Details

sample299.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
14.0ms	51×	body	640	valid
9.0ms	126×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify25.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series201.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

117 → 117

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	138	1632
1	312	1486
2	842	1368
3	2993	1346
done	5000	1345

prune253.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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)

rewrite9.0ms

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:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series70.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
18.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify1.6s

Counts

84 → 84

Iterations

Useful iterations: 4 (493.0ms)

Iter	Nodes	Cost
0	64	576
1	138	492
2	304	432
3	784	432
4	3027	424
done	5000	424

prune226.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

37.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(- (sqrt 1.0) (tan x))
14.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))

series347.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(- (sqrt 1.0) (tan x))
93.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))

simplify935.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (349.0ms)

Iter	Nodes	Cost
0	220	2757
1	561	2524
2	1994	2324
done	5000	2324

prune336.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

134.0ms	(* (+ (tan x) (sqrt 1.0)) (- (/ (sqrt 1.0) (+ 1.0 (* (tan x) (tan x)))) (/ (tan x) (+ 1.0 (* (tan x) (tan x))))))
43.0ms	(- (/ (sqrt 1.0) (+ 1.0 (* (tan x) (tan x)))) (/ (tan x) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series406.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (+ (tan x) (sqrt 1.0)) (- (/ (sqrt 1.0) (+ 1.0 (* (tan x) (tan x)))) (/ (tan x) (+ 1.0 (* (tan x) (tan x))))))
126.0ms	(- (/ (sqrt 1.0) (+ 1.0 (* (tan x) (tan x)))) (/ (tan x) (+ 1.0 (* (tan x) (tan x)))))
33.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

simplify890.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (311.0ms)

Iter	Nodes	Cost
0	216	3466
1	570	3235
2	2177	2982
done	5001	2982

prune338.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	13	19
done	13	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

683.0ms	1521×	body	1280	valid
363.0ms	1285×	body	640	valid
258.0ms	4286×	body	80	valid
115.0ms	606×	body	320	valid
44.0ms	302×	body	160	valid