Details

sample350.0ms

Algorithm

intervals

Results

19.0ms	45×	body	1280	valid
12.0ms	44×	body	640	valid
9.0ms	133×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9
done	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `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 → 119

Calls

4 calls:

22.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series205.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 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))
43.0ms	(* (tan x) (tan x))

simplify43.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882
done	5001	882

prune277.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`add-cube-cbrt`
27×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`tan-quot` `div-inv` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate-/l/`
2×	`flip3--` `frac-2neg` `associate-*l/` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod`
1×	`pow2` `frac-times` `sub-neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `unswap-sqr`

Counts

4 → 136

Calls

4 calls:

36.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
13.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
14.0ms	(* (tan x) (tan x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
57.0ms	(/ (* (tan x) (sin x)) (cos x))
53.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
32.0ms	(* (tan x) (tan x))

simplify90.0ms

Counts

148 → 148

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	574	1974
1	2573	1594
2	5002	1555
done	5002	1555

prune347.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
20.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)

simplify60.0ms

Counts

92 → 92

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1669	260
3	5001	256
done	5001	256

prune237.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)
0.6b	(expm1 (pow (cos x) 2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow`
7×	`pow1` `add-exp-log`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 71

Calls

4 calls:

3.0ms	(pow (sin x) 2)
6.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
1.0ms	(expm1 (pow (cos x) 2))

series111.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
21.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
55.0ms	(expm1 (pow (cos x) 2))

simplify68.0ms

Counts

83 → 83

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	182	292
1	612	248
2	2096	248
3	5001	245
done	5001	245

prune229.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15
done	15	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

649.0ms	1436×	body	1280	valid
356.0ms	1280×	body	640	valid
254.0ms	4330×	body	80	valid
124.0ms	659×	body	320	valid
38.0ms	295×	body	160	valid