Details

sample425.0ms

Algorithm

intervals

Results

231.0ms	94×	body	10240	exit
125.0ms	75×	body	1280	valid
36.0ms	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

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

Counts

4 → 41

Calls

4 calls:

0.0ms	(expm1 a)
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series150.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(expm1 a)
81.0ms	(expm1 (sin (expm1 a)))
54.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify144.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 4 (141.0ms)

Iter	Nodes	Cost
0	116	244
1	307	214
2	893	214
3	3768	214
4	5001	213

prune207.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 33.7b

localize17.0ms

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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

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)

series260.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (expm1 a))
85.0ms	(cbrt (expm1 a))
87.0ms	(cbrt (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

simplify77.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (72.0ms)

Iter	Nodes	Cost
0	86	381
1	186	339
2	492	333
3	1848	326
4	5002	323

prune299.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 33.2b

localize12.0ms

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

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

Counts

4 → 41

Calls

4 calls:

0.0ms	(expm1 a)
0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series150.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(expm1 a)
81.0ms	(expm1 (sin (expm1 a)))
55.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify142.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 4 (138.0ms)

Iter	Nodes	Cost
0	116	244
1	307	214
2	893	214
3	3768	214
4	5001	213

prune215.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 33.2b

localize25.0ms

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 51

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)

series265.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (expm1 a))
87.0ms	(cbrt (expm1 a))
87.0ms	(cbrt (cbrt (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (* (cbrt (* (cbrt (expm1 a)) (cbrt (expm1 a)))) (cbrt (cbrt (expm1 a))))))) (atan a)) a)

simplify148.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 4 (143.0ms)

Iter	Nodes	Cost
0	145	522
1	341	459
2	977	453
3	4084	453
4	5002	448

prune266.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 32.9b

regimes480.0ms

Accuracy

0% (1.5b remaining)

Error of 33.6b against oracle of 32.1b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.4s	2574×	body	10240	exit
3.8s	2262×	body	1280	valid
1.2s	1725×	body	640	valid
274.0ms	2776×	body	80	valid
259.0ms	807×	body	320	valid
88.0ms	427×	body	160	valid
6.0ms	3×	body	2560	valid