Details

sample144.0ms

Algorithm

intervals

Results

77.0ms	64×	body	2560	valid
41.0ms	91×	body	1280	valid
11.0ms	50×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify7.0ms

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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

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

41.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify38.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune194.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	59	15	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	15	75

Merged error: 0.2b

Counts

75 → 15

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.2b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series179.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
125.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify37.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	61	148
1	188	130
2	1009	130
3	5002	130

prune112.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	26	15	41

Merged error: 0.2b

Counts

41 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite31.0ms

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-log-exp`
6×	`add-exp-log` `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` `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 → 132

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
23.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune360.0ms

Filtered

144 candidates to 101 candidates (70.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	136	8	144
Fresh	8	5	13
Picked	1	0	1
Done	0	1	1
Total	145	14	159

Merged error: 0.2b

Counts

159 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
1.5b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 265

Calls

3 calls:

3.0ms	(/ 1.0 (sin x))
4.0ms	(/ (cos x) (sin x))
18.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1.0 (sin x))
24.0ms	(/ (cos x) (sin x))
84.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	810	7180
1	2234	5060
2	5001	4434

prune347.0ms

Filtered

274 candidates to 114 candidates (41.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	271	3	274
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	273	15	288

Merged error: 0.2b

Counts

288 → 15

regimes162.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.0b

bsearch69.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.02222452111566249
10	-1421.6155834850151	-1.485944467815708e-07	-0.020610258751472033

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1640×	body	2560	valid
1.2s	2761×	body	1280	valid
405.0ms	1824×	body	640	valid
139.0ms	913×	body	320	valid
52.0ms	483×	body	160	valid
31.0ms	376×	body	80	valid
10.0ms	3×	body	5120	valid