Details

analyze751.0ms

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

sample135.0ms

Algorithm

intervals

Results

61.0ms	103×	body	1280	valid
28.0ms	24×	body	2560	valid
21.0ms	61×	body	640	valid
6.0ms	22×	body	320	valid
3.0ms	37×	body	80	valid
2.0ms	9×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	77	7
1	77	7

prune6.0ms

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: 36.2b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
5.3b	(tan (+ x eps))

rewrite19.0ms

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:

12.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series52.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
25.0ms	(tan (+ x eps))

simplify38.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4905	332
1	4905	332

prune65.0ms

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: 11.9b

Counts

31 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5516	1532

prune178.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

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: 11.8b

Counts

104 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
20.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series161.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
22.0ms	(/ (* (tan x) (sin eps)) (cos eps))
15.0ms	(* (tan x) (sin eps))
103.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4943	1069
1	4943	1069

prune149.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 11.8b

Counts

93 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (* (tan eps) (tan eps)))
0.2b	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
0.3b	(* (tan eps) (tan eps))
2.0b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

53×	`tan-quot`
25×	`pow1` `frac-times` `associate-*r/`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`associate-*l/`
10×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
6×	`add-log-exp`
5×	`associate-r` `frac-sub`
3×	`swap-sqr` `*-commutative`
2×	`flip3-+` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 108

Calls

4 calls:

8.0ms	(* (tan x) (* (tan eps) (tan eps)))
13.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
5.0ms	(* (tan eps) (tan eps))
12.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series411.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (tan x) (* (tan eps) (tan eps)))
54.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
12.0ms	(* (tan eps) (tan eps))
317.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify36.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5160	1988

prune136.0ms

Filtered

76 candidates to 120 candidates (-57.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	118	14	132

Merged error: 11.7b

Counts

132 → 14

regimes221.0ms

Accuracy

85.8% (1.0b remaining)

Error of 15.3b against oracle of 14.2b and baseline of 21.5b

bsearch88.0ms

Steps

Iters	Range		Point
11	3.168576286413647e-95	1.26152579152076e-72	1.240783246872505e-72
10	-0.00015952590304140683	-2.3349431189946093e-18	-1.3369941042866534e-17

simplify14.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	543	108
1	543	108

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3349×	body	1280	valid
579.0ms	648×	body	2560	valid
410.0ms	1803×	body	640	valid
116.0ms	786×	body	320	valid
53.0ms	1086×	body	80	valid
35.0ms	328×	body	160	valid

Details

analyze751.0ms

sample135.0ms

simplify7.0ms

prune6.0ms

localize14.0ms

rewrite19.0ms

series52.0ms

simplify38.0ms

prune65.0ms

localize11.0ms

rewrite30.0ms

series197.0ms

simplify59.0ms

prune178.0ms

localize17.0ms

rewrite36.0ms

series161.0ms

simplify62.0ms

prune149.0ms

localize16.0ms

rewrite41.0ms

series411.0ms

simplify36.0ms

prune136.0ms

regimes221.0ms

bsearch88.0ms

simplify14.0ms

end0.0ms

sample2.8s

Profiling