Details

sample288.0ms

Algorithm

intervals

Results

12.0ms	42×	body	1280	valid
7.0ms	44×	body	640	valid
5.0ms	142×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

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: 0.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`tan-quot`
2×	`pow2` `frac-times` `flip3--` `associate-r/` `associate-l/` `associate-/r/` `*-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+` `div-inv`

Counts

4 → 22

Calls

4 calls:

4.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
3.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
48.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify138.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (134.0ms)

Iter	Nodes	Cost
0	154	226
1	411	224
2	1148	224
3	4447	214
4	5001	213

prune89.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	25	9	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	9	35

Merged error: 0.1b

Counts

35 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow-to-exp` `unpow2` `sqr-pow`

Counts

4 → 12

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series75.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
20.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify121.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	60
1	197	60
2	590	60
3	2839	60
4	5001	60

prune67.0ms

Filtered

24 candidates to 12 candidates (50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	24	9	33

Merged error: 0.1b

Counts

33 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.3b	(* (tan x) (tan x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`tan-quot`
3×	`associate-l/` `-commutative`
2×	`associate-/l*`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `frac-2neg` `associate-*r/` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 17

Calls

4 calls:

3.0ms	(* (tan x) (sin x))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
2.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
4.0ms	(* (tan x) (tan x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (tan x) (sin x))
62.0ms	(/ (* (tan x) (sin x)) (cos x))
50.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
35.0ms	(* (tan x) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	122	152
1	327	152
2	1169	152
3	5001	152

prune91.0ms

Filtered

29 candidates to 19 candidates (65.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	28	10	38

Merged error: 0.1b

Counts

38 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow-to-exp` `associate-/l*` `unpow2` `sqr-pow`
1×	`tan-quot` `sub-neg` `flip3--` `frac-2neg` `associate-l/` `clear-num` `-commutative` `flip--` `div-inv` `associate-/l/`

Counts

4 → 16

Calls

4 calls:

5.0ms	(/ (* (tan x) (sin x)) (cos x))
2.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
1.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)

series152.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* (tan x) (sin x)) (cos x))
54.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)

simplify65.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	138
1	472	138
2	1978	138
3	5001	138

prune76.0ms

Filtered

28 candidates to 18 candidates (64.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	28	10	38

Merged error: 0.1b

Counts

38 → 10

regimes161.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample913.0ms

Algorithm

intervals

Results

369.0ms	1538×	body	1280	valid
195.0ms	1266×	body	640	valid
148.0ms	4303×	body	80	valid
64.0ms	595×	body	320	valid
23.0ms	298×	body	160	valid