Details

sample423.0ms

Algorithm

intervals

Results

208.0ms	73×	body	5120	exit
136.0ms	82×	body	1280	valid
38.0ms	53×	body	640	valid
11.0ms	30×	body	320	valid
9.0ms	76×	body	80	valid
5.0ms	1×	body	5120	valid
3.0ms	14×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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:

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

series71.0ms

Counts

3 → 9

Calls

3 calls:

1.0ms	(expm1 (sin (expm1 a)))
61.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify117.0ms

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

prune120.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	20	10	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	11	31

Merged error: 35.2b

Counts

31 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.6b	(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:

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(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)

simplify106.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

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

prune211.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	32	8	40
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	33	18	51

Merged error: 34.9b

Counts

51 → 18

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
41.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite12.0ms

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:

9.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series187.0ms

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)

simplify57.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (50.0ms)

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

prune443.0ms

Filtered

73 candidates to 45 candidates (61.6%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	59	14	73
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	61	30	91

Merged error: 34.5b

Counts

91 → 30

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
41.6b	(fmod (atan2 (expm1 (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

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:

7.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series186.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (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)

simplify222.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 5 (217.0ms)

Iter	Nodes	Cost
0	60	534
1	111	446
2	283	444
3	796	444
4	3917	444
5	5001	443

prune250.0ms

Filtered

42 candidates to 32 candidates (76.2%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	32	10	42
Fresh	3	25	28
Picked	1	0	1
Done	0	1	1
Total	36	36	72

Merged error: 34.3b

Counts

72 → 36

regimes826.0ms

Accuracy

0% (1.5b remaining)

Error of 33.7b against oracle of 32.2b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	42
1	28	42

end0.0ms

sample13.4s

Algorithm

intervals

Results

7.3s	2641×	body	5120	exit
4.0s	2310×	body	1280	valid
1.2s	1675×	body	640	valid
318.0ms	2770×	body	80	valid
296.0ms	816×	body	320	valid
102.0ms	425×	body	160	valid
6.0ms	3×	body	2560	valid
5.0ms	1×	body	5120	valid

Details

sample423.0ms

simplify3.0ms

prune4.0ms

localize12.0ms

rewrite5.0ms

series71.0ms

simplify117.0ms

prune120.0ms

localize19.0ms

rewrite4.0ms

series61.0ms

simplify106.0ms

prune211.0ms

localize32.0ms

rewrite12.0ms

series187.0ms

simplify57.0ms

prune443.0ms

localize37.0ms

rewrite10.0ms

series186.0ms

simplify222.0ms

prune250.0ms

regimes826.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.4s

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