Details

analyze805.0ms (14.4%)

Algorithm

1×

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

sample91.0ms (1.6%)

Algorithm

1×

intervals

Results

41.0ms	111×	body	1280	valid
17.0ms	19×	body	2560	valid
13.0ms	61×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	31×	body	80	valid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune6.0ms (0.1%)

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: 37.5b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
4.8b	(tan (+ x eps))

rewrite11.0ms (0.2%)

Algorithm

1×	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))

series43.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (tan (+ x eps)) (tan x))
18.0ms	(tan (+ x eps))

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune65.0ms (1.2%)

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: 14.3b

Counts

31 → 7

localize13.0ms (0.2%)

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))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms (0.6%)

Algorithm

1×	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:

12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
4.0ms	(+ (tan x) (tan eps))

series206.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
59.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(* (tan x) (tan eps))
21.0ms	(+ (tan x) (tan eps))

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5109	1560

prune183.0ms (3.3%)

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: 14.2b

Counts

104 → 12

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.5b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 109

Calls

4 calls:

12.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))

series415.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

335.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
32.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
25.0ms	(* (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4984	1908
1	4984	1908

prune230.0ms (4.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	118	15	133

Merged error: 14.1b

Counts

133 → 15

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
0.3b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

20.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
12.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
5.0ms	(* (sin x) (sin eps))

series197.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
59.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
23.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
10.0ms	(* (sin x) (sin eps))

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4991	2589
1	4991	2589

prune150.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 12.3b

Counts

135 → 12

regimes160.0ms (2.9%)

Accuracy

Total 0.3b remaining (2.7%)

Threshold costs 0.3b (2.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	43
1	57	43

end0.0ms (0%)

sample2.7s (47.6%)

Algorithm

1×

intervals

Results

1.3s	3331×	body	1280	valid
526.0ms	603×	body	2560	valid
390.0ms	1758×	body	640	valid
123.0ms	816×	body	320	valid
50.0ms	1145×	body	80	valid
37.0ms	347×	body	160	valid

Details

analyze805.0ms (14.4%)

sample91.0ms (1.6%)

simplify5.0ms (0.1%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

rewrite11.0ms (0.2%)

series43.0ms (0.8%)

simplify51.0ms (0.9%)

prune65.0ms (1.2%)

localize13.0ms (0.2%)

rewrite32.0ms (0.6%)

series206.0ms (3.7%)

simplify50.0ms (0.9%)

prune183.0ms (3.3%)

localize15.0ms (0.3%)

rewrite36.0ms (0.6%)

series415.0ms (7.4%)

simplify31.0ms (0.6%)

prune230.0ms (4.1%)

localize23.0ms (0.4%)

rewrite49.0ms (0.9%)

series197.0ms (3.5%)

simplify48.0ms (0.9%)

prune150.0ms (2.7%)

regimes160.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (47.6%)

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