Details

sample408.0ms

Algorithm

intervals

Results

215.0ms	87×	body	10240	exit
120.0ms	70×	body	1280	valid
41.0ms	58×	body	640	valid
9.0ms	93×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.1b	(sin (expm1 a))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

3 → 30

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series155.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(expm1 (sin (expm1 a)))
63.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify122.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	215
1	231	188
2	706	188
3	2915	188
4	5001	188

prune165.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sin (expm1 a))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

1.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series68.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify65.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	67	360
1	138	315
2	360	315
3	1390	315
4	5001	315

prune288.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
37.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series162.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify68.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	151	788
1	447	697
2	1900	571
3	5001	561

prune525.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 31.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.9b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 38

Calls

4 calls:

3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series160.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify73.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	110	789
1	229	672
2	570	670
3	1672	670
4	5001	670

prune329.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 31.4b

regimes506.0ms

Accuracy

0% (1.5b remaining)

Error of 33.2b against oracle of 31.7b and baseline of 33.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	53
1	29	53

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.3s	2524×	body	10240	exit
3.8s	2232×	body	1280	valid
1.2s	1659×	body	640	valid
288.0ms	2842×	body	80	valid
277.0ms	838×	body	320	valid
92.0ms	423×	body	160	valid
23.0ms	5×	body	5120	valid
2.0ms	1×	body	2560	valid