Details

sample136.0ms

Algorithm

intervals

Results

48.0ms	26×	body	2560	valid
32.0ms	45×	body	1280	valid
15.0ms	33×	body	640	valid
13.0ms	124×	body	80	valid
8.0ms	20×	body	320	valid
2.0ms	8×	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: 35.7b

localize15.0ms

Local error

Found 3 expressions with local error:

5.5b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
29.6b	(sin (/ x (* y 2.0)))
29.9b	(tan (/ x (* y 2.0)))

rewrite45.0ms

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:

34.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
6.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series130.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
12.0ms	(sin (/ x (* y 2.0)))
51.0ms	(tan (/ x (* y 2.0)))

simplify1.6s

Counts

58 → 58

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	83	878
1	152	865
2	508	789
3	3237	789
done	5002	789

prune406.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 27.4b

localize1.0ms

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

prune93.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 27.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (expm1 (tan (/ x (* y 2.0)))))
5.5b	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
29.6b	(sin (/ x (* y 2.0)))
29.9b	(tan (/ x (* y 2.0)))

rewrite38.0ms

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`
1×	`tan-quot` `cbrt-undiv` `log1p-udef` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(log1p (expm1 (tan (/ x (* y 2.0)))))
15.0ms	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
14.0ms	(sin (/ x (* y 2.0)))
6.0ms	(tan (/ x (* y 2.0)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(log1p (expm1 (tan (/ x (* y 2.0)))))
159.0ms	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
11.0ms	(sin (/ x (* y 2.0)))
55.0ms	(tan (/ x (* y 2.0)))

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	93	1077
1	161	956
2	445	868
3	2595	868
done	5000	868

prune518.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 27.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
5.5b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
29.6b	(sin (/ x (* y 2.0)))
29.9b	(tan (/ x (* y 2.0)))

rewrite72.0ms

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:

33.0ms	(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
23.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
6.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(pow (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) 3)
82.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
20.0ms	(sin (/ x (* y 2.0)))
83.0ms	(tan (/ x (* y 2.0)))

simplify1.5s

Counts

109 → 109

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	130	2153
1	456	1994
2	2165	1844
done	5000	1841

prune511.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 27.4b

regimes741.0ms

Accuracy

38.2% (1.5b remaining)

Error of 27.3b against oracle of 25.8b and baseline of 28.2b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	47
1	18	47
done	18	47

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.0s	1358×	body	1280	valid
1.4s	642×	body	2560	valid
1.2s	4136×	body	80	valid
832.0ms	981×	body	640	valid
374.0ms	610×	body	320	valid
128.0ms	273×	body	160	valid