Details

analyze663.0ms

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

26.0ms	69×	body	1280	valid
14.0ms	59×	body	640	valid
5.0ms	28×	body	320	valid
4.0ms	85×	body	80	valid
1.0ms	15×	body	160	valid

simplify483.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5131	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: 41.3b

Counts

2 → 1

localize10.0ms

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)
4.5b	(- (pow (exp x) 2.0) 1.0)
4.6b	(- (exp x) 1.0)

rewrite31.0ms

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)

series50.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
26.0ms	(pow (exp x) 2.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4908	1696
1	4908	1696

prune214.0ms

Filtered

90 candidates to 124 candidates (-37.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	2	125

Merged error: 0b

Counts

125 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ 2 (* x (* x 1/2))))
10.5b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite10.0ms

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:

5.0ms	(+ 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)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5225	486

prune50.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	36	2	38

Merged error: 0b

Counts

38 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2)
4.5b	(- (pow (exp x) 2.0) 1.0)
4.5b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite20.0ms

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)
6.0ms	(- (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))

simplify29.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4908	612
1	4908	612

prune133.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	83	2	85

Merged error: 0b

Counts

85 → 2

regimes30.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.0b

bsearch21.0ms

Steps

Iters	Range		Point
9	-0.0001949386799872467	-1.4496366832131268e-13	-1.175086435680937e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

827.0ms	2319×	body	1280	valid
376.0ms	1632×	body	640	valid
127.0ms	854×	body	320	valid
122.0ms	2813×	body	80	valid
37.0ms	382×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze663.0ms

sample60.0ms

simplify483.0ms

prune10.0ms

localize10.0ms

rewrite31.0ms

series50.0ms

simplify89.0ms

prune214.0ms

localize6.0ms

rewrite10.0ms

series8.0ms

simplify37.0ms

prune50.0ms

localize12.0ms

rewrite20.0ms

series25.0ms

simplify29.0ms

prune133.0ms

regimes30.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling