Details

sample392.0ms

Algorithm

intervals

Results

180.0ms	69×	body	10240	exit
142.0ms	75×	body	1280	valid
36.0ms	50×	body	640	valid
10.0ms	99×	body	80	valid
7.0ms	20×	body	320	valid
3.0ms	12×	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: 31.8b

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)))
0.1b	(sin (expm1 a))
36.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

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

prune158.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (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` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series299.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (expm1 (sin (expm1 a))))
99.0ms	(cbrt (expm1 (sin (expm1 a))))
99.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify89.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	39	474
1	69	412
2	146	406
3	479	395
4	2429	395
5	5001	395

prune254.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
0.6b	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
19×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`pow1/3` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down`
1×	`pow3` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 62

Calls

4 calls:

5.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
18.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series321.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
100.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
100.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify49.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	131	1236
1	379	1094
2	1391	1067
3	5002	971

prune410.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 30.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
2.4b	(exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))
36.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

4.0ms	(log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
6.0ms	(exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series404.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))
100.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
118.0ms	(exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (exp (log (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify54.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (43.0ms)

Iter	Nodes	Cost
0	108	969
1	192	832
2	356	807
3	1077	800
4	5001	796

prune258.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 29.6b

regimes464.0ms

Accuracy

0% (2.2b remaining)

Error of 33.3b against oracle of 31.0b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	32
1	23	32
2	23	32

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.7s	2693×	body	10240	exit
3.8s	2262×	body	1280	valid
1.1s	1664×	body	640	valid
281.0ms	2844×	body	80	valid
269.0ms	801×	body	320	valid
89.0ms	417×	body	160	valid
36.0ms	7×	body	5120	valid
10.0ms	5×	body	2560	valid