Details

sample110.0ms

Algorithm

intervals

Results

34.0ms	23×	body	2560	valid
26.0ms	39×	body	1280	valid
16.0ms	39×	body	640	valid
13.0ms	122×	body	80	valid
8.0ms	24×	body	320	valid
2.0ms	9×	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: 36.3b

localize11.0ms

Local error

Found 3 expressions with local error:

5.8b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
30.0b	(sin (/ x (* y 2.0)))
30.3b	(tan (/ x (* y 2.0)))

rewrite8.0ms

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:

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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	138	457
1	421	413
2	1765	413
3	5001	413

prune173.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 28.2b

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

prune32.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 28.2b

localize15.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
30.0b	(sin (/ x (* y 2.0)))
30.0b	(sin (/ x (* y 2.0)))
30.4b	(cos (/ x (* y 2.0)))

rewrite16.0ms

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)))

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)))))
9.0ms	(sin (/ x (* y 2.0)))
9.0ms	(sin (/ x (* y 2.0)))
11.0ms	(cos (/ x (* y 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	147	493
1	478	347
2	2436	345
3	5001	339

prune183.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 28.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos (/ x (* y 2.0))))
0.3b	(cbrt (pow (/ 1 (cos (/ x (* y 2.0)))) 3))
0.4b	(pow (/ 1 (cos (/ x (* y 2.0)))) 3)
30.4b	(cos (/ x (* y 2.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`div-inv`
4×	`div-exp` `pow-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `rec-exp` `pow-flip` `1-exp` `unpow3` `inv-pow` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ 1 (cos (/ x (* y 2.0))))
4.0ms	(cbrt (pow (/ 1 (cos (/ x (* y 2.0)))) 3))
4.0ms	(pow (/ 1 (cos (/ x (* y 2.0)))) 3)
2.0ms	(cos (/ x (* y 2.0)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (cos (/ x (* y 2.0))))
20.0ms	(cbrt (pow (/ 1 (cos (/ x (* y 2.0)))) 3))
42.0ms	(pow (/ 1 (cos (/ x (* y 2.0)))) 3)
11.0ms	(cos (/ x (* y 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	333	1051
1	1398	938
2	5001	930

prune204.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 28.1b

regimes506.0ms

Accuracy

20.9% (1.9b remaining)

Error of 28.5b against oracle of 26.6b and baseline of 29.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	18
1	28	18

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	1426×	body	1280	valid
950.0ms	666×	body	2560	valid
438.0ms	4033×	body	80	valid
427.0ms	971×	body	640	valid
187.0ms	603×	body	320	valid
81.0ms	301×	body	160	valid