Details

sample78.0ms

Algorithm

intervals

Results

39.0ms	38×	body	2560	valid
11.0ms	56×	body	640	valid
10.0ms	38×	body	1280	valid
3.0ms	80×	body	80	valid
3.0ms	25×	body	320	valid
2.0ms	19×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- 1.0 (cos x))
12.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

11.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- 1.0 (cos x))
66.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune246.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1.0 x) x)
0.1b	(/ (cos x) x)
0.2b	(/ (/ (cos x) x) x)
14.7b	(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

rewrite576.0ms

Algorithm

rewrite-expression-head

Rules

5967×	`times-frac`
3193×	`add-sqr-sqrt`
3183×	`*-un-lft-identity`
3157×	`add-cube-cbrt`
1849×	`prod-diff`
367×	`div-inv`
43×	`fma-neg`
29×	`associate-/l*`
16×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `distribute-rgt-out--` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 2107

Calls

4 calls:

9.0ms	(/ (/ 1.0 x) x)
7.0ms	(/ (cos x) x)
20.0ms	(/ (/ (cos x) x) x)
226.0ms	(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (/ 1.0 x) x)
36.0ms	(/ (cos x) x)
41.0ms	(/ (/ (cos x) x) x)
137.0ms	(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

simplify1.2s

Counts

2119 → 2119

Iterations

Iter	Nodes
done	5001
0	2352

prune15.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 x) x)
0.1b	(/ (/ 1 x) x)
14.7b	(fma 1.0 (/ (/ 1 x) x) (* (- (/ (/ 1 x) x)) (cos x)))
28.6b	(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
88×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
26×	`associate-/l*`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`div-exp`
10×	`pow1` `div-inv`
6×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `pow-div`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 172

Calls

4 calls:

19.0ms	(/ (/ 1 x) x)
14.0ms	(/ (/ 1 x) x)
0.0ms	(fma 1.0 (/ (/ 1 x) x) (* (- (/ (/ 1 x) x)) (cos x)))
1.0ms	(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (/ 1 x) x)
18.0ms	(/ (/ 1 x) x)
121.0ms	(fma 1.0 (/ (/ 1 x) x) (* (- (/ (/ 1 x) x)) (cos x)))
94.0ms	(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))

simplify956.0ms

Counts

184 → 184

Iterations

Iter	Nodes
done	5002
2	1720
1	405
0	178

prune756.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 x) x)
0.1b	(/ (/ 1 x) x)
28.6b	(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
28.8b	(fma (/ 1.0 x) (/ 1 x) (* (- (/ (/ 1 x) x)) (cos x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
88×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
26×	`associate-/l*`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`div-exp`
10×	`pow1` `div-inv`
6×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `pow-div`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 172

Calls

4 calls:

17.0ms	(/ (/ 1 x) x)
11.0ms	(/ (/ 1 x) x)
0.0ms	(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
1.0ms	(fma (/ 1.0 x) (/ 1 x) (* (- (/ (/ 1 x) x)) (cos x)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ 1 x) x)
25.0ms	(/ (/ 1 x) x)
126.0ms	(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
154.0ms	(fma (/ 1.0 x) (/ 1 x) (* (- (/ (/ 1 x) x)) (cos x)))

simplify1.0s

Counts

184 → 184

Iterations

Iter	Nodes
done	5001
2	1509
1	384
0	179

prune620.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.3b

bsearch121.0ms

Steps

Iters	Range		Point
8	0.00104763160503943	5.1212688054922095	0.0329978667264259
9	-205.8624528279525	-0.0007095347148853646	-0.0346527842528457

simplify7.0ms

Iterations

Iter	Nodes
done	43
2	43
1	37
0	26

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	1504×	body	2560	valid
657.0ms	1298×	body	1280	valid
452.0ms	1529×	body	640	valid
283.0ms	980×	body	320	valid
126.0ms	2199×	body	80	valid
67.0ms	490×	body	160	valid