Details

sample111.0ms

Algorithm

intervals

Results

26.0ms	342×	body	80	nan
22.0ms	50×	body	1280	valid
13.0ms	187×	body	80	valid
8.0ms	26×	body	640	valid
7.0ms	10×	body	2560	valid
4.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	10
1	55	10
2	76	10
3	89	10
4	92	10
5	92	10

prune3.0ms

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: 17.9b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.2b	(/ a (* b 3.0))
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
21.5b	(cos (- y (/ (* z t) 3.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`cos-sum` `frac-2neg` `clear-num` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

4.0ms	(/ (* z t) 3.0)
4.0ms	(/ a (* b 3.0))
6.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
5.0ms	(cos (- y (/ (* z t) 3.0)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (* z t) 3.0)
18.0ms	(/ a (* b 3.0))
93.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
33.0ms	(cos (- y (/ (* z t) 3.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	404	507
1	1689	429
2	5001	426

prune331.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	61	23	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	23	85

Merged error: 15.0b

Counts

85 → 23

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
0.3b	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
0.4b	(/ t (cbrt 3.0))
21.7b	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
46×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log`
25×	`associate-r`
24×	`add-cbrt-cube`
23×	`cbrt-prod`
11×	`pow1` `prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp` `associate-l`
6×	`associate-/r*` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`cos-diff` `div-inv` `associate-/l*`
2×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 128

Calls

4 calls:

6.0ms	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
15.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
4.0ms	(/ t (cbrt 3.0))
3.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
93.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
58.0ms	(/ t (cbrt 3.0))
102.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	609	1376
1	3001	1200
2	5001	1171

prune594.0ms

Filtered

140 candidates to 102 candidates (72.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	127	13	140
Fresh	7	15	22
Picked	1	0	1
Done	0	0	0
Total	135	28	163

Merged error: 14.9b

Counts

163 → 28

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ t (cbrt 3.0))
0.4b	(/ t (cbrt 3.0))
25.5b	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
25.7b	(sin (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod`
12×	`associate-/r*`
8×	`add-exp-log`
6×	`add-cbrt-cube` `associate-/l*`
4×	`pow1` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(/ t (cbrt 3.0))
4.0ms	(/ t (cbrt 3.0))
2.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
2.0ms	(sin (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ t (cbrt 3.0))
62.0ms	(/ t (cbrt 3.0))
66.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
73.0ms	(sin (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	136	628
1	322	584
2	833	584
3	2334	568
4	5001	568

prune615.0ms

Filtered

104 candidates to 78 candidates (75.0%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	4	23	27
Picked	1	0	1
Done	0	0	0
Total	102	30	132

Merged error: 14.8b

Counts

132 → 30

localize34.0ms

Local error

Found 4 expressions with local error:

25.5b	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
25.5b	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
25.5b	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
25.7b	(sin (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

2.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
2.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
2.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
2.0ms	(sin (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
55.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
61.0ms	(cos (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))
74.0ms	(sin (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	45	386
1	75	318
2	119	318
3	170	318
4	209	318
5	297	318
6	856	318
7	2563	318
8	5001	318

prune246.0ms

Filtered

40 candidates to 36 candidates (90.0%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	2	27	29
Picked	0	1	1
Done	0	0	0
Total	39	31	70

Merged error: 14.8b

Counts

70 → 31

regimes3.1s

Accuracy

58.7% (1.6b remaining)

Error of 17.5b against oracle of 16.0b and baseline of 19.8b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	61
1	57	61

end0.0ms

sample3.2s

Algorithm

intervals

Results

705.0ms	1560×	body	1280	valid
646.0ms	9214×	body	80	nan
423.0ms	5671×	body	80	valid
306.0ms	944×	body	640	valid
244.0ms	336×	body	2560	valid
106.0ms	452×	body	320	valid
33.0ms	207×	body	160	valid