Details

sample429.0ms

Algorithm

intervals

Results

228.0ms	87×	body	10240	exit
116.0ms	67×	body	1280	valid
42.0ms	56×	body	640	valid
15.0ms	92×	body	80	valid
11.0ms	29×	body	320	valid
3.0ms	12×	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: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
37.9b	(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:

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

series158.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sin (expm1 a))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
91.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify125.0ms

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	2934	264
4	5001	264

prune211.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 31.5b

localize17.0ms

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))))
37.9b	(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)

series431.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (sin (expm1 a)))
140.0ms	(cbrt (sin (expm1 a)))
155.0ms	(* (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)

simplify122.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (115.0ms)

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

prune402.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 31.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sin (expm1 a)))
0.5b	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
37.9b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
20×	`pow1/3`
18×	`add-exp-log` `cbrt-prod`
14×	`pow-prod-down` `pow-prod-up`
13×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
10×	`-un-lft-identity` `associate-r*`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l` `add-cbrt-cube`
6×	`pow-plus`
4×	`expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow2` `*-commutative`
1×	`swap-sqr` `pow3`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
20.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
56.0ms	(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series427.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (sin (expm1 a)))
137.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
151.0ms	(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify58.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	309	1548
1	1176	1193
2	5002	940

prune454.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 31.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
37.9b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite105.0ms

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:

50.0ms	(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
49.0ms	(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
6.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series467.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
151.0ms	(cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))
156.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
5.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (cbrt (* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify81.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (19.0ms)

Iter	Nodes	Cost
0	114	1393
1	222	1176
2	529	928
3	1756	922
4	5001	922

prune326.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 30.7b

regimes493.0ms

Accuracy

0% (2.0b remaining)

Error of 33.3b against oracle of 31.3b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	59
1	25	59

end0.0ms

sample13.1s

Algorithm

intervals

Results

6.7s	2599×	body	10240	exit
4.0s	2274×	body	1280	valid
1.2s	1659×	body	640	valid
467.0ms	2829×	body	80	valid
324.0ms	822×	body	320	valid
118.0ms	411×	body	160	valid
19.0ms	4×	body	5120	valid
2.0ms	1×	body	2560	valid