Details

sample398.0ms

Algorithm

intervals

Results

105.0ms	56×	body	1280	valid
95.0ms	37×	body	640	valid
32.0ms	136×	body	80	valid
17.0ms	23×	body	320	valid
2.0ms	4×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

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` `insert-posit16` `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 → 128

Calls

4 calls:

6.0ms	(- 1 (* (tan x) (tan x)))
57.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
19.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

series489.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1 (* (tan x) (tan x)))
133.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
111.0ms	(* (tan x) (tan x))
201.0ms	(* (tan x) (tan x))

simplify4.8s

Counts

140 → 140

Iterations

Iter	Nodes
3	2926
2	985
1	383
0	157

prune1.3s

Pruning

11 alts after pruning (11 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))
0.2b	(* (+ 1 (tan x)) (- 1 (tan x)))
0.3b	(* (tan x) (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
27×	`prod-diff`
13×	`pow1`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`expm1-log1p-u` `flip3-+` `flip3--` `tan-quot` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`sub-neg` `fma-def` `fma-neg` `swap-sqr` `associate-l/` `associate-r/`
2×	`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 → 134

Calls

4 calls:

6.0ms	(- 1 (tan x))
5.0ms	(+ 1 (tan x))
37.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
28.0ms	(* (tan x) (tan x))

series168.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- 1 (tan x))
28.0ms	(+ 1 (tan x))
75.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
37.0ms	(* (tan x) (tan x))

simplify7.2s

Counts

146 → 146

Iterations

Iter	Nodes
3	3958
2	1402
1	535
0	188

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
8.2b	(cbrt (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

232×	`tan-quot`
148×	`frac-times`
129×	`pow1`
88×	`associate-*l/`
76×	`associate-*r/`
63×	`cbrt-div`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
20×	`pow-plus` `add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
15×	`pow2`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 219

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
127.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
201.0ms	(cbrt (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))
59.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
37.0ms	(cbrt (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))

simplify1.1s

Counts

231 → 231

Iterations

Iter	Nodes
2	2294
1	702
0	266

prune2.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

15.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))
111.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))
73.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.2s

Counts

186 → 186

Iterations

Iter	Nodes
3	2206
2	896
1	299
0	112

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes319.0ms

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	12
1	12
0	9

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	1518×	body	1280	valid
1.7s	1247×	body	640	valid
1.0s	4361×	body	80	valid
374.0ms	576×	body	320	valid
150.0ms	298×	body	160	valid