Details

sample47.0ms

Algorithm

intervals

Results

15.0ms	50×	body	1280	valid
8.0ms	133×	body	80	valid
7.0ms	38×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	37	15
done	37	15

prune12.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

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))

rewrite28.0ms

Algorithm

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 → 105

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
7.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series80.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- 1.0 (* (tan x) (tan x)))
38.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
11.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

117 → 117

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	138	1632
1	314	1488
2	933	1370
3	3435	1350
done	5001	1345

prune206.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

5.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(- (sqrt 1.0) (tan x))
15.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
6.0ms	(* (tan x) (tan x))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (sqrt 1.0) (tan x))
8.0ms	(- (sqrt 1.0) (tan x))
20.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
10.0ms	(* (tan x) (tan x))

simplify437.0ms

Counts

101 → 101

Iterations

Useful iterations: done (434.0ms)

Iter	Nodes	Cost
0	134	1238
1	336	1055
2	1329	966
done	5000	961

prune193.0ms

Filtered

67 candidates to 101 candidates (-50.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 0.0b

Counts

113 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

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

series15.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.4s

Counts

84 → 84

Iterations

Useful iterations: 4 (612.0ms)

Iter	Nodes	Cost
0	64	576
1	144	508
2	375	432
3	1109	432
4	3443	424
done	5000	424

prune172.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

9.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(* (sin x) (tan x))
7.0ms	(/ (* (sin x) (tan x)) (cos x))
6.0ms	(* (tan x) (tan x))

series86.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms	(* (sin x) (tan x))
18.0ms	(/ (* (sin x) (tan x)) (cos x))
10.0ms	(* (tan x) (tan x))

simplify555.0ms

Counts

121 → 121

Iterations

Useful iterations: done (552.0ms)

Iter	Nodes	Cost
0	190	1949
1	452	1859
2	1635	1707
done	5000	1693

prune132.0ms

Filtered

85 candidates to 121 candidates (-42.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	119	14	133

Merged error: 0.0b

Counts

133 → 14

regimes322.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
done	13	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

390.0ms	1509×	body	1280	valid
223.0ms	1205×	body	640	valid
192.0ms	4390×	body	80	valid
83.0ms	612×	body	320	valid
26.0ms	284×	body	160	valid

Details

sample47.0ms

simplify24.0ms

prune12.0ms

localize10.0ms

rewrite28.0ms

series80.0ms

simplify1.0s

prune206.0ms

localize11.0ms

rewrite34.0ms

series46.0ms

simplify437.0ms

prune193.0ms

localize16.0ms

rewrite13.0ms

series15.0ms

simplify1.4s

prune172.0ms

localize14.0ms

rewrite31.0ms

series86.0ms

simplify555.0ms

prune132.0ms

regimes322.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

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