Details

sample436.0ms

Algorithm

intervals

Results

237.0ms	94×	body	10240	exit
128.0ms	75×	body	1280	valid
37.0ms	57×	body	640	valid
8.0ms	84×	body	80	valid
8.0ms	24×	body	320	valid
3.0ms	16×	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: 34.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.1b	(sin (expm1 a))
39.3b	(fmod (atan2 (expm1 (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`

Counts

4 → 28

Calls

4 calls:

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

series63.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 a)
2.0ms	(expm1 (sin (expm1 a)))
57.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify117.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	196
1	44	168
2	54	168
3	68	168
4	114	168
5	228	168
6	919	168
7	3184	168
8	5001	168

prune148.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 33.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 a))
0.4b	(cbrt (expm1 a))
0.4b	(cbrt (expm1 a))
39.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series307.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (expm1 a))
102.0ms	(cbrt (expm1 a))
102.0ms	(cbrt (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

simplify92.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	41	320
1	71	278
2	148	272
3	481	265
4	2431	265
5	5001	265

prune250.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 33.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 a))
0.4b	(cbrt (expm1 a))
0.5b	(cbrt (cbrt (expm1 a)))
39.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (* (cbrt (* (cbrt (expm1 a)) (cbrt (expm1 a)))) (cbrt (cbrt (expm1 a))))))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

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

series309.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (expm1 a))
100.0ms	(cbrt (expm1 a))
105.0ms	(cbrt (cbrt (expm1 a)))
4.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (* (cbrt (* (cbrt (expm1 a)) (cbrt (expm1 a)))) (cbrt (cbrt (expm1 a))))))) (atan a)) a)

simplify49.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	66	440
1	123	380
2	283	374
3	1121	374
4	5001	374

prune338.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 32.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 a))
39.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)
39.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)
39.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

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

series109.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

simplify90.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	41	528
1	71	442
2	148	440
3	481	419
4	2431	419
5	5001	419

prune214.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 32.7b

regimes694.0ms

Accuracy

0% (1.7b remaining)

Error of 33.6b against oracle of 31.9b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	53
1	27	53

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.6s	2574×	body	10240	exit
3.9s	2262×	body	1280	valid
1.2s	1725×	body	640	valid
269.0ms	2776×	body	80	valid
268.0ms	807×	body	320	valid
90.0ms	427×	body	160	valid
6.0ms	3×	body	2560	valid