Details

sample240.0ms

Algorithm

intervals

Results

88.0ms	45×	body	1280	valid
36.0ms	44×	body	640	valid
24.0ms	138×	body	80	valid
10.0ms	20×	body	320	valid
3.0ms	9×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	38
5	38
4	36
3	28
2	23
1	15
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

161×	`*-un-lft-identity`
143×	`add-sqr-sqrt`
75×	`times-frac`
70×	`difference-of-squares`
34×	`add-cube-cbrt`
32×	`distribute-lft-out`
29×	`associate-l`
20×	`swap-sqr`
18×	`pow1`
16×	`*-commutative` `unswap-sqr`
15×	`associate-/l*`
14×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`associate-r` `add-log-exp`
5×	`associate-/r*`
4×	`insert-posit16`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up` `cbrt-unprod` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 196

Calls

4 calls:

120.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
34.0ms	(- 1 (* (tan x) (tan x)))
27.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
55.0ms	(- 1 (* (tan x) (tan x)))
43.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

simplify2.6s

Counts

208 → 208

Iterations

Iter	Nodes
done	5180
3	3246
2	1016
1	438
0	180

prune629.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ 1 (tan x))
0.2b	(- 1 (tan x))
0.2b	(* (+ 1 (tan x)) (- 1 (tan x)))
0.3b	(* (tan x) (tan x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`flip3-+` `flip3--` `tan-quot` `flip-+` `insert-posit16` `flip--` `difference-of-squares`
3×	`sub-neg` `swap-sqr` `associate-l/` `associate-r/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up`

Counts

4 → 93

Calls

4 calls:

11.0ms	(+ 1 (tan x))
11.0ms	(- 1 (tan x))
42.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
23.0ms	(* (tan x) (tan x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ 1 (tan x))
36.0ms	(- 1 (tan x))
96.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
41.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1190
1	382
0	136

prune502.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (tan x))
0.2b	(/ (* (- 1 (* (tan x) (tan x))) (- 1 (tan x))) (- 1 (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

292×	`add-sqr-sqrt`
232×	`*-un-lft-identity`
162×	`times-frac`
142×	`difference-of-squares`
118×	`associate-l`
61×	`add-cube-cbrt`
50×	`distribute-lft-out--`
48×	`associate-r`
27×	`associate-/l*`
23×	`*-commutative` `unswap-sqr`
20×	`swap-sqr`
18×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
8×	`flip3--` `tan-quot` `flip--` `associate-/l/`
6×	`frac-times` `associate-/r*` `add-log-exp`
4×	`associate-l/` `associate-r/` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`pow2` `cbrt-undiv` `pow-plus` `div-exp` `pow-prod-down` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv`

Counts

4 → 294

Calls

4 calls:

11.0ms	(- 1 (tan x))
342.0ms	(/ (* (- 1 (* (tan x) (tan x))) (- 1 (tan x))) (- 1 (tan x)))
25.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1 (tan x))
43.0ms	(/ (* (- 1 (* (tan x) (tan x))) (- 1 (tan x))) (- 1 (tan x)))
38.0ms	(* (tan x) (tan x))
40.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

306 → 306

Iterations

Iter	Nodes
done	5059
2	2872
1	977
0	357

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (tan x))
0.2b	(- 1 (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`pow1` `*-un-lft-identity`
12×	`add-cube-cbrt`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`insert-posit16` `difference-of-squares`
2×	`pow2` `frac-times` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

9.0ms	(- 1 (tan x))
15.0ms	(- 1 (tan x))
30.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series136.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1 (tan x))
30.0ms	(- 1 (tan x))
35.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	1644
2	467
1	204
0	84

prune444.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes471.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.6s	1443×	body	1280	valid
1.8s	1183×	body	640	valid
1.1s	4414×	body	80	valid
515.0ms	647×	body	320	valid
286.0ms	313×	body	160	valid