Details

sample380.0ms

Algorithm

intervals

Results

203.0ms	81×	body	10240	exit
97.0ms	61×	body	1280	valid
42.0ms	50×	body	640	valid
14.0ms	41×	body	320	valid
9.0ms	89×	body	80	valid
3.0ms	15×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

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

series156.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
87.0ms	(expm1 (sin (expm1 a)))
64.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify123.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2933	264
4	5001	264

prune202.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.4b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.3b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite10.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 77

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
7.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series426.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (sin (expm1 a)))
136.0ms	(cbrt (sin (expm1 a)))
154.0ms	(* (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)

simplify118.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	182	758
1	639	657
2	3589	621
3	5001	605

prune392.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 31.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
38.2b	(fmod (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)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (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)) a)

series455.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
152.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
148.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(fmod (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)) a)

simplify75.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	91	843
1	182	714
2	466	708
3	1540	708
4	5001	708

prune369.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 31.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.4b	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
38.3b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `exp-sum` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
2×	`log-pow`
1×	`rem-exp-log`

Counts

4 → 50

Calls

4 calls:

3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series456.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
149.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
154.0ms	(exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (exp (log (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify78.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	130	955
1	242	822
2	560	788
3	1820	780
4	5002	780

prune280.0ms

Pruning

43 alts after pruning (42 fresh and 1 done)

Merged error: 31.0b

regimes754.0ms

Accuracy

0% (2.3b remaining)

Error of 33.5b against oracle of 31.3b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	114
1	22	114

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.6s	2597×	body	10240	exit
3.9s	2321×	body	1280	valid
1.2s	1658×	body	640	valid
276.0ms	2808×	body	80	valid
274.0ms	820×	body	320	valid
83.0ms	387×	body	160	valid
9.0ms	2×	body	5120	valid
8.0ms	4×	body	2560	valid