Details

sample237.0ms

Algorithm

intervals

Results

117.0ms	59×	body	1280	valid
32.0ms	40×	body	640	valid
25.0ms	129×	body	80	valid
12.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	42
5	42
4	37
3	29
2	22
1	13
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 124

Calls

4 calls:

13.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(- 1 (* (tan x) (tan x)))
19.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
65.0ms	(- 1 (* (tan x) (tan x)))
57.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify4.7s

Counts

136 → 136

Iterations

Iter	Nodes
3	2961
2	988
1	380
0	154

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 170

Calls

4 calls:

25.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))
62.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))
60.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.3s

Counts

182 → 182

Iterations

Iter	Nodes
3	2319
2	886
1	297
0	110

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

264×	`tan-quot`
233×	`pow1`
147×	`associate-*r/`
113×	`frac-times`
88×	`associate-*l/`
73×	`pow-prod-up`
47×	`pow-prod-down`
45×	`pow-sqr` `frac-sub`
37×	`pow-plus`
30×	`add-cbrt-cube` `add-exp-log`
27×	`pow2`
17×	`prod-exp` `cbrt-unprod`
14×	`sub-div`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

4 → 266

Calls

4 calls:

25.0ms	(* (tan x) (tan x))
170.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))
80.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
104.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (tan x) (tan x))
101.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))
64.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
71.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify876.0ms

Counts

278 → 278

Iterations

Iter	Nodes
2	2399
1	886
0	260

prune3.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(- 1 (/ (* (sin x) (tan x)) (cos x)))
0.2b	(* (sin x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

21.0ms	(/ (* (sin x) (tan x)) (cos x))
9.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
10.0ms	(* (sin x) (tan x))
12.0ms	(* (tan x) (tan x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* (sin x) (tan x)) (cos x))
69.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
66.0ms	(* (sin x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify8.1s

Counts

128 → 128

Iterations

Iter	Nodes
3	5374
2	1332
1	475
0	192

prune1.4s

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

simplify2.0ms

Iterations

Iter	Nodes
2	10
1	10
0	9

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.6s	1557×	body	1280	valid
1.6s	1246×	body	640	valid
935.0ms	4227×	body	80	valid
464.0ms	635×	body	320	valid
175.0ms	335×	body	160	valid