Details

analyze264.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

sample132.0ms

Algorithm

intervals

Results

63.0ms	161×	body	640	valid
28.0ms	295×	body	80	nan
15.0ms	54×	body	320	valid
3.0ms	27×	body	80	valid
2.0ms	11×	body	160	valid
1.0ms	3×	body	1280	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5040	31

prune17.0ms

Filtered

1 candidates to 1 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: 4.6b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))

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 → 72

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
15.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4985	1360
1	4985	1360

prune248.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 0.7b

Counts

86 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite43.0ms

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 → 104

Calls

4 calls:

14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series41.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4993	1837
1	4993	1837

prune312.0ms

Filtered

78 candidates to 116 candidates (-48.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 0.3b

Counts

124 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite44.0ms

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 → 127

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify61.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5570	2128

prune371.0ms

Filtered

90 candidates to 139 candidates (-54.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	137	12	149

Merged error: 0.3b

Counts

149 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

263×	`*-un-lft-identity`
242×	`sqrt-prod`
126×	`times-frac`
112×	`add-sqr-sqrt`
101×	`distribute-lft-out`
68×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
19×	`pow1`
10×	`associate-/r/`
9×	`unswap-sqr`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
6×	`flip3-+` `associate-/r*` `flip-+` `distribute-lft-out--`
5×	`pow-prod-up` `div-inv`
4×	`sqrt-div` `associate-/l*`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 218

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
38.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series48.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
17.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify101.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4877	3690
1	4877	3690

prune780.0ms

Filtered

124 candidates to 230 candidates (-85.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	230	12	242

Merged error: 0.3b

Counts

242 → 12

regimes1.4s

Accuracy

0% (2.3b remaining)

Error of 2.7b against oracle of 0.4b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	35
1	55	35

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.0s	5209×	body	640	valid
930.0ms	9757×	body	80	nan
458.0ms	1614×	body	320	valid
79.0ms	430×	body	160	valid
60.0ms	128×	body	1280	valid
58.0ms	619×	body	80	valid

Details

analyze264.0ms

sample132.0ms

simplify41.0ms

prune17.0ms

localize25.0ms

rewrite35.0ms

series46.0ms

simplify46.0ms

prune248.0ms

localize25.0ms

rewrite43.0ms

series41.0ms

simplify40.0ms

prune312.0ms

localize31.0ms

rewrite44.0ms

series45.0ms

simplify61.0ms

prune371.0ms

localize31.0ms

rewrite80.0ms

series48.0ms

simplify101.0ms

prune780.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.0s

Profiling