Details

sample458.0ms

Algorithm

intervals

Results

255.0ms	94×	body	10240	exit
118.0ms	67×	body	1280	valid
43.0ms	52×	body	640	valid
16.0ms	39×	body	320	valid
12.0ms	87×	body	80	valid
3.0ms	11×	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: 34.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
39.4b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 30

Calls

3 calls:

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

series146.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(sin (expm1 a))
88.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify127.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	215
1	231	188
2	706	188
3	2916	188
4	5002	188

prune147.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 33.4b

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))))
39.3b	(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` `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:

169.0ms	(cbrt (expm1 (sin (expm1 a))))
165.0ms	(cbrt (expm1 (sin (expm1 a))))
166.0ms	(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)

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

prune283.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 32.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(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))))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
39.3b	(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)

rewrite12.0ms

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×	`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 → 70

Calls

4 calls:

3.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
7.0ms	(* (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)

series527.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))))
168.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
172.0ms	(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)

simplify88.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	248	1381
1	715	1230
2	2647	1203
3	5001	1111

prune462.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 32.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.3b	(pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3)
39.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-exp-log`
12×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow-pow` `associate-r` `unswap-sqr`
8×	`pow1/3`
6×	`prod-exp`
5×	`unpow-prod-down` `associate-l` `add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down`
2×	`pow-to-exp` `unpow1/3` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `pow-plus` `*-commutative`

Counts

4 → 92

Calls

4 calls:

8.0ms	(* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
4.0ms	(pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3)
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series620.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))
172.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
271.0ms	(pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3)
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (pow (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) 1/3) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	334	1623
1	1181	1422
2	5001	1265

prune438.0ms

Pruning

43 alts after pruning (42 fresh and 1 done)

Merged error: 31.9b

regimes773.0ms

Accuracy

0% (2.3b remaining)

Error of 34.1b against oracle of 31.8b and baseline of 34.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	20	43

end0.0ms

sample14.1s

Algorithm

intervals

Results

7.3s	2706×	body	10240	exit
4.4s	2405×	body	1280	valid
1.3s	1622×	body	640	valid
352.0ms	855×	body	320	valid
348.0ms	2715×	body	80	valid
110.0ms	398×	body	160	valid
14.0ms	3×	body	5120	valid
4.0ms	2×	body	2560	valid