Details

analyze694.0ms (17%)

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

sample37.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	40×	body	1280	valid
8.0ms	46×	body	640	valid
6.0ms	141×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify504.0ms (12.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

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:

0.2b	(- 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)))

series67.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
18.0ms	(* (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

prune263.0ms (6.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	13	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 0.1b

Counts

117 → 13

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
30×	`associate-r`
25×	`times-frac`
18×	`add-cube-cbrt`
10×	`add-exp-log` `difference-of-squares`
9×	`add-cbrt-cube`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1`
5×	`sqrt-prod` `distribute-lft-out--`
4×	`flip3-+` `associate-l` `flip-+`
3×	`unpow-prod-down` `pow-unpow`
2×	`frac-times` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `sum-log` `-commutative` `flip--` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

20.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
4.0ms	(+ (tan x) (sqrt 1.0))
4.0ms	(- (sqrt 1.0) (tan x))
3.0ms	(pow (tan x) 2)

series65.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
9.0ms	(pow (tan x) 2)
7.0ms	(- (sqrt 1.0) (tan x))
7.0ms	(+ (tan x) (sqrt 1.0))

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5078	1401

prune297.0ms (7.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow (tan x) 2)
0.3b	(* (tan x) (tan x))
0.3b	(cbrt (pow (- 1.0 (pow (tan x) 2)) 3))
0.4b	(pow (- 1.0 (pow (tan x) 2)) 3)

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`unpow-prod-down`
22×	`cbrt-prod`
16×	`add-cube-cbrt` `cube-prod` `difference-of-squares`
13×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube` `sqr-pow`
6×	`pow-unpow`
5×	`unpow2`
4×	`tan-quot` `cube-div` `distribute-lft-out--` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `unpow3` `pow-exp` `flip--`
1×	`pow2` `frac-times` `pow-plus` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

9.0ms	(pow (- 1.0 (pow (tan x) 2)) 3)
7.0ms	(cbrt (pow (- 1.0 (pow (tan x) 2)) 3))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 2)

series46.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (- 1.0 (pow (tan x) 2)) 3)
9.0ms	(cbrt (pow (- 1.0 (pow (tan x) 2)) 3))
9.0ms	(* (tan x) (tan x))
8.0ms	(pow (tan x) 2)

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4989	1086
1	4989	1086

prune274.0ms (6.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 0.0b

Counts

138 → 11

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
25×	`times-frac`
12×	`add-cube-cbrt`
11×	`unpow-prod-down`
10×	`difference-of-squares`
9×	`pow-unpow`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r/` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-to-exp` `distribute-rgt-out--` `pow-pow` `pow-exp`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 87

Calls

4 calls:

42.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series79.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))
9.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)

simplify33.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5194	1408

prune227.0ms (5.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	97	13	110

Merged error: 0.0b

Counts

110 → 13

regimes148.0ms (3.6%)

Accuracy

Total 0.3b remaining (81.9%)

Threshold costs 0.3b (81.9%)

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%)

sample987.0ms (24.2%)

Algorithm

1×

intervals

Results

386.0ms	1512×	body	1280	valid
214.0ms	1251×	body	640	valid
165.0ms	4357×	body	80	valid
71.0ms	581×	body	320	valid
25.0ms	299×	body	160	valid

Details

analyze694.0ms (17%)

sample37.0ms (0.9%)

simplify504.0ms (12.4%)

prune7.0ms (0.2%)

localize19.0ms (0.5%)

rewrite25.0ms (0.6%)

series67.0ms (1.7%)

simplify57.0ms (1.4%)

prune263.0ms (6.5%)

localize12.0ms (0.3%)

rewrite35.0ms (0.9%)

series65.0ms (1.6%)

simplify30.0ms (0.7%)

prune297.0ms (7.3%)

localize13.0ms (0.3%)

rewrite26.0ms (0.6%)

series46.0ms (1.1%)

simplify61.0ms (1.5%)

prune274.0ms (6.7%)

localize10.0ms (0.2%)

rewrite53.0ms (1.3%)

series79.0ms (1.9%)

simplify33.0ms (0.8%)

prune227.0ms (5.6%)

regimes148.0ms (3.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample987.0ms (24.2%)

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