Details

analyze501.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample144.0ms

Algorithm

intervals

Results

72.0ms	52×	body	2560	valid
38.0ms	77×	body	1280	valid
17.0ms	68×	body	640	valid
6.0ms	34×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	11×	body	80	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	485	7
1	485	7

prune7.0ms

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: 32.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series10.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5388	605

prune141.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	42	15	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	15	58

Merged error: 0.1b

Counts

58 → 15

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
0.1b	(* 1/24 (pow x 3))
0.5b	(* 1/240 (pow x 5))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

8.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
5.0ms	(* 1/24 (pow x 3))
5.0ms	(* 1/240 (pow x 5))

series13.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
3.0ms	(* 1/24 (pow x 3))
4.0ms	(* 1/240 (pow x 5))

simplify48.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4998	704
1	4998	704

prune167.0ms

Filtered

50 candidates to 78 candidates (-56.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	78	15	93

Merged error: 0.1b

Counts

93 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.6b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 158

Calls

3 calls:

8.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series18.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify65.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5148	2252

prune204.0ms

Filtered

95 candidates to 167 candidates (-75.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	4	9	13
Picked	0	1	1
Done	0	1	1
Total	168	14	182

Merged error: 0.1b

Counts

182 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.2b	(/ (log (exp (- 1.0 (cos x)))) (sin x))
1.6b	(- 1.0 (cos x))
1.6b	(log (exp (- 1.0 (cos x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
4×	`log-prod`
3×	`sub-neg` `exp-diff` `associate-/r*`
2×	`log-div` `diff-log` `exp-sum` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 100

Calls

4 calls:

6.0ms	(exp (- 1.0 (cos x)))
7.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
3.0ms	(- 1.0 (cos x))
4.0ms	(log (exp (- 1.0 (cos x))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (- 1.0 (cos x)))
7.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify78.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4891	1057
1	4891	1057

prune126.0ms

Filtered

72 candidates to 112 candidates (-55.6%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	110	16	126

Merged error: 0.1b

Counts

126 → 16

regimes195.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 31.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	112	63
1	112	63

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	1552×	body	2560	valid
1.4s	2742×	body	1280	valid
492.0ms	1872×	body	640	valid
180.0ms	981×	body	320	valid
60.0ms	482×	body	160	valid
32.0ms	370×	body	80	valid
3.0ms	1×	body	5120	valid

Details

analyze501.0ms

sample144.0ms

simplify25.0ms

prune7.0ms

localize7.0ms

rewrite10.0ms

series10.0ms

simplify42.0ms

prune141.0ms

localize12.0ms

rewrite20.0ms

series13.0ms

simplify48.0ms

prune167.0ms

localize8.0ms

rewrite24.0ms

series18.0ms

simplify65.0ms

prune204.0ms

localize10.0ms

rewrite25.0ms

series21.0ms

simplify78.0ms

prune126.0ms

regimes195.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample4.5s

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