Details

analyze740.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.2%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.6%	52.3%	0.1%	14

sample83.0ms

Algorithm

intervals

Results

24.0ms	49×	body	1280	valid
21.0ms	22×	body	2560	valid
14.0ms	46×	body	640	valid
8.0ms	111×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	13
1	13	13

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 39.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

7.0b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
31.8b	(sin (/ x (* y 2.0)))
32.3b	(tan (/ x (* y 2.0)))

rewrite14.0ms

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` `associate-/r` `associate-/l` `add-log-exp`
2×	`tan-quot`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate-/l/`

Counts

3 → 43

Calls

3 calls:

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

series35.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
4.0ms	(sin (/ x (* y 2.0)))
14.0ms	(tan (/ x (* y 2.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5037	733

prune196.0ms

Filtered

44 candidates to 52 candidates (-18.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	36	16	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	16	53

Merged error: 29.5b

Counts

53 → 16

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune66.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	15	15
Picked	1	1
Done	0	0
Total	16	16

Merged error: 29.5b

Counts

16 → 16

localize12.0ms

Local error

Found 4 expressions with local error:

7.0b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
31.8b	(sin (/ x (* y 2.0)))
31.8b	(sin (/ x (* y 2.0)))
32.4b	(cos (/ x (* y 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `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 → 43

Calls

4 calls:

9.0ms	(/ (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)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
4.0ms	(sin (/ x (* y 2.0)))
4.0ms	(sin (/ x (* y 2.0)))
5.0ms	(cos (/ x (* y 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4681	542
1	4681	542

prune189.0ms

Filtered

45 candidates to 55 candidates (-22.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	47	8	55
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	51	20	71

Merged error: 29.5b

Counts

71 → 20

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
32.4b	(cos (/ x (* y 2.0)))
32.4b	(cos (/ x (* y 2.0)))
32.4b	(cos (/ x (* y 2.0)))

rewrite25.0ms

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×	`cbrt-div` `add-cbrt-cube` `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 → 108

Calls

4 calls:

12.0ms	(* (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)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
4.0ms	(cos (/ x (* y 2.0)))
4.0ms	(cos (/ x (* y 2.0)))
5.0ms	(cos (/ x (* y 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4944	2077
1	4944	2077

prune261.0ms

Filtered

74 candidates to 120 candidates (-62.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	7	11	18
Picked	1	0	1
Done	0	1	1
Total	121	19	140

Merged error: 29.3b

Counts

140 → 19

regimes625.0ms

Accuracy

0% (2.6b remaining)

Error of 28.5b against oracle of 25.9b and baseline of 28.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	1	1

end0.0ms

sample2.3s

Algorithm

intervals

Results

701.0ms	1402×	body	1280	valid
638.0ms	650×	body	2560	valid
310.0ms	976×	body	640	valid
304.0ms	4104×	body	80	valid
134.0ms	564×	body	320	valid
53.0ms	304×	body	160	valid

Details

analyze740.0ms

sample83.0ms

simplify3.0ms

prune4.0ms

localize10.0ms

rewrite14.0ms

series35.0ms

simplify37.0ms

prune196.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune66.0ms

localize12.0ms

rewrite17.0ms

series20.0ms

simplify82.0ms

prune189.0ms

localize12.0ms

rewrite25.0ms

series40.0ms

simplify51.0ms

prune261.0ms

regimes625.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling