Details

sample84.0ms

Algorithm

intervals

Results

27.0ms	53×	body	1280	valid
19.0ms	19×	body	2560	valid
11.0ms	33×	body	640	valid
9.0ms	123×	body	80	valid
5.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	7
1	13	7
2	13	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (* y 2.0))
8.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
29.8b	(sin (/ x (* y 2.0)))
30.9b	(tan (/ x (* y 2.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

3.0ms	(/ x (* y 2.0))
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)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ x (* y 2.0))
41.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
9.0ms	(sin (/ x (* y 2.0)))
45.0ms	(tan (/ x (* y 2.0)))

simplify107.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	239	574
1	856	518
2	4398	518
3	5001	518

prune300.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 27.4b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune51.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 27.4b

localize12.0ms

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)))))
29.8b	(sin (/ x (* y 2.0)))
29.8b	(sin (/ x (* y 2.0)))
30.3b	(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` `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:

10.0ms	(/ (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)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
10.0ms	(sin (/ x (* y 2.0)))
9.0ms	(sin (/ x (* y 2.0)))
12.0ms	(cos (/ x (* y 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	154	539
1	486	393
2	2459	391
3	5001	385

prune237.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 27.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (pow (/ 1 (cos (/ x (* y 2.0)))) 3))
0.2b	(/ x (* y 2.0))
0.4b	(pow (/ 1 (cos (/ x (* y 2.0)))) 3)
30.3b	(cos (/ x (* y 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
14×	`add-exp-log`
12×	`add-cbrt-cube`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `div-exp` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `pow-pow` `associate-/l*`
2×	`cube-div` `cube-mult` `unpow3` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rec-exp` `cbrt-div` `pow-flip` `frac-2neg` `pow1/3` `1-exp` `prod-exp` `clear-num` `associate-/r*` `rem-cbrt-cube` `cbrt-unprod` `inv-pow`

Counts

4 → 128

Calls

4 calls:

4.0ms	(cbrt (pow (/ 1 (cos (/ x (* y 2.0)))) 3))
3.0ms	(/ x (* y 2.0))
4.0ms	(pow (/ 1 (cos (/ x (* y 2.0)))) 3)
2.0ms	(cos (/ x (* y 2.0)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (pow (/ 1 (cos (/ x (* y 2.0)))) 3))
20.0ms	(/ x (* y 2.0))
48.0ms	(pow (/ 1 (cos (/ x (* y 2.0)))) 3)
13.0ms	(cos (/ x (* y 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	426	973
1	1703	851
2	5002	845

prune232.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 26.9b

regimes546.0ms

Accuracy

0% (3.6b remaining)

Error of 29.0b against oracle of 25.4b and baseline of 29.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

695.0ms	1399×	body	1280	valid
634.0ms	643×	body	2560	valid
338.0ms	1039×	body	640	valid
302.0ms	4033×	body	80	valid
138.0ms	586×	body	320	valid
53.0ms	300×	body	160	valid