Details

analyze754.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample83.0ms

Algorithm

intervals

Results

40.0ms	103×	body	1280	valid
15.0ms	18×	body	2560	valid
12.0ms	55×	body	640	valid
4.0ms	32×	body	320	valid
1.0ms	34×	body	80	valid
1.0ms	14×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

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: 38.2b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
2.2b	(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 → 24

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))

simplify86.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4868	332
1	4868	332

prune61.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.8b

Counts

31 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (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))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
10.0ms	(/ (+ (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))

series204.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (tan x) (tan eps))
59.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(* (tan x) (tan eps))
102.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5066	1559

prune155.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 14.7b

Counts

104 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (+ (tan x) (tan eps)) (cos x))
9.4b	(- (* (+ (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 → 81

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
7.0ms	(* (+ (tan x) (tan eps)) (cos x))
9.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
26.0ms	(* (+ (tan x) (tan eps)) (cos x))
51.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5796	1385

prune158.0ms

Filtered

72 candidates to 93 candidates (-29.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0.2b

Counts

105 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x))))
0.3b	(pow (sin x) 2)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
32×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt` `associate-l`
11×	`times-frac`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1` `cbrt-undiv` `div-exp`
7×	`associate-r`
5×	`frac-times` `associate-r/` `associate-l/` `associate-/l/`
4×	`tan-quot` `flip3-+` `flip-+` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `unswap-sqr`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `pow-exp` `clear-num` `associate-/r` `flip--` `distribute-lft-out` `associate-/l` `unpow2` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

20.0ms	(/ (* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
5.0ms	(* (tan x) (tan eps))
15.0ms	(* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x))))
3.0ms	(pow (sin x) 2)

series142.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
22.0ms	(* (tan x) (tan eps))
36.0ms	(* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x))))
4.0ms	(pow (sin x) 2)

simplify51.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5039	2051

prune164.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	8	122
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 0b

Counts

132 → 11

regimes171.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	33
1	26	33

end0.0ms

analyze755.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample2.6s

Algorithm

intervals

Results

1.2s	3209×	body	1280	valid
564.0ms	655×	body	2560	valid
397.0ms	1868×	body	640	valid
109.0ms	778×	body	320	valid
53.0ms	1136×	body	80	valid
34.0ms	354×	body	160	valid

Details

analyze754.0ms

sample83.0ms

simplify3.0ms

prune3.0ms

localize11.0ms

rewrite10.0ms

series40.0ms

simplify86.0ms

prune61.0ms

localize11.0ms

rewrite33.0ms

series204.0ms

simplify45.0ms

prune155.0ms

localize18.0ms

rewrite29.0ms

series124.0ms

simplify41.0ms

prune158.0ms

localize24.0ms

rewrite47.0ms

series142.0ms

simplify51.0ms

prune164.0ms

regimes171.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze755.0ms

sample2.6s

Profiling