Details

sample409.0ms

Algorithm

intervals

Results

220.0ms	87×	body	10240	exit
116.0ms	70×	body	1280	valid
42.0ms	58×	body	640	valid
9.0ms	93×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify2.0ms

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

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

3 → 21

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)

series62.0ms

Counts

3 → 9

Calls

3 calls:

1.0ms	(expm1 (sin (expm1 a)))
58.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify111.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	173
1	35	148
2	43	148
3	54	148
4	91	148
5	185	148
6	781	148
7	2680	148
8	5001	148

prune117.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.1b

localize19.0ms

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` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

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)

series61.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(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)

simplify102.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	300
1	26	256
2	32	256
3	40	256
4	68	256
5	142	256
6	643	256
7	2176	256
8	5001	256

prune224.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.8b

localize29.0ms

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)

rewrite9.0ms

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×	`add-cbrt-cube` `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 → 61

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)

series186.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(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)

simplify53.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	104	703
1	308	616
2	1499	509
3	5001	499

prune451.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 31.5b

localize37.0ms

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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

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)

series189.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(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)

simplify92.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	62	664
1	115	550
2	243	548
3	453	548
4	1335	548
5	5001	548

prune254.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 31.4b

regimes476.0ms

Accuracy

0% (1.4b 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

sample12.1s

Algorithm

intervals

Results

6.4s	2524×	body	10240	exit
3.8s	2232×	body	1280	valid
1.1s	1659×	body	640	valid
280.0ms	838×	body	320	valid
276.0ms	2842×	body	80	valid
88.0ms	423×	body	160	valid
23.0ms	5×	body	5120	valid
2.0ms	1×	body	2560	valid