Details

sample448.0ms

Algorithm

intervals

Results

243.0ms	95×	body	10240	exit
139.0ms	79×	body	1280	valid
34.0ms	53×	body	640	valid
9.0ms	87×	body	80	valid
8.0ms	24×	body	320	valid
3.0ms	13×	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: 34.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
39.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`log1p-expm1-u`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`expm1-log1p` `expm1-udef`

Counts

2 → 20

Calls

2 calls:

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

series90.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	63	161
1	136	140
2	407	140
3	1240	140
4	5002	140

prune106.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.4b

localize17.0ms

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))))
39.2b	(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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

0.0ms	(cbrt (expm1 (sin (expm1 a))))
0.0ms	(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)

series503.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (expm1 (sin (expm1 a))))
166.0ms	(cbrt (expm1 (sin (expm1 a))))
165.0ms	(cbrt (expm1 (sin (expm1 a))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify73.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (68.0ms)

Iter	Nodes	Cost
0	88	549
1	181	487
2	472	481
3	1562	470
4	5001	467

prune279.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 33.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(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)))))
39.2b	(fmod (atan2 (* (* (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
20×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`expm1-log1p-u` `pow1/3` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down`
1×	`pow3` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 72

Calls

4 calls:

0.0ms	(cbrt (expm1 (sin (expm1 a))))
8.0ms	(* (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 (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series515.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (expm1 (sin (expm1 a))))
173.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
168.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	206	1323
1	571	1188
2	1808	1180
3	5001	1157

prune455.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 32.7b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
39.2b	(fmod (atan2 (* (* (* (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (* (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series520.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
172.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
171.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
4.0ms	(fmod (atan2 (* (* (* (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (* (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a)))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify117.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 5 (108.0ms)

Iter	Nodes	Cost
0	116	1245
1	200	1105
2	453	1099
3	1013	1099
4	3817	1099
5	5001	1096

prune427.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 32.5b

regimes611.0ms

Accuracy

0% (1.7b remaining)

Error of 32.8b against oracle of 31.1b and baseline of 32.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	22	45

end0.0ms

sample12.4s

Algorithm

intervals

Results

6.7s	2657×	body	10240	exit
3.7s	2210×	body	1280	valid
1.2s	1679×	body	640	valid
285.0ms	2908×	body	80	valid
263.0ms	788×	body	320	valid
89.0ms	407×	body	160	valid
23.0ms	5×	body	5120	valid
6.0ms	3×	body	2560	valid