Details

sample54.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
10.0ms	36×	body	640	valid
9.0ms	149×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	5×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

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: 16.3b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

8.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series170.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
77.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune198.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	13	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 0.1b

Counts

89 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin x)) (cbrt (sin x)))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
1.0ms	(cbrt (sin x))
5.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))

series576.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
273.0ms	(cbrt (sin x))
94.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))

simplify89.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	154	453
1	551	401
2	3082	369
3	5002	363

prune255.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	82	16	98

Merged error: 0.1b

Counts

98 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))

series386.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (sin x))
100.0ms	(cbrt (sin x))
94.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))

simplify151.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	59	244
1	124	224
2	321	216
3	984	216
4	4844	216
5	5002	216

prune241.0ms

Filtered

56 candidates to 44 candidates (78.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	56	16	72

Merged error: 0.1b

Counts

72 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series385.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))
95.0ms	(cbrt (sin x))
94.0ms	(cbrt (sin x))

simplify147.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	59	244
1	124	224
2	321	216
3	984	216
4	4844	216
5	5002	216

prune184.0ms

Filtered

56 candidates to 44 candidates (78.6%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	56	16	72

Merged error: 0.1b

Counts

72 → 16

regimes127.0ms

Accuracy

0% (1.3b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	16
1	20	16
2	20	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

723.0ms	1559×	body	1280	valid
364.0ms	1233×	body	640	valid
273.0ms	4281×	body	80	valid
136.0ms	649×	body	320	valid
39.0ms	278×	body	160	valid