Details

sample184.0ms

Algorithm

intervals

Results

50.0ms	17×	body	2560	valid
46.0ms	41×	body	1280	valid
23.0ms	32×	body	640	valid
22.0ms	135×	body	80	valid
10.0ms	18×	body	320	valid
5.0ms	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize24.0ms

Local error

Found 3 expressions with local error:

5.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.2b	(sin (/ x (* y 2.0)))
27.8b	(tan (/ x (* y 2.0)))

rewrite79.0ms

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:

58.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
11.0ms	(sin (/ x (* y 2.0)))
8.0ms	(tan (/ x (* y 2.0)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
19.0ms	(sin (/ x (* y 2.0)))
82.0ms	(tan (/ x (* y 2.0)))

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 3 (239.0ms)

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

prune339.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.9b

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

prune68.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.9b

localize25.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
27.2b	(sin (/ x (* y 2.0)))
27.2b	(sin (/ x (* y 2.0)))
27.5b	(cos (/ x (* y 2.0)))

rewrite84.0ms

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:

57.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
10.0ms	(sin (/ x (* y 2.0)))
8.0ms	(sin (/ x (* y 2.0)))
7.0ms	(cos (/ x (* y 2.0)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
25.0ms	(sin (/ x (* y 2.0)))
15.0ms	(sin (/ x (* y 2.0)))
22.0ms	(cos (/ x (* y 2.0)))

simplify7.9s

Counts

63 → 63

Iterations

Useful iterations: 3 (489.0ms)

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

prune345.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 24.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos (/ x (* y 2.0))))
0.8b	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
0.9b	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
27.5b	(cos (/ x (* y 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

11.0ms	(/ 1 (cos (/ x (* y 2.0))))
1.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
0.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
7.0ms	(cos (/ x (* y 2.0)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1 (cos (/ x (* y 2.0))))
106.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
160.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
26.0ms	(cos (/ x (* y 2.0)))

simplify7.6s

Counts

76 → 76

Iterations

Useful iterations: 5 (1.2s)

Iter	Nodes	Cost
0	91	887
1	150	807
2	250	731
3	462	731
4	978	731
5	1562	729
6	2008	729
7	3260	729
done	5000	729

prune305.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 24.8b

regimes513.0ms

Accuracy

0% (2.5b remaining)

Error of 28.9b against oracle of 26.3b and baseline of 28.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12
1	15	12
done	15	12

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.1s	1416×	body	1280	valid
1.4s	602×	body	2560	valid
997.0ms	1024×	body	640	valid
886.0ms	4045×	body	80	valid
449.0ms	600×	body	320	valid
173.0ms	313×	body	160	valid