Details

sample310.0ms

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

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

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))

rewrite37.0ms

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:

9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

117 → 117

Iterations

Useful iterations: 3 (822.0ms)

Iter	Nodes	Cost
0	138	1632
1	312	1486
2	930	1368
3	4833	1346
done	5000	1346

prune251.0ms

Pruning

12 alts after pruning (12 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)

rewrite7.0ms

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)
2.0ms	(pow (sin x) 2)

series73.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify795.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	64	576
1	138	492
2	374	432
3	1173	432
done	5000	432

prune220.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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:

40.0ms	(* (+ (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))

series352.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
36.0ms	(- (sqrt 1.0) (tan x))
92.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))

simplify767.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (231.0ms)

Iter	Nodes	Cost
0	220	2757
1	561	2524
2	2221	2316
done	5000	2316

prune336.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

22.0ms	(/ (/ (- 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series356.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (/ (- 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
110.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (sqrt 1.0) (tan x)))
31.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

218 → 218

Iterations

Useful iterations: 2 (344.0ms)

Iter	Nodes	Cost
0	298	5616
1	749	5312
2	2995	5091
done	5000	5091

prune533.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes132.0ms

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	12	27
1	14	27
done	14	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

681.0ms	1521×	body	1280	valid
350.0ms	1285×	body	640	valid
256.0ms	4286×	body	80	valid
115.0ms	606×	body	320	valid
42.0ms	302×	body	160	valid