Details

analyze873.0ms

Algorithm: search

sample97.0ms

Algorithm

intervals

Results

46.0ms	105×	body	1280	valid
20.0ms	24×	body	2560	valid
11.0ms	53×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	36×	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

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: 36.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (tan (+ x eps)) (tan x))
3.4b	(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))

simplify75.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

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

prune61.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 13.3b

Counts

32 → 8

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))))
0.2b	(* (tan x) (tan eps))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

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:

3.0ms	(- 1 (* (tan x) (tan eps)))
7.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
13.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series199.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- 1 (* (tan x) (tan eps)))
56.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (36.0ms)

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

prune157.0ms

Filtered

72 candidates to 97 candidates (-34.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	11	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Merged error: 13.1b

Counts

105 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps))))))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
4.0b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

9.0ms	(/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps))))))
3.0ms	(exp (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
17.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps))))))
33.0ms	(exp (- 1 (* (tan x) (tan eps))))
22.0ms	(* (tan x) (tan eps))
102.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	428	1466
1	1420	1343
2	5002	1315

prune175.0ms

Filtered

79 candidates to 118 candidates (-49.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	117	15	132

Merged error: 13.1b

Counts

132 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

10.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series199.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
25.0ms	(/ (* (sin x) (tan eps)) (cos x))
16.0ms	(* (sin x) (tan eps))
101.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify56.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	500	1555
1	1945	1463
2	5001	1462

prune105.0ms

Filtered

83 candidates to 120 candidates (-44.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	119	16	135

Merged error: 13.1b

Counts

135 → 16

regimes398.0ms

Accuracy

89.1% (0.8b remaining)

Error of 15.5b against oracle of 14.7b and baseline of 21.9b

bsearch263.0ms

Steps

Iters	Range		Point
11	1.0708920349319885e-67	2.1983141014525456e-42	1.0303244886229992e-49
9	-8.594436925852833e-18	-3.1199035123669896e-24	-7.576183345293225e-22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

analyze740.0ms

Algorithm: search

sample2.7s

Algorithm

intervals

Results

1.3s	3357×	body	1280	valid
568.0ms	649×	body	2560	valid
382.0ms	1776×	body	640	valid
107.0ms	750×	body	320	valid
50.0ms	1111×	body	80	valid
36.0ms	357×	body	160	valid

Details

analyze873.0ms

sample97.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series40.0ms

simplify75.0ms

prune61.0ms

localize11.0ms

rewrite30.0ms

series199.0ms

simplify46.0ms

prune157.0ms

localize15.0ms

rewrite38.0ms

series214.0ms

simplify47.0ms

prune175.0ms

localize16.0ms

rewrite42.0ms

series199.0ms

simplify56.0ms

prune105.0ms

regimes398.0ms

bsearch263.0ms

simplify2.0ms

end0.0ms

analyze740.0ms

sample2.7s

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