Details

sample403.0ms

Algorithm

intervals

Results

226.0ms	91×	body	10240	exit
106.0ms	59×	body	1280	valid
37.0ms	57×	body	640	valid
10.0ms	29×	body	320	valid
9.0ms	92×	body	80	valid
4.0ms	19×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
38.0b	(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`
1×	`expm1-log1p` `expm1-udef`

Counts

3 → 29

Calls

3 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series100.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
90.0ms	(expm1 (sin (expm1 a)))
8.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify52.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	73	248
1	147	216
2	421	216
3	1258	216
4	5001	216

prune157.0ms

Filtered

38 candidates to 28 candidates (73.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 31.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
38.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

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

series123.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify61.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	104	472
1	205	410
2	516	410
3	1518	410
4	5002	410

prune256.0ms

Filtered

62 candidates to 42 candidates (67.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
38.0b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

2.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series175.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify101.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 7 (95.0ms)

Iter	Nodes	Cost
0	76	773
1	100	678
2	127	678
3	187	678
4	358	678
5	884	678
6	3890	678
7	5001	666

prune366.0ms

Filtered

69 candidates to 53 candidates (76.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 31.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
38.0b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
38.0b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
38.0b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

1.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
0.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
0.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series39.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
3.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
3.0ms	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify79.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	48	894
1	68	747
2	87	747
3	128	747
4	228	747
5	550	747
6	2633	747
7	5001	747

prune267.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 31.5b

regimes305.0ms

Accuracy

0% (1.6b remaining)

Error of 33.5b against oracle of 31.9b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.4s	2570×	body	10240	exit
3.9s	2295×	body	1280	valid
1.1s	1656×	body	640	valid
272.0ms	823×	body	320	valid
266.0ms	2802×	body	80	valid
85.0ms	418×	body	160	valid
18.0ms	4×	body	5120	valid
4.0ms	2×	body	2560	valid