Details

sample137.0ms

Algorithm

intervals

Results

64.0ms	50×	body	2560	valid
39.0ms	91×	body	1280	valid
14.0ms	61×	body	640	valid
5.0ms	1×	body	5120	valid
4.0ms	25×	body	320	valid
2.0ms	21×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

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

prune7.0ms

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: 31.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
3.2b	(- 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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	230	396
1	662	373
2	2605	373
3	5002	373

prune124.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	47	11	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	11	59

Merged error: 0.4b

Counts

59 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
2.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.2b	(- 1.0 (cos x))

rewrite32.0ms

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-exp-log` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `rem-log-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `clear-num` `rem-exp-log`

Counts

4 → 113

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series142.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
20.0ms	(- 1.0 (cos x))

simplify91.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	300	818
1	788	768
2	2918	766
3	5002	766

prune255.0ms

Filtered

125 candidates to 87 candidates (69.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	115	10	125
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	119	17	136

Merged error: 0.3b

Counts

136 → 17

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
3.2b	(- 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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	230	396
1	662	373
2	2605	373
3	5002	373

prune134.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	59	16	75

Merged error: 0.3b

Counts

75 → 16

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
3.3b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
71×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
68×	`associate-/r*`
60×	`associate-/l*`
59×	`add-cube-cbrt`
28×	`times-frac`
22×	`frac-2neg`
20×	`clear-num`
7×	`add-exp-log` `add-cbrt-cube` `sub-div`
5×	`add-log-exp`
4×	`div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `div-exp`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--`

Counts

3 → 163

Calls

3 calls:

4.0ms	(/ 1.0 (sin x))
4.0ms	(/ (cos x) (sin x))
21.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ 1.0 (sin x))
19.0ms	(/ (cos x) (sin x))
88.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify108.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	955	1962
1	4456	1864
2	5001	1864

prune272.0ms

Filtered

172 candidates to 116 candidates (67.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	5	172
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	176	12	188

Merged error: 0.1b

Counts

188 → 12

regimes134.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 31.1b

bsearch83.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	0.022801616735990637
7	-0.05767290693153419	-0.00024695944164034034	-0.014503396267940102

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	44
1	71	44
2	74	44
3	74	44

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1548×	body	2560	valid
1.3s	2820×	body	1280	valid
457.0ms	1821×	body	640	valid
149.0ms	932×	body	320	valid
63.0ms	490×	body	160	valid
26.0ms	385×	body	80	valid
13.0ms	4×	body	5120	valid