Details

analyze679.0ms

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

sample230.0ms

Algorithm

intervals

Results

94.0ms	59×	body	5120	exit
54.0ms	109×	body	1280	valid
30.0ms	90×	body	640	valid
20.0ms	52×	body	1280	nan
6.0ms	21×	body	640	nan
5.0ms	24×	body	320	valid
4.0ms	19×	body	320	nan
3.0ms	18×	body	160	valid
1.0ms	15×	body	80	valid
0.0ms	6×	body	80	nan
0.0ms	3×	body	160	nan

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4797	9
1	4797	9

prune7.0ms

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: 59.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (cos x))
0.3b	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
3.6b	(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)))

series11.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (cos x))
6.0ms	(/ (fmod (exp x) (sqrt (cos x))) (exp x))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5687	564

prune71.0ms

Filtered

41 candidates to 56 candidates (-36.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 59.0b

Counts

57 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
2.0b	(- (log (fmod (exp x) (sqrt (cos x)))) x)
2.6b	(log (fmod (exp x) (sqrt (cos x))))
3.6b	(fmod (exp x) (sqrt (cos x)))

rewrite12.0ms

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)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (- (log (fmod (exp x) (sqrt (cos x)))) x))
20.0ms	(- (log (fmod (exp x) (sqrt (cos x)))) x)
16.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4902	681
1	4902	681

prune83.0ms

Filtered

45 candidates to 68 candidates (-51.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 59.0b

Counts

73 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (cbrt (pow (log (fmod (exp x) (sqrt (cos x)))) 3)) x))
2.0b	(- (cbrt (pow (log (fmod (exp x) (sqrt (cos x)))) 3)) x)
2.6b	(log (fmod (exp x) (sqrt (cos x))))
3.6b	(fmod (exp x) (sqrt (cos x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `difference-of-squares`
9×	`exp-prod` `add-log-exp`
8×	`cbrt-prod`
6×	`add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`log-prod`
2×	`sub-neg` `unpow-prod-down` `diff-log` `cube-prod` `rem-exp-log` `distribute-lft-out--` `sqr-pow`
1×	`flip3--` `exp-diff` `rem-log-exp` `exp-sum` `log-pow` `flip--`

Counts

4 → 56

Calls

4 calls:

9.0ms	(exp (- (cbrt (pow (log (fmod (exp x) (sqrt (cos x)))) 3)) x))
8.0ms	(- (cbrt (pow (log (fmod (exp x) (sqrt (cos x)))) 3)) x)
1.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (- (cbrt (pow (log (fmod (exp x) (sqrt (cos x)))) 3)) x))
20.0ms	(- (cbrt (pow (log (fmod (exp x) (sqrt (cos x)))) 3)) x)
15.0ms	(log (fmod (exp x) (sqrt (cos x))))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4945	748
1	4945	748

prune109.0ms

Filtered

47 candidates to 68 candidates (-44.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 59.0b

Counts

73 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (log (* (pow (cbrt (fmod (exp x) (sqrt (cos x)))) 2) (cbrt (fmod (exp x) (sqrt (cos x)))))) x)
2.6b	(log (* (pow (cbrt (fmod (exp x) (sqrt (cos x)))) 2) (cbrt (fmod (exp x) (sqrt (cos x))))))
3.6b	(fmod (exp x) (sqrt (cos x)))
3.6b	(fmod (exp x) (sqrt (cos x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log`
7×	`pow1` `*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`log-pow` `add-log-exp`
4×	`add-cube-cbrt` `rem-log-exp` `add-cbrt-cube`
3×	`prod-exp`
2×	`log-prod` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-plus` `diff-log` `pow3` `pow-exp` `associate--l+` `pow-prod-up` `flip--` `unpow2` `difference-of-squares`

Counts

4 → 45

Calls

4 calls:

8.0ms	(- (log (* (pow (cbrt (fmod (exp x) (sqrt (cos x)))) 2) (cbrt (fmod (exp x) (sqrt (cos x)))))) x)
5.0ms	(log (* (pow (cbrt (fmod (exp x) (sqrt (cos x)))) 2) (cbrt (fmod (exp x) (sqrt (cos x))))))
1.0ms	(fmod (exp x) (sqrt (cos x)))
1.0ms	(fmod (exp x) (sqrt (cos x)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (log (* (pow (cbrt (fmod (exp x) (sqrt (cos x)))) 2) (cbrt (fmod (exp x) (sqrt (cos x)))))) x)
18.0ms	(log (* (pow (cbrt (fmod (exp x) (sqrt (cos x)))) 2) (cbrt (fmod (exp x) (sqrt (cos x))))))
1.0ms	(fmod (exp x) (sqrt (cos x)))
1.0ms	(fmod (exp x) (sqrt (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5249	505

prune72.0ms

Filtered

40 candidates to 57 candidates (-42.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	57	4	61

Merged error: 59.0b

Counts

61 → 4

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 59.6b against oracle of 59.6b and baseline of 59.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	21
1	23	21

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.3s	1552×	body	5120	exit
1.6s	3142×	body	1280	valid
843.0ms	2499×	body	640	valid
509.0ms	1303×	body	1280	nan
290.0ms	1270×	body	320	valid
276.0ms	1016×	body	640	nan
100.0ms	502×	body	320	nan
90.0ms	608×	body	160	valid
39.0ms	481×	body	80	valid
30.0ms	230×	body	160	nan
17.0ms	227×	body	80	nan

Details

analyze679.0ms

sample230.0ms

simplify80.0ms

prune7.0ms

localize8.0ms

rewrite7.0ms

series11.0ms

simplify54.0ms

prune71.0ms

localize13.0ms

rewrite12.0ms

series41.0ms

simplify56.0ms

prune83.0ms

localize16.0ms

rewrite21.0ms

series41.0ms

simplify61.0ms

prune109.0ms

localize15.0ms

rewrite15.0ms

series41.0ms

simplify43.0ms

prune72.0ms

regimes39.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.4s

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