Details

sample83.0ms

Algorithm

intervals

Results

27.0ms	39×	body	1280	valid
16.0ms	13×	body	2560	valid
11.0ms	31×	body	640	valid
10.0ms	135×	body	80	valid
6.0ms	24×	body	320	valid
3.0ms	14×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize10.0ms

Local error

Found 3 expressions with local error:

7.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.0b	(tan (/ x (* y 2.0)))
27.1b	(sin (/ 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:

5.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
1.0ms	(tan (/ x (* y 2.0)))
2.0ms	(sin (/ x (* y 2.0)))

series94.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
46.0ms	(tan (/ x (* y 2.0)))
9.0ms	(sin (/ x (* y 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	146	485
1	433	441
2	1789	441
3	5001	441

prune220.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 24.5b

localize1.0ms

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

prune47.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 24.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
7.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.0b	(tan (/ x (* y 2.0)))
27.1b	(sin (/ x (* y 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
4.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
1.0ms	(tan (/ x (* y 2.0)))
2.0ms	(sin (/ x (* y 2.0)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
42.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
47.0ms	(tan (/ x (* y 2.0)))
10.0ms	(sin (/ x (* y 2.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	178	614
1	530	553
2	2057	551
3	5001	551

prune498.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))) 3)
7.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.0b	(tan (/ x (* y 2.0)))
27.1b	(sin (/ x (* y 2.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `associate-/r` `associate-/l`
2×	`tan-quot`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `div-exp` `pow-exp` `clear-num` `div-inv` `associate-/l/` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

1.0ms	(pow (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))) 3)
8.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
1.0ms	(tan (/ x (* y 2.0)))
2.0ms	(sin (/ x (* y 2.0)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(pow (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))) 3)
41.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
41.0ms	(tan (/ x (* y 2.0)))
10.0ms	(sin (/ x (* y 2.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	296	848
1	1252	754
2	5002	748

prune281.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 24.5b

regimes466.0ms

Accuracy

39.7% (1.5b remaining)

Error of 27.8b against oracle of 26.3b and baseline of 28.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	20
1	21	20

end0.0ms

sample3.0s

Algorithm

intervals

Results

912.0ms	1407×	body	1280	valid
877.0ms	638×	body	2560	valid
402.0ms	989×	body	640	valid
325.0ms	4057×	body	80	valid
158.0ms	593×	body	320	valid
79.0ms	316×	body	160	valid