

prune565.0ms

Filtered

110 candidates to 72 candidates (65.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Merged error: 2.4b

Counts

121 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(+ z (- 1.0 z))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite37.0ms

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:

9.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
5.0ms	(+ z (- 1.0 z))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series578.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(+ z (- 1.0 z))
184.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
183.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify70.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	723	926
1	3076	871
2	5001	854

prune468.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	110	12	122

Merged error: 1.3b

Counts

122 → 12

regimes1.0s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.0s

Algorithm

intervals

Results

672.0ms	7526×	body	80	nan
100.0ms	279×	body	640	valid
24.0ms	92×	body	320	valid
5.0ms	31×	body	160	valid
5.0ms	11×	body	1280	valid
4.0ms	37×	body	80	valid

Details

sample596.0ms

simplify28.0ms

prune5.0ms

localize22.0ms

rewrite36.0ms

series732.0ms

simplify69.0ms

prune468.0ms

localize27.0ms

rewrite35.0ms

series551.0ms

simplify59.0ms

prune453.0ms

localize29.0ms

rewrite37.0ms

series756.0ms

simplify81.0ms

prune565.0ms

localize28.0ms

rewrite37.0ms

series578.0ms

simplify70.0ms

prune468.0ms

regimes1.0s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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