Details

sample183.0ms

Algorithm

intervals

Results

84.0ms	66×	body	1280	valid
38.0ms	21×	body	2560	valid
16.0ms	29×	body	640	valid
14.0ms	108×	body	80	valid
9.0ms	21×	body	320	valid
4.0ms	11×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (* y 2.0))
5.1b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
33.6b	(sin (/ x (* y 2.0)))
33.8b	(tan (/ x (* y 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

14.0ms	(/ x (* y 2.0))
20.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
8.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ x (* y 2.0))
75.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
13.0ms	(sin (/ x (* y 2.0)))
67.0ms	(tan (/ x (* y 2.0)))

simplify499.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	125	1075
1	243	1053
2	1063	957
done	5000	957

prune380.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.7b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune59.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 29.7b

localize24.0ms

Local error

Found 4 expressions with local error:

33.6b	(sin (/ x (* y 2.0)))
33.8b	(tan (/ x (* y 2.0)))
33.8b	(tan (/ x (* y 2.0)))
33.8b	(tan (/ x (* y 2.0)))

rewrite21.0ms

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:

7.0ms	(sin (/ x (* y 2.0)))
6.0ms	(tan (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))
3.0ms	(tan (/ x (* y 2.0)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sin (/ x (* y 2.0)))
46.0ms	(tan (/ x (* y 2.0)))
41.0ms	(tan (/ x (* y 2.0)))
57.0ms	(tan (/ x (* y 2.0)))

simplify1.6s

Counts

51 → 51

Iterations

Useful iterations: 4 (604.0ms)

Iter	Nodes	Cost
0	37	476
1	62	470
2	139	422
3	496	422
4	2489	410
done	5001	410

prune244.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 29.7b

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
33.6b	(sin (/ x (* y 2.0)))
33.6b	(sin (/ x (* y 2.0)))
34.0b	(cos (/ x (* y 2.0)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `associate-/r/` `sin-cos-mult` `cbrt-unprod` `div-inv`

Counts

4 → 51

Calls

4 calls:

49.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
7.0ms	(sin (/ x (* y 2.0)))
11.0ms	(sin (/ x (* y 2.0)))
8.0ms	(cos (/ x (* y 2.0)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
16.0ms	(sin (/ x (* y 2.0)))
15.0ms	(sin (/ x (* y 2.0)))
20.0ms	(cos (/ x (* y 2.0)))

simplify2.0s

Counts

63 → 63

Iterations

Useful iterations: 3 (466.0ms)

Iter	Nodes	Cost
0	77	989
1	152	777
2	491	604
3	3703	600
done	5001	600

prune215.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 29.7b

regimes423.0ms

Accuracy

34.6% (1.9b remaining)

Error of 27.1b against oracle of 25.2b and baseline of 28.1b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	23	28
done	23	28

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.5s	1427×	body	1280	valid
1.2s	967×	body	640	valid
1.1s	651×	body	2560	valid
934.0ms	4132×	body	80	valid
283.0ms	544×	body	320	valid
86.0ms	279×	body	160	valid