Details

sample507.0ms

Algorithm

intervals

Results

282.0ms	103×	body	10240	exit
147.0ms	84×	body	1280	valid
43.0ms	55×	body	640	valid
10.0ms	29×	body	320	valid
8.0ms	78×	body	80	valid
2.0ms	10×	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: 35.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.1b	(sin (expm1 a))
41.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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

series154.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify120.0ms

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	2915	188
4	5001	188

prune164.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 34.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
41.0b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite8.0ms

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:

4.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series531.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (expm1 (sin (expm1 a))))
175.0ms	(cbrt (expm1 (sin (expm1 a))))
176.0ms	(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)

simplify70.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (65.0ms)

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

prune314.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 34.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(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)))))
41.0b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite15.0ms

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:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
10.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
2.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series536.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (expm1 (sin (expm1 a))))
177.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
178.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	206	1323
1	566	1188
2	1787	1180
3	5001	1157

prune491.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 33.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(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)))))
41.0b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (* 1 (cbrt (expm1 (sin (expm1 a)))))) (atan a)) a)

rewrite12.0ms

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:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
7.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
2.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (* 1 (cbrt (expm1 (sin (expm1 a)))))) (atan a)) a)

series532.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (expm1 (sin (expm1 a))))
177.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
175.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (* 1 (cbrt (expm1 (sin (expm1 a)))))) (atan a)) a)

simplify65.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	211	1335
1	616	1198
2	1987	1190
3	5001	1167

prune383.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 33.9b

regimes387.0ms

Accuracy

0% (1.6b remaining)

Error of 33.6b against oracle of 32.0b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	31
1	28	31
2	28	31

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.0s	2583×	body	10240	exit
3.9s	2290×	body	1280	valid
1.1s	1669×	body	640	valid
298.0ms	2793×	body	80	valid
275.0ms	811×	body	320	valid
98.0ms	430×	body	160	valid
19.0ms	4×	body	5120	valid
6.0ms	3×	body	2560	valid