Details

analyze678.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample60.0ms

Algorithm

intervals

Results

22.0ms	60×	body	1280	valid
16.0ms	64×	body	640	valid
6.0ms	42×	body	320	valid
4.0ms	78×	body	80	valid
1.0ms	12×	body	160	valid

simplify468.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4920	12
1	4920	12

prune10.0ms

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: 44.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.0b	(pow (exp x) 2.0)
4.6b	(- (pow (exp x) 2.0) 1.0)
4.7b	(- (exp x) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
35×	`times-frac`
30×	`difference-of-squares`
21×	`add-cube-cbrt`
16×	`distribute-lft-out--`
10×	`unpow-prod-down`
8×	`add-log-exp` `sqr-pow`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`flip3--` `pow-pow` `flip--`
3×	`pow-unpow` `exp-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `div-sub` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 112

Calls

4 calls:

11.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
3.0ms	(pow (exp x) 2.0)
5.0ms	(- (pow (exp x) 2.0) 1.0)
6.0ms	(- (exp x) 1.0)

series39.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
16.0ms	(pow (exp x) 2.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5038	1696

prune211.0ms

Filtered

90 candidates to 124 candidates (-37.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	3	125

Merged error: 0b

Counts

125 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ 2 (* x (* x 1/2))))
7.5b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `sqrt-prod`
3×	`pow1` `add-cube-cbrt` `sum-log`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

2 → 30

Calls

2 calls:

4.0ms	(+ x (+ 2 (* x (* x 1/2))))
4.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(+ x (+ 2 (* x (* x 1/2))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4911	474
1	4911	474

prune53.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Merged error: 0b

Counts

39 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2)
4.6b	(- (pow (exp x) 2.0) 1.0)
4.6b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `pow-pow` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1` `pow-unpow` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `unpow2`
1×	`distribute-lft-out--`

Counts

4 → 71

Calls

4 calls:

3.0ms	(pow (exp x) 2.0)
3.0ms	(pow (exp x) 2)
5.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series25.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (exp x) 2.0)
3.0ms	(pow (exp x) 2)
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4921	600
1	4921	600

prune119.0ms

Filtered

54 candidates to 83 candidates (-53.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	83	3	86

Merged error: 0b

Counts

86 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
4.6b	(- (pow (exp x) 2.0) 1.0)
4.7b	(- (exp x) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
20×	`cbrt-prod`
18×	`*-un-lft-identity`
13×	`unpow-prod-down`
10×	`add-cube-cbrt` `difference-of-squares`
8×	`add-log-exp`
7×	`cube-prod`
5×	`pow1` `sqr-pow`
4×	`add-exp-log` `pow-pow` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow-unpow` `exp-prod` `flip3--` `flip--`
2×	`cube-div` `sub-neg` `cbrt-div` `diff-log`
1×	`cube-mult` `pow-to-exp` `pow1/3` `unpow3` `pow-exp` `rem-cbrt-cube`

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (exp x) 2.0)
7.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
6.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (exp x) 1.0)

series24.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (exp x) 2.0)
4.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
4.0ms	(- (pow (exp x) 2.0) 1.0)
2.0ms	(- (exp x) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4952	836
1	4952	836

prune137.0ms

Filtered

62 candidates to 91 candidates (-46.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	91	3	94

Merged error: 0b

Counts

94 → 3

regimes34.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.0b

bsearch32.0ms

Steps

Iters	Range		Point
10	-3.841503056709872e-05	-6.528543796546641e-17	-1.4525342540035974e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	35
1	29	35

end0.0ms

analyze477.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample1.7s

Algorithm

intervals

Results

848.0ms	2275×	body	1280	valid
397.0ms	1692×	body	640	valid
132.0ms	833×	body	320	valid
129.0ms	2810×	body	80	valid
40.0ms	390×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze678.0ms

sample60.0ms

simplify468.0ms

prune10.0ms

localize11.0ms

rewrite30.0ms

series39.0ms

simplify62.0ms

prune211.0ms

localize8.0ms

rewrite9.0ms

series8.0ms

simplify51.0ms

prune53.0ms

localize14.0ms

rewrite18.0ms

series25.0ms

simplify69.0ms

prune119.0ms

localize11.0ms

rewrite22.0ms

series24.0ms

simplify47.0ms

prune137.0ms

regimes34.0ms

bsearch32.0ms

simplify1.0ms

end0.0ms

analyze477.0ms

sample1.7s

Profiling