Details

sample90.0ms

Algorithm

intervals

Results

30.0ms	23×	body	2560	valid
25.0ms	43×	body	1280	valid
10.0ms	134×	body	80	valid
8.0ms	23×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.3b

localize10.0ms

Local error

Found 3 expressions with local error:

8.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.3b	(sin (/ x (* y 2.0)))
27.9b	(tan (/ x (* y 2.0)))

rewrite9.0ms

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:

4.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
1.0ms	(tan (/ x (* y 2.0)))

series90.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
9.0ms	(sin (/ x (* y 2.0)))
43.0ms	(tan (/ x (* y 2.0)))

simplify763.0ms

Counts

58 → 58

Iterations

Useful iterations: 3 (168.0ms)

Iter	Nodes	Cost
0	83	878
1	150	865
2	436	789
3	1883	785
done	5001	785

prune419.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 25.1b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune32.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 25.1b

localize11.0ms

Local error

Found 4 expressions with local error:

8.6b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
27.3b	(sin (/ x (* y 2.0)))
27.3b	(sin (/ x (* y 2.0)))
27.6b	(cos (/ x (* y 2.0)))

rewrite19.0ms

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:

12.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(cos (/ x (* y 2.0)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
8.0ms	(sin (/ x (* y 2.0)))
8.0ms	(sin (/ x (* y 2.0)))
11.0ms	(cos (/ x (* y 2.0)))

simplify2.6s

Counts

63 → 63

Iterations

Useful iterations: 3 (185.0ms)

Iter	Nodes	Cost
0	77	989
1	154	777
2	478	606
3	2445	600
done	5000	600

prune208.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 25.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
27.6b	(cos (/ x (* y 2.0)))
27.6b	(cos (/ x (* y 2.0)))
27.6b	(cos (/ x (* y 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
76×	`add-sqr-sqrt`
52×	`times-frac`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `div-inv`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

22.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
2.0ms	(cos (/ x (* y 2.0)))
2.0ms	(cos (/ x (* y 2.0)))
2.0ms	(cos (/ x (* y 2.0)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
11.0ms	(cos (/ x (* y 2.0)))
11.0ms	(cos (/ x (* y 2.0)))
12.0ms	(cos (/ x (* y 2.0)))

simplify2.6s

Counts

128 → 128

Iterations

Useful iterations: 3 (747.0ms)

Iter	Nodes	Cost
0	142	2816
1	219	2589
2	755	2451
3	2388	2230
done	5001	2230

prune339.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.8b

regimes246.0ms

Accuracy

0% (2.7b remaining)

Error of 28.8b against oracle of 26.1b and baseline of 28.8b

bsearch0.0ms

simplify0.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
done	1	1

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	690×	body	2560	valid
813.0ms	1381×	body	1280	valid
338.0ms	984×	body	640	valid
306.0ms	4076×	body	80	valid
138.0ms	569×	body	320	valid
60.0ms	300×	body	160	valid