Details

sample618.0ms

Algorithm

intervals

Results

405.0ms	4339×	body	80	nan
66.0ms	160×	body	640	valid
15.0ms	53×	body	320	valid
4.0ms	19×	body	160	valid
2.0ms	5×	body	1280	valid
2.0ms	19×	body	80	valid

simplify25.0ms

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

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

localize21.0ms

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))

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:

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))

series270.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
64.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify40.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (32.0ms)

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

prune368.0ms

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: 0.6b

Counts

89 → 7

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite44.0ms

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:

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

series390.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
98.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
90.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify73.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	627	1069
1	2306	979
2	5002	943

prune453.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 0.2b

Counts

126 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
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))

rewrite46.0ms

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:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series469.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
163.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
86.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
81.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify75.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (62.0ms)

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

prune591.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	140	6	146

Merged error: 0.2b

Counts

146 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.1b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(+ x (- 1.0 x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite42.0ms

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

series345.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
139.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(+ x (- 1.0 x))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify83.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (71.0ms)

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

prune540.0ms

Filtered

139 candidates to 82 candidates (59.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	139	6	145

Merged error: 0.1b

Counts

145 → 6

regimes541.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	50	23
2	50	23

end0.0ms

sample1.0s

Algorithm

intervals

Results

697.0ms	7526×	body	80	nan
106.0ms	279×	body	640	valid
26.0ms	92×	body	320	valid
6.0ms	31×	body	160	valid
5.0ms	11×	body	1280	valid
3.0ms	37×	body	80	valid

Details

sample618.0ms

simplify25.0ms

prune5.0ms

localize21.0ms

rewrite35.0ms

series270.0ms

simplify40.0ms

prune368.0ms

localize41.0ms

rewrite44.0ms

series390.0ms

simplify73.0ms

prune453.0ms

localize26.0ms

rewrite46.0ms

series469.0ms

simplify75.0ms

prune591.0ms

localize28.0ms

rewrite42.0ms

series345.0ms

simplify83.0ms

prune540.0ms

regimes541.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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