Details

analyze665.0ms

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

sample59.0ms

Algorithm

intervals

Results

28.0ms	80×	body	1280	valid
10.0ms	43×	body	640	valid
5.0ms	31×	body	320	valid
5.0ms	89×	body	80	valid
1.0ms	13×	body	160	valid

simplify490.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5131	12

prune11.0ms

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: 40.8b

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)
3.5b	(- (pow (exp x) 2.0) 1.0)
3.5b	(- (exp x) 1.0)

rewrite46.0ms

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:

10.0ms	(/ (- (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))
15.0ms	(pow (exp x) 2.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4908	1696
1	4908	1696

prune232.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ 2 (* x (* x 1/2))))
9.9b	(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)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5225	486

prune58.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2)
3.5b	(- (pow (exp x) 2.0) 1.0)
3.5b	(- (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)
7.0ms	(- (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:

14.0ms	(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))

simplify28.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4908	612
1	4908	612

prune145.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	83	3	86

Merged error: 0b

Counts

86 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
0.0b	(pow (- (pow (exp x) 2.0) 1.0) 3)
3.5b	(- (pow (exp x) 2) (* 1.0 1.0))
3.5b	(- (pow (exp x) 2.0) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
20×	`cbrt-prod` `unpow-prod-down` `*-un-lft-identity`
19×	`difference-of-squares`
14×	`cube-prod`
10×	`add-cube-cbrt`
8×	`add-log-exp` `sqr-pow`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `unpow2` `rem-cube-cbrt`

Counts

4 → 94

Calls

4 calls:

7.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
6.0ms	(pow (- (pow (exp x) 2.0) 1.0) 3)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
6.0ms	(- (pow (exp x) 2.0) 1.0)

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
10.0ms	(pow (- (pow (exp x) 2.0) 1.0) 3)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(- (pow (exp x) 2.0) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4945	1210
1	4945	1210

prune188.0ms

Filtered

64 candidates to 106 candidates (-65.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	106	3	109

Merged error: 0b

Counts

109 → 3

regimes38.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.1b

bsearch18.0ms

Steps

Iters	Range		Point
9	-0.00013038933953490083	-2.2587095510235223e-11	-1.09869912468553e-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	2286×	body	1280	valid
381.0ms	1640×	body	640	valid
130.0ms	813×	body	320	valid
127.0ms	2832×	body	80	valid
43.0ms	429×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze665.0ms

sample59.0ms

simplify490.0ms

prune11.0ms

localize10.0ms

rewrite46.0ms

series39.0ms

simplify88.0ms

prune232.0ms

localize6.0ms

rewrite10.0ms

series8.0ms

simplify39.0ms

prune58.0ms

localize13.0ms

rewrite20.0ms

series25.0ms

simplify28.0ms

prune145.0ms

localize18.0ms

rewrite26.0ms

series22.0ms

simplify41.0ms

prune188.0ms

regimes38.0ms

bsearch18.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling