Details

analyze777.0ms

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

sample94.0ms

Algorithm

intervals

Results

41.0ms	106×	body	1280	valid
25.0ms	29×	body	2560	valid
14.0ms	63×	body	640	valid
2.0ms	16×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune8.0ms

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: 38.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite11.0ms

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

series39.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(tan (+ x eps))

simplify47.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune61.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 17.5b

Counts

31 → 8

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))
1.8b	(- (/ (+ (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))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series195.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (tan x) (tan eps))
55.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(* (tan x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5109	1560

prune171.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	83	14	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	88	17	105

Merged error: 17.3b

Counts

105 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (* (tan eps) (tan eps)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan eps) (tan eps))
1.8b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

8.0ms	(* (tan x) (* (tan eps) (tan eps)))
5.0ms	(* (tan x) (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))

series377.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (tan x) (* (tan eps) (tan eps)))
23.0ms	(* (tan x) (tan eps))
8.0ms	(* (tan eps) (tan eps))
319.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4983	1620
1	4983	1620

prune176.0ms

Filtered

72 candidates to 105 candidates (-45.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	106	16	122

Merged error: 17.3b

Counts

122 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (* (tan eps) (tan eps)))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan eps) (tan eps))
1.8b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

22×	`tan-quot`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`frac-times` `associate-*r/`
6×	`associate-l` `associate-*l/` `add-log-exp`
5×	`prod-exp` `frac-sub` `cbrt-unprod`
4×	`associate-r` `pow-prod-down`
3×	`times-frac` `swap-sqr` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate--l+` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv` `associate-/l/` `associate-/l*`

Counts

4 → 94

Calls

4 calls:

8.0ms	(* (tan x) (* (tan eps) (tan eps)))
6.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan eps) (tan eps))
14.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series396.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (tan x) (* (tan eps) (tan eps)))
22.0ms	(/ (* (tan x) (sin eps)) (cos eps))
8.0ms	(* (tan eps) (tan eps))
339.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4984	1834
1	4984	1834

prune111.0ms

Filtered

73 candidates to 106 candidates (-45.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	106	16	122

Merged error: 17.3b

Counts

122 → 16

regimes205.0ms

Accuracy

80.3% (1.5b remaining)

Error of 16.0b against oracle of 14.5b and baseline of 22.1b

bsearch93.0ms

Steps

Iters	Range		Point
10	2.7247153317066202e-86	5.559643754350374e-72	1.9461005157827348e-72
7	-4.7507238382498537e-144	-4.704089064816693e-146	-4.683864053063239e-144

simplify13.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	596	110
1	596	110

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3223×	body	1280	valid
553.0ms	642×	body	2560	valid
417.0ms	1893×	body	640	valid
121.0ms	831×	body	320	valid
46.0ms	1058×	body	80	valid
34.0ms	353×	body	160	valid

Details

analyze777.0ms

sample94.0ms

simplify5.0ms

prune8.0ms

localize9.0ms

rewrite11.0ms

series39.0ms

simplify47.0ms

prune61.0ms

localize11.0ms

rewrite33.0ms

series195.0ms

simplify51.0ms

prune171.0ms

localize20.0ms

rewrite33.0ms

series377.0ms

simplify46.0ms

prune176.0ms

localize25.0ms

rewrite36.0ms

series396.0ms

simplify48.0ms

prune111.0ms

regimes205.0ms

bsearch93.0ms

simplify13.0ms

end0.0ms

sample2.6s

Profiling