Details

sample92.0ms

Algorithm

intervals

Results

41.0ms	102×	body	1280	valid
15.0ms	17×	body	2560	valid
12.0ms	61×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	14×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 33.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (tan (+ x eps)) (tan x))
4.9b	(tan (+ x eps))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

6.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series40.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify81.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune58.0ms

Filtered

31 candidates to 25 candidates (19.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 14.5b

Counts

32 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`tan-quot`
6×	`pow1`
4×	`distribute-lft-out` `associate-/l*`
3×	`flip3--` `associate-r` `associate-l` `associate-/r*` `flip--` `associate-/l/`
2×	`sub-neg` `diff-log` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

2.0ms	(- 1 (* (tan x) (tan eps)))
7.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- 1 (* (tan x) (tan eps)))
54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms	(* (tan x) (tan eps))
94.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	401	1066
1	1532	1014
2	5001	1003

prune168.0ms

Filtered

97 candidates to 72 candidates (25.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	89	8	97
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 14.4b

Counts

104 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
7.8b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
7.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
8.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ (tan x) (tan eps)) (cos x))
22.0ms	(* (tan x) (tan eps))
20.0ms	(* (tan x) (tan eps))
48.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	527	955
1	2405	907
2	5002	907

prune143.0ms

Filtered

94 candidates to 72 candidates (23.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 0.1b

Counts

106 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (sin x) 2) (sin eps))
0.3b	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(pow (sin x) 2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`div-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r` `cbrt-unprod`
5×	`unswap-sqr`
4×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp` `add-log-exp`
3×	`pow-unpow` `unpow2` `sqr-pow`
2×	`*-commutative`
1×	`frac-times` `pow-pow` `frac-2neg` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `div-inv` `associate-/l`

Counts

4 → 92

Calls

4 calls:

5.0ms	(* (pow (sin x) 2) (sin eps))
8.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
5.0ms	(* (tan x) (tan eps))
2.0ms	(pow (sin x) 2)

series60.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (pow (sin x) 2) (sin eps))
23.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
22.0ms	(* (tan x) (tan eps))
4.0ms	(pow (sin x) 2)

simplify55.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	443	718
1	2027	593
2	5001	593

prune119.0ms

Filtered

104 candidates to 66 candidates (36.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Merged error: 0.1b

Counts

113 → 14

regimes191.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3306×	body	1280	valid
561.0ms	659×	body	2560	valid
383.0ms	1834×	body	640	valid
100.0ms	720×	body	320	valid
46.0ms	1117×	body	80	valid
34.0ms	364×	body	160	valid

Details

sample92.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series40.0ms

simplify81.0ms

prune58.0ms

localize11.0ms

rewrite27.0ms

series192.0ms

simplify44.0ms

prune168.0ms

localize19.0ms

rewrite29.0ms

series116.0ms

simplify66.0ms

prune143.0ms

localize27.0ms

rewrite23.0ms

series60.0ms

simplify55.0ms

prune119.0ms

regimes191.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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