Details

sample475.0ms

Algorithm

intervals

Results

261.0ms	95×	body	5120	exit
131.0ms	75×	body	1280	valid
50.0ms	61×	body	640	valid
10.0ms	86×	body	80	valid
8.0ms	24×	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

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: 34.0b

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)))
0.0b	(sin (expm1 a))
39.2b	(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:

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)

series63.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
58.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify118.0ms

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

prune157.0ms

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: 32.7b

Counts

41 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(cbrt (sin (expm1 a)))
0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
39.3b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `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 → 69

Calls

4 calls:

2.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
7.0ms	(* (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)

series504.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (sin (expm1 a)))
161.0ms	(cbrt (sin (expm1 a)))
180.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify79.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	99	673
1	366	578
2	2587	543
3	5002	526

prune351.0ms

Filtered

81 candidates to 54 candidates (66.7%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	65	16	81
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	68	25	93

Merged error: 32.1b

Counts

93 → 25

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
39.3b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`cbrt-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
13×	`pow1/3`
12×	`swap-sqr` `associate-r` `associate-l`
8×	`add-exp-log` `unswap-sqr`
4×	`pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 96

Calls

4 calls:

7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series547.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
179.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
184.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	116	1086
1	365	958
2	1762	884
3	5001	863

prune504.0ms

Filtered

108 candidates to 66 candidates (61.1%)

Pruning

35 alts after pruning (34 fresh and 1 done)

	Pruned	Kept	Total
New	95	13	108
Fresh	2	21	23
Picked	1	0	1
Done	0	1	1
Total	98	35	133

Merged error: 32.0b

Counts

133 → 35

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.5b	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
39.2b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`log-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `exp-prod`
4×	`exp-sum` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 47

Calls

4 calls:

3.0ms	(log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series614.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))
182.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
181.0ms	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (* (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify183.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (39.0ms)

Iter	Nodes	Cost
0	95	806
1	168	685
2	312	657
3	839	649
4	4069	645
5	5002	645

prune249.0ms

Filtered

59 candidates to 42 candidates (71.2%)

Pruning

43 alts after pruning (43 fresh and 0 done)

	Pruned	Kept	Total
New	46	13	59
Fresh	3	30	33
Picked	1	0	1
Done	1	0	1
Total	51	43	94

Merged error: 31.7b

Counts

94 → 43

regimes533.0ms

Accuracy

0% (2.3b remaining)

Error of 33.5b against oracle of 31.2b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	40
1	23	40

end0.0ms

sample13.5s

Algorithm

intervals

Results

7.4s	2697×	body	5120	exit
4.0s	2313×	body	1280	valid
1.2s	1693×	body	640	valid
314.0ms	2804×	body	80	valid
289.0ms	796×	body	320	valid
93.0ms	390×	body	160	valid
10.0ms	1×	body	5120	valid
6.0ms	3×	body	2560	valid

Details

sample475.0ms

simplify2.0ms

prune3.0ms

localize12.0ms

rewrite4.0ms

series63.0ms

simplify118.0ms

prune157.0ms

localize17.0ms

rewrite12.0ms

series504.0ms

simplify79.0ms

prune351.0ms

localize22.0ms

rewrite22.0ms

series547.0ms

simplify66.0ms

prune504.0ms

localize27.0ms

rewrite14.0ms

series614.0ms

simplify183.0ms

prune249.0ms

regimes533.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.5s

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