Details

analyze718.0ms (16.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample42.0ms (1%)

Algorithm

1×

intervals

Results

15.0ms	56×	body	1280	valid
7.0ms	41×	body	640	valid
6.0ms	131×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify535.0ms (12.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5284	15

prune7.0ms (0.2%)

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: 0.3b

Counts

2 → 1

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

7.0ms	(* (tan x) (tan x))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
3.0ms	(- 1.0 (* (tan x) (tan x)))

series69.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
19.0ms	(* (tan x) (tan x))
9.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune266.0ms (6.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	11	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)

series14.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5266	424

prune220.0ms (5.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.0b

Counts

95 → 11

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.6b	(pow (tan x) 6)
9.6b	(cbrt (pow (tan x) 6))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`times-frac`
19×	`cbrt-prod`
16×	`difference-of-squares`
12×	`pow1`
10×	`unpow-prod-down`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`sqr-pow`
4×	`tan-quot` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

9.0ms	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(cbrt (pow (tan x) 6))
3.0ms	(pow (tan x) 6)

series65.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(pow (tan x) 6)
9.0ms	(cbrt (pow (tan x) 6))
9.0ms	(* (tan x) (tan x))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4946	1517
1	4946	1517

prune289.0ms (6.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 0.0b

Counts

135 → 12

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
0.2b	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
0.3b	(pow (tan x) 2)

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
49×	`times-frac`
30×	`add-cube-cbrt` `associate-r`
20×	`difference-of-squares`
14×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`sqrt-prod` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `associate-l` `associate-/r*` `associate-/r/` `flip-+`
3×	`unpow-prod-down` `pow-unpow`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `unpow2` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

19.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
11.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
4.0ms	(- (sqrt 1.0) (tan x))
3.0ms	(pow (tan x) 2)

series90.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
27.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
12.0ms	(pow (tan x) 2)
7.0ms	(- (sqrt 1.0) (tan x))

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4966	2307
1	4966	2307

prune361.0ms (8.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	149	12	161

Merged error: 0.0b

Counts

161 → 12

regimes143.0ms (3.4%)

Accuracy

Total 0.3b remaining (79.8%)

Threshold costs 0.3b (79.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms (0%)

sample1.0s (24.7%)

Algorithm

1×

intervals

Results

419.0ms	1574×	body	1280	valid
216.0ms	1219×	body	640	valid
169.0ms	4244×	body	80	valid
82.0ms	641×	body	320	valid
28.0ms	322×	body	160	valid

Details

analyze718.0ms (16.9%)

sample42.0ms (1%)

simplify535.0ms (12.6%)

prune7.0ms (0.2%)

localize19.0ms (0.5%)

rewrite25.0ms (0.6%)

series69.0ms (1.6%)

simplify57.0ms (1.4%)

prune266.0ms (6.3%)

localize13.0ms (0.3%)

rewrite11.0ms (0.3%)

series14.0ms (0.3%)

simplify39.0ms (0.9%)

prune220.0ms (5.2%)

localize10.0ms (0.2%)

rewrite24.0ms (0.6%)

series65.0ms (1.5%)

simplify56.0ms (1.3%)

prune289.0ms (6.8%)

localize11.0ms (0.3%)

rewrite43.0ms (1%)

series90.0ms (2.1%)

simplify67.0ms (1.6%)

prune361.0ms (8.5%)

regimes143.0ms (3.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (24.7%)

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