Details

sample584.0ms

Algorithm

intervals

Results

377.0ms	3610×	body	80	nan
75.0ms	181×	body	640	valid
14.0ms	46×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	14×	body	80	valid
1.0ms	2×	body	1280	valid

simplify32.0ms

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: 4.4b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite39.0ms

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:

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

series293.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune370.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 0.5b

Counts

89 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
44×	`sqrt-prod`
40×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`times-frac`
16×	`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` `associate-/l*`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 107

Calls

4 calls:

13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify73.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	627	1069
1	2306	979
2	5001	943

prune464.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 0.3b

Counts

126 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series442.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
147.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
80.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify84.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	721	1294
1	2693	1180
2	5001	1137

prune615.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 0.3b

Counts

150 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.2b	(+ x (- 1.0 x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
46×	`distribute-lft-out`
44×	`sqrt-prod`
42×	`times-frac`
35×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
12×	`associate-/r*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
4×	`pow1` `flip3-+` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
13.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
6.0ms	(+ x (- 1.0 x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series359.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
139.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.0ms	(+ x (- 1.0 x))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify74.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	683	1179
1	2548	1076
2	5001	1033

prune582.0ms

Filtered

139 candidates to 82 candidates (59.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	139	11	150

Merged error: 0.3b

Counts

150 → 11

regimes1.0s

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	53	25
2	53	25

end0.0ms

sample872.0ms

Algorithm

intervals

Results

569.0ms	5421×	body	80	nan
112.0ms	258×	body	640	valid
21.0ms	66×	body	320	valid
5.0ms	22×	body	160	valid
3.0ms	26×	body	80	valid
1.0ms	2×	body	1280	valid

Details

sample584.0ms

simplify32.0ms

prune5.0ms

localize25.0ms

rewrite39.0ms

series293.0ms

simplify44.0ms

prune370.0ms

localize29.0ms

rewrite42.0ms

series351.0ms

simplify73.0ms

prune464.0ms

localize31.0ms

rewrite45.0ms

series442.0ms

simplify84.0ms

prune615.0ms

localize30.0ms

rewrite45.0ms

series359.0ms

simplify74.0ms

prune582.0ms

regimes1.0s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample872.0ms

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