Details

sample269.0ms

Algorithm

intervals

Results

132.0ms	51×	body	1280	valid
32.0ms	30×	body	640	valid
31.0ms	139×	body	80	valid
21.0ms	27×	body	320	valid
5.0ms	9×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	39
3	31
2	24
1	15
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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

rewrite88.0ms

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:

5.0ms	(- 1 (* (tan x) (tan x)))
22.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
25.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- 1 (* (tan x) (tan x)))
96.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
52.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	2001
2	1114
1	399
0	157

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
58×	`times-frac`
52×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`swap-sqr` `associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `quot-tan` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 163

Calls

4 calls:

22.0ms	(/ (sin x) (cos x))
17.0ms	(/ (sin x) (cos x))
38.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
15.0ms	(* (tan x) (tan x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin x) (cos x))
30.0ms	(/ (sin x) (cos x))
60.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
38.0ms	(* (tan x) (tan x))

simplify1.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	2004
2	1720
1	527
0	173

prune833.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

240×	`pow1`
74×	`pow-prod-up`
72×	`tan-quot`
48×	`pow-prod-down`
46×	`pow-sqr`
38×	`pow-plus`
36×	`frac-times`
32×	`add-cbrt-cube` `add-exp-log`
28×	`pow2`
24×	`associate-l/` `associate-r/`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

29.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
120.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
102.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
74.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
52.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify823.0ms

Counts

236 → 236

Iterations

Iter	Nodes
done	2000
2	901
1	324
0	112

prune736.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
100×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
80×	`add-cube-cbrt`
32×	`difference-of-squares`
26×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp` `tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `clear-num` `frac-2neg` `pow-plus` `1-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 215

Calls

4 calls:

30.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x))))
13.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
14.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))

series307.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x))))
103.0ms	(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
33.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

227 → 227

Iterations

Iter	Nodes
done	2001
2	1743
1	765
0	290

prune953.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.3s	1537×	body	1280	valid
1.5s	1235×	body	640	valid
875.0ms	4274×	body	80	valid
533.0ms	662×	body	320	valid
133.0ms	292×	body	160	valid