Details

analyze691.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

sample231.0ms

Algorithm

intervals

Results

90.0ms	58×	body	5120	exit
59.0ms	111×	body	1280	valid
25.0ms	77×	body	640	valid
15.0ms	38×	body	1280	nan
10.0ms	39×	body	640	nan
8.0ms	33×	body	320	valid
4.0ms	22×	body	320	nan
3.0ms	24×	body	160	valid
1.0ms	10×	body	160	nan
1.0ms	11×	body	80	valid
1.0ms	10×	body	80	nan

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4797	9
1	4797	9

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 60.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (cos x))
0.2b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
5.4b	(fmod (exp x) (sqrt (cos x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`pow1` `add-exp-log`
3×	`associate-/r` `sqrt-prod` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

3 → 47

Calls

3 calls:

1.0ms	(sqrt (cos x))
4.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (cos x))
6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
3.0ms	(fmod (exp x) (sqrt (cos x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5687	564

prune68.0ms

Filtered

41 candidates to 56 candidates (-36.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Merged error: 60.5b

Counts

57 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (cos x))
0.1b	(cbrt (cos x))
0.2b	(/ (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x))))) (exp x))
5.4b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1/3`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
4.0ms	(/ (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x))))) (exp x))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (cos x))
17.0ms	(cbrt (cos x))
10.0ms	(/ (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x))))) (exp x))
3.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5285	932

prune84.0ms

Filtered

51 candidates to 68 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 60.5b

Counts

72 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))) (/ (cbrt (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))) (* (cbrt (exp x)) (cbrt (exp x)))))
5.4b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
5.4b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
5.4b	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
13×	`add-exp-log`
11×	`cbrt-prod`
10×	`times-frac` `associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `associate-l` `add-cbrt-cube` `unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
2×	`cbrt-undiv` `div-exp`
1×	`associate-r/` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 59

Calls

4 calls:

10.0ms	(* (cbrt (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))) (/ (cbrt (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))) (* (cbrt (exp x)) (cbrt (exp x)))))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
1.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cbrt (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))) (/ (cbrt (fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))) (* (cbrt (exp x)) (cbrt (exp x)))))
2.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
2.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))
3.0ms	(fmod (exp x) (* (fabs (cbrt (cos x))) (sqrt (cbrt (cos x)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5063	1605

prune101.0ms

Filtered

55 candidates to 71 candidates (-29.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Merged error: 60.5b

Counts

75 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
1.7b	(- (log (fmod (exp x) (sqrt (cos x)))) x)
2.5b	(log (fmod (exp x) (sqrt (cos x))))
5.4b	(fmod (exp x) (sqrt (cos x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1` `add-log-exp`
6×	`exp-prod` `associate--l+`
5×	`add-exp-log`
4×	`exp-sum` `add-cbrt-cube` `distribute-lft-out--`
3×	`log-pow`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`flip3--` `exp-diff` `rem-log-exp` `flip--`

Counts

4 → 56

Calls

4 calls:

5.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
4.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
1.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
19.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
15.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4902	681
1	4902	681

prune60.0ms

Filtered

46 candidates to 68 candidates (-47.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	68	4	72

Merged error: 60.5b

Counts

72 → 4

regimes41.0ms

Accuracy

0% (0.0b remaining)

Error of 59.4b against oracle of 59.4b and baseline of 59.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.4s	1587×	body	5120	exit
1.6s	3139×	body	1280	valid
844.0ms	2502×	body	640	valid
481.0ms	1192×	body	1280	nan
284.0ms	1035×	body	640	nan
280.0ms	1223×	body	320	valid
100.0ms	507×	body	320	nan
98.0ms	622×	body	160	valid
47.0ms	514×	body	80	valid
37.0ms	282×	body	160	nan
20.0ms	268×	body	80	nan

Details

analyze691.0ms

sample231.0ms

simplify79.0ms

prune8.0ms

localize8.0ms

rewrite7.0ms

series12.0ms

simplify55.0ms

prune68.0ms

localize14.0ms

rewrite8.0ms

series46.0ms

simplify51.0ms

prune84.0ms

localize22.0ms

rewrite14.0ms

series66.0ms

simplify41.0ms

prune101.0ms

localize10.0ms

rewrite11.0ms

series39.0ms

simplify55.0ms

prune60.0ms

regimes41.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.4s

Profiling