Details

sample184.0ms

Algorithm

intervals

Results

66.0ms	28×	body	2560	valid
42.0ms	41×	body	1280	valid
24.0ms	36×	body	640	valid
18.0ms	124×	body	80	valid
6.0ms	14×	body	320	valid
4.0ms	13×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	13	13
done	13	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize12.0ms

Local error

Found 3 expressions with local error:

6.3b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
30.0b	(sin (/ x (* y 2.0)))
30.7b	(tan (/ x (* y 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`tan-quot`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate-/l/`

Counts

3 → 49

Calls

3 calls:

38.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
5.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
14.0ms	(sin (/ x (* y 2.0)))
51.0ms	(tan (/ x (* y 2.0)))

simplify2.3s

Counts

58 → 58

Iterations

Useful iterations: 3 (177.0ms)

Iter	Nodes	Cost
0	83	878
1	147	865
2	330	789
3	814	785
4	2543	785
done	5001	785

prune345.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 28.1b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune42.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 28.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
6.3b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
30.0b	(sin (/ x (* y 2.0)))
30.7b	(tan (/ x (* y 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `div-inv` `associate-/l`
2×	`tan-quot` `cbrt-undiv` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

12.0ms	(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
14.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
9.0ms	(tan (/ x (* y 2.0)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
52.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
25.0ms	(sin (/ x (* y 2.0)))
66.0ms	(tan (/ x (* y 2.0)))

simplify1.2s

Counts

109 → 109

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	130	2153
1	346	1994
2	1132	1844
done	5001	1805

prune449.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 28.1b

localize37.0ms

Local error

Found 4 expressions with local error:

30.0b	(sin (/ x (* y 2.0)))
30.7b	(tan (/ x (* y 2.0)))
30.7b	(tan (/ x (* y 2.0)))
30.7b	(tan (/ x (* y 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot`

Counts

4 → 39

Calls

4 calls:

5.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sin (/ x (* y 2.0)))
80.0ms	(tan (/ x (* y 2.0)))
67.0ms	(tan (/ x (* y 2.0)))
60.0ms	(tan (/ x (* y 2.0)))

simplify2.0s

Counts

51 → 51

Iterations

Useful iterations: 4 (655.0ms)

Iter	Nodes	Cost
0	37	476
1	62	470
2	133	422
3	429	422
4	1858	410
done	5000	410

prune383.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 28.0b

regimes678.0ms

Accuracy

0% (2.3b remaining)

Error of 28.4b against oracle of 26.1b and baseline of 28.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
done	1	1

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.3s	1429×	body	1280	valid
2.1s	633×	body	2560	valid
845.0ms	977×	body	640	valid
768.0ms	4098×	body	80	valid
270.0ms	540×	body	320	valid
179.0ms	323×	body	160	valid