Details

sample128.0ms

Algorithm

intervals

Results

61.0ms	51×	body	2560	valid
38.0ms	86×	body	1280	valid
14.0ms	67×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite28.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
24.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune180.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.2b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series183.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
126.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify708.0ms

Counts

26 → 26

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	36	358
1	62	349
2	177	307
3	967	307
done	5001	307

prune100.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite29.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune155.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))
0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

591×	`add-sqr-sqrt`
537×	`times-frac`
411×	`*-un-lft-identity`
279×	`add-cube-cbrt`
234×	`unpow-prod-down` `cube-prod`
208×	`difference-of-squares`
144×	`prod-diff`
130×	`sqr-pow`
79×	`associate-/l*`
65×	`distribute-lft-out--`
26×	`cube-mult` `unpow3`
13×	`difference-cubes`
12×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `fma-def` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 571

Calls

4 calls:

80.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))
3.0ms	(pow (cos x) 3)
6.0ms	(+ 1.0 (cos x))
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series266.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (sin x))
29.0ms	(pow (cos x) 3)
11.0ms	(+ 1.0 (cos x))
56.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.0s

Counts

583 → 583

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	695	21873
1	1577	17698
2	4514	16508
done	5000	16507

prune1.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 0.2b

regimes224.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.2b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	50	111
1	59	107
done	59	107

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1706×	body	2560	valid
1.2s	2759×	body	1280	valid
442.0ms	1810×	body	640	valid
135.0ms	907×	body	320	valid
49.0ms	461×	body	160	valid
30.0ms	7×	body	5120	valid
22.0ms	350×	body	80	valid