Details

sample414.0ms

Algorithm

intervals

Results

191.0ms	71×	body	10240	exit
153.0ms	88×	body	1280	valid
36.0ms	53×	body	640	valid
8.0ms	82×	body	80	valid
7.0ms	22×	body	320	valid
5.0ms	1×	body	5120	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

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: 35.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
40.6b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

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

series72.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
60.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	248
1	44	212
2	54	212
3	68	212
4	114	212
5	228	212
6	919	212
7	3184	212
8	5001	212

prune156.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	28	12	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	12	41

Merged error: 34.2b

Counts

41 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.6b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
40.6b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
4.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series95.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
33.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify128.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	112	584
1	390	527
2	2787	521
3	5001	521

prune217.0ms

Filtered

70 candidates to 35 candidates (50.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	64	18	82

Merged error: 33.9b

Counts

82 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.6b	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
40.5b	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
7×	`add-exp-log` `pow1/3`
6×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
5×	`add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqr-pow`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 91

Calls

4 calls:

7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
2.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series219.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
33.0ms	(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
5.0ms	(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify179.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	186	1576
1	694	1424
2	4575	1224
3	5002	1224

prune396.0ms

Filtered

103 candidates to 58 candidates (56.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	95	26	121

Merged error: 33.6b

Counts

121 → 26

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
1.0b	(pow (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 (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
40.6b	(fmod (cbrt (pow (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 (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`cbrt-prod` `pow1/3`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 48

Calls

4 calls:

5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.0ms	(pow (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 (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (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 (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series402.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
180.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
37.0ms	(pow (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 (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)
4.0ms	(fmod (cbrt (pow (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 (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify136.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	122	1720
1	400	1414
2	2904	1406
3	5002	1406

prune217.0ms

Filtered

60 candidates to 39 candidates (65.0%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	53	7	60
Fresh	2	23	25
Picked	0	1	1
Done	0	0	0
Total	55	31	86

Merged error: 33.4b

Counts

86 → 31

regimes400.0ms

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.5b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	21	39

end0.0ms

sample12.9s

Algorithm

intervals

Results

7.1s	2639×	body	10240	exit
3.8s	2311×	body	1280	valid
1.1s	1679×	body	640	valid
287.0ms	2816×	body	80	valid
270.0ms	802×	body	320	valid
86.0ms	383×	body	160	valid
19.0ms	4×	body	5120	valid
10.0ms	5×	body	2560	valid

Details

sample414.0ms

simplify3.0ms

prune3.0ms

localize12.0ms

rewrite6.0ms

series72.0ms

simplify121.0ms

prune156.0ms

localize15.0ms

rewrite10.0ms

series95.0ms

simplify128.0ms

prune217.0ms

localize21.0ms

rewrite14.0ms

series219.0ms

simplify179.0ms

prune396.0ms

localize27.0ms

rewrite14.0ms

series402.0ms

simplify136.0ms

prune217.0ms

regimes400.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample12.9s

Profiling