Details

analyze533.0ms

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

sample155.0ms

Algorithm

intervals

Results

77.0ms	53×	body	2560	valid
42.0ms	80×	body	1280	valid
18.0ms	67×	body	640	valid
6.0ms	34×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	10×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune3.0ms

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: 31.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite12.0ms

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 → 52

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify78.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2640	373
3	5002	373

prune145.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 0.1b

Counts

59 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
8.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms	(* 1/240 (pow x 5))
7.0ms	(* 1/24 (pow x 3))

series28.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	355	458
1	1538	429
2	5002	428

prune164.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	92	14	106

Merged error: 0.1b

Counts

106 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.0b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
9.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify88.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune184.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	124	14	138

Merged error: 0.0b

Counts

138 → 14

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)))
1.5b	(- 1.0 (cos x))

rewrite29.0ms

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 → 159

Calls

3 calls:

11.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series18.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
8.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify61.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	510	1593
1	2396	1450
2	5002	1337

prune115.0ms

Filtered

86 candidates to 168 candidates (-95.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	168	14	182

Merged error: 0.0b

Counts

182 → 14

regimes218.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

end0.0ms

analyze503.0ms

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

sample4.8s

Algorithm

intervals

Results

2.4s	1629×	body	2560	valid
1.4s	2774×	body	1280	valid
496.0ms	1835×	body	640	valid
167.0ms	918×	body	320	valid
70.0ms	485×	body	160	valid
28.0ms	356×	body	80	valid
18.0ms	3×	body	5120	valid

Details

analyze533.0ms

sample155.0ms

simplify5.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series13.0ms

simplify78.0ms

prune145.0ms

localize11.0ms

rewrite26.0ms

series28.0ms

simplify52.0ms

prune164.0ms

localize11.0ms

rewrite29.0ms

series29.0ms

simplify88.0ms

prune184.0ms

localize8.0ms

rewrite29.0ms

series18.0ms

simplify61.0ms

prune115.0ms

regimes218.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze503.0ms

sample4.8s

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