Details

sample264.0ms

Algorithm

intervals

Results

104.0ms	38×	body	2560	valid
91.0ms	91×	body	1280	valid
36.0ms	72×	body	640	valid
8.0ms	25×	body	320	valid
4.0ms	19×	body	160	valid
2.0ms	11×	body	80	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

30.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
49.0ms	(- 1.0 (cos x))

simplify943.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune388.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.6b	(- 1.0 (cos x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 177

Calls

3 calls:

30.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
26.0ms	(/ (sin x) (- 1.0 (cos x)))
12.0ms	(- 1.0 (cos x))

series145.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
57.0ms	(/ (sin x) (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	3505
1	656
0	269

prune639.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ 1.0 (cos x)) (- 1.0 (cos x)))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.6b	(- 1.0 (cos x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
27×	`prod-diff` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `associate-r` `flip-+`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-l` `log1p-expm1-u` `flip--`
3×	`sub-neg` `fma-neg` `distribute-lft-out`
2×	`+-commutative` `sum-log` `associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

41.0ms	(* (+ 1.0 (cos x)) (- 1.0 (cos x)))
6.0ms	(+ 1.0 (cos x))
5.0ms	(+ 1.0 (cos x))
16.0ms	(- 1.0 (cos x))

series112.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (+ 1.0 (cos x)) (- 1.0 (cos x)))
19.0ms	(+ 1.0 (cos x))
12.0ms	(+ 1.0 (cos x))
23.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	3248
1	458
0	155

prune586.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.1b	(/ (cos x) (sin x))
1.7b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
222×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
210×	`add-cube-cbrt`
169×	`prod-diff`
31×	`div-inv`
13×	`fma-neg`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 265

Calls

3 calls:

8.0ms	(/ 1.0 (sin x))
16.0ms	(/ (cos x) (sin x))
76.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ 1.0 (sin x))
40.0ms	(/ (cos x) (sin x))
138.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.7s

Counts

274 → 274

Iterations

Iter	Nodes
done	5001
2	2829
1	846
0	371

prune807.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

regimes260.0ms

Accuracy

97.5% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 30.4b

bsearch2.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.5s	1504×	body	2560	valid
2.5s	2754×	body	1280	valid
1.6s	1935×	body	640	valid
542.0ms	490×	body	160	valid
350.0ms	977×	body	320	valid
40.0ms	339×	body	80	valid
9.0ms	1×	body	5120	valid