Details

sample125.0ms

Algorithm

intervals

Results

35.0ms	42×	body	1280	valid
30.0ms	19×	body	2560	valid
18.0ms	35×	body	640	valid
16.0ms	132×	body	80	valid
6.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify5.0ms

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: 36.9b

localize21.0ms

Local error

Found 3 expressions with local error:

8.2b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.0b	(sin (/ x (* y 2.0)))
28.8b	(tan (/ x (* y 2.0)))

rewrite85.0ms

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:

66.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
6.0ms	(tan (/ x (* y 2.0)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
18.0ms	(sin (/ x (* y 2.0)))
76.0ms	(tan (/ x (* y 2.0)))

simplify1.8s

Counts

58 → 58

Iterations

Useful iterations: 3 (187.0ms)

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

prune285.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.9b

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

prune30.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 25.9b

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
8.2b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.0b	(sin (/ x (* y 2.0)))
28.8b	(tan (/ x (* y 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
22.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
14.0ms	(sin (/ x (* y 2.0)))
6.0ms	(tan (/ x (* y 2.0)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
51.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
46.0ms	(tan (/ x (* y 2.0)))

simplify1.9s

Counts

72 → 72

Iterations

Useful iterations: 3 (210.0ms)

Iter	Nodes	Cost
0	94	1109
1	159	1070
2	346	968
3	830	964
4	2574	964
done	5000	964

prune352.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 25.9b

localize27.0ms

Local error

Found 4 expressions with local error:

8.1b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
28.0b	(sin (/ x (* y 2.0)))
28.0b	(sin (/ x (* y 2.0)))
28.1b	(cos (/ x (* y 2.0)))

rewrite95.0ms

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:

54.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
10.0ms	(sin (/ x (* y 2.0)))
12.0ms	(sin (/ x (* y 2.0)))
18.0ms	(cos (/ x (* y 2.0)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
15.0ms	(sin (/ x (* y 2.0)))
14.0ms	(sin (/ x (* y 2.0)))
14.0ms	(cos (/ x (* y 2.0)))

simplify6.0s

Counts

63 → 63

Iterations

Useful iterations: 3 (541.0ms)

Iter	Nodes	Cost
0	77	989
1	152	777
2	416	604
3	1226	600
done	5000	600

prune249.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 25.9b

regimes468.0ms

Accuracy

0% (2.3b remaining)

Error of 28.6b against oracle of 26.3b and baseline of 28.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
done	1	1

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.1s	1446×	body	1280	valid
1.5s	621×	body	2560	valid
963.0ms	995×	body	640	valid
703.0ms	4072×	body	80	valid
297.0ms	556×	body	320	valid
167.0ms	310×	body	160	valid