Details

sample433.0ms

Algorithm

intervals

Results

225.0ms	82×	body	10240	exit
120.0ms	66×	body	1280	valid
47.0ms	62×	body	640	valid
17.0ms	96×	body	80	valid
8.0ms	19×	body	320	valid
4.0ms	13×	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: 32.6b

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)))
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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)

series152.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sin (expm1 a))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
88.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

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

prune194.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.5b

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))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.8b	(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:

86.0ms	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify58.0ms

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

prune246.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.8b	(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)

series171.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
31.0ms	(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)

simplify100.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 7 (93.0ms)

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

prune349.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.8b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
37.8b	(fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
37.8b	(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

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:

3.0ms	(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)))
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)
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

prune260.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 31.0b

regimes294.0ms

Accuracy

0% (1.7b remaining)

Error of 33.4b against oracle of 31.8b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19

end0.0ms

sample13.6s

Algorithm

intervals

Results

7.0s	2592×	body	10240	exit
4.1s	2238×	body	1280	valid
1.3s	1662×	body	640	valid
507.0ms	2804×	body	80	valid
354.0ms	827×	body	320	valid
146.0ms	463×	body	160	valid
14.0ms	3×	body	5120	valid
6.0ms	3×	body	2560	valid