Details

sample106.0ms

Algorithm

intervals

Results

35.0ms	28×	body	2560	valid
33.0ms	56×	body	1280	valid
14.0ms	32×	body	640	valid
8.0ms	114×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 37.5b

localize10.0ms

Local error

Found 3 expressions with local error:

5.3b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
32.1b	(sin (/ x (* y 2.0)))
32.5b	(tan (/ 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:

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

series84.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
8.0ms	(sin (/ x (* y 2.0)))
40.0ms	(tan (/ x (* y 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (5.0ms)

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

prune195.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 29.8b

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 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune34.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 29.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
5.3b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
32.1b	(sin (/ x (* y 2.0)))
32.5b	(tan (/ x (* y 2.0)))

rewrite9.0ms

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

series162.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
36.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
8.0ms	(sin (/ x (* y 2.0)))
41.0ms	(tan (/ x (* y 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (15.0ms)

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

prune257.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 29.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(log1p (expm1 (tan (/ x (* y 2.0)))))
5.3b	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
32.1b	(sin (/ x (* y 2.0)))
32.5b	(tan (/ x (* y 2.0)))

rewrite7.0ms

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`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
1×	`tan-quot` `cbrt-undiv` `log1p-udef` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(log1p (expm1 (tan (/ x (* y 2.0)))))
3.0ms	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
1.0ms	(tan (/ x (* y 2.0)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(log1p (expm1 (tan (/ x (* y 2.0)))))
97.0ms	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
8.0ms	(sin (/ x (* y 2.0)))
40.0ms	(tan (/ x (* y 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	157	605
1	415	531
2	1749	518
3	5001	512

prune200.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 29.8b

regimes374.0ms

Accuracy

40.2% (1.5b remaining)

Error of 27.1b against oracle of 25.7b and baseline of 28.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	18
1	18	18

end0.0ms

sample2.7s

Algorithm

intervals

Results

871.0ms	675×	body	2560	valid
811.0ms	1317×	body	1280	valid
337.0ms	948×	body	640	valid
335.0ms	4167×	body	80	valid
144.0ms	579×	body	320	valid
60.0ms	314×	body	160	valid