Details

sample134.0ms

Algorithm

intervals

Results

63.0ms	50×	body	2560	valid
38.0ms	91×	body	1280	valid
13.0ms	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

prune2.0ms

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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
24.0ms	(- 1.0 (cos x))

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	289	569
1	941	460
2	5001	460

prune145.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	63	11	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	11	75

Merged error: 0.4b

Counts

75 → 11

localize10.0ms

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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-exp-log` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `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 → 133

Calls

4 calls:

10.0ms	(/ (- 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))))
5.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
48.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	365	1009
1	1075	873
2	5001	871

prune279.0ms

Filtered

145 candidates to 101 candidates (69.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	135	10	145
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	140	16	156

Merged error: 0.3b

Counts

156 → 16

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	289	569
1	941	460
2	5001	460

prune150.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	74	16	90

Merged error: 0.3b

Counts

90 → 16

localize9.0ms

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)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
260×	`add-sqr-sqrt`
258×	`*-un-lft-identity`
248×	`add-cube-cbrt`
169×	`prod-diff`
81×	`frac-sub`
68×	`associate-/r*`
60×	`associate-/l*`
31×	`div-inv`
22×	`frac-2neg`
20×	`clear-num`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube` `sub-div`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--`

Counts

3 → 351

Calls

3 calls:

4.0ms	(/ 1.0 (sin x))
4.0ms	(/ (cos x) (sin x))
31.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1.0 (sin x))
20.0ms	(/ (cos x) (sin x))
89.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1541	8565
1	5001	6321

prune434.0ms

Filtered

360 candidates to 175 candidates (48.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	354	6	360
Fresh	8	6	14
Picked	0	1	1
Done	0	1	1
Total	362	14	376

Merged error: 0.1b

Counts

376 → 14

regimes149.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 31.0b

bsearch73.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	0.024683183633800634
7	-0.05767290693153419	-0.00024695944164034034	-0.014503396267940102

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	30
1	38	30
2	38	30

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	1548×	body	2560	valid
1.3s	2820×	body	1280	valid
578.0ms	1821×	body	640	valid
162.0ms	932×	body	320	valid
52.0ms	490×	body	160	valid
24.0ms	385×	body	80	valid
13.0ms	4×	body	5120	valid