Details

analyze231.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample83.0ms

Algorithm

intervals

Results

40.0ms	73×	body	1280	valid
10.0ms	31×	body	640	valid
10.0ms	122×	body	80	valid
4.0ms	19×	body	320	valid
4.0ms	6×	body	5120	exit
2.0ms	11×	body	160	valid
1.0ms	7×	body	80	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5720	27

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 31.6b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(exp (neg (* (+ 1.0 eps) x)))
0.0b	(exp (neg (* (- 1.0 eps) x)))
2.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
3.0ms	(exp (neg (* (+ 1.0 eps) x)))
4.0ms	(exp (neg (* (- 1.0 eps) x)))
18.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(exp (neg (* (+ 1.0 eps) x)))
6.0ms	(exp (neg (* (- 1.0 eps) x)))
49.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4982	6540
1	4982	6540

prune340.0ms

Filtered

92 candidates to 166 candidates (-80.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	5	168

Merged error: 0.6b

Counts

168 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
0.2b	(/ (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x)))) 2.0)
4.4b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-log-exp`
7×	`add-cbrt-cube`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `associate-l` `prod-exp` `associate-/r` `associate-/l`
2×	`associate-+r-` `flip3-+` `sum-log` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
9.0ms	(/ (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x)))) 2.0)
7.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x))))

series13.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
5.0ms	(/ (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x)))) 2.0)
5.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5064	1068

prune134.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 0.6b

Counts

89 → 6

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (* x x) (- (* x 0.33333333333333337) 0.5))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-cube-cbrt` `sub-neg` `-un-lft-identity` `associate-r/`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-l` `*-commutative` `flip--` `add-log-exp` `unswap-sqr`

Counts

1 → 23

Calls

1 calls:

9.0ms

(* (* x x) (- (* x 0.33333333333333337) 0.5))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* (* x x) (- (* x 0.33333333333333337) 0.5))

simplify49.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4934	272
1	4934	272

prune51.0ms

Filtered

16 candidates to 26 candidates (-62.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Merged error: 0.6b

Counts

32 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
9.3b	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))
9.3b	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))
9.3b	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt 2.0)
3.0ms	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))
3.0ms	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))
3.0ms	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))

series32.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 2.0)
12.0ms	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))
9.0ms	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))
11.0ms	(cbrt (+ 2.0 (* (* x x) (- (* 0.6666666666666667 x) 1.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4953	1088
1	4953	1088

prune227.0ms

Filtered

59 candidates to 60 candidates (-1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	60	6	66

Merged error: 0.6b

Counts

66 → 6

regimes135.0ms

Accuracy

96.6% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch59.0ms

Steps

Iters	Range		Point
6	226.83727372543933	3216.9668642398738	296.438625869069

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	97
1	70	97

end0.0ms

sample2.2s

Algorithm

intervals

Results

973.0ms	1751×	body	1280	valid
425.0ms	1222×	body	640	valid
326.0ms	4088×	body	80	valid
152.0ms	643×	body	320	valid
119.0ms	205×	body	5120	exit
45.0ms	296×	body	160	valid
21.0ms	218×	body	80	invalid
7.0ms	13×	body	1280	invalid
5.0ms	12×	body	640	invalid
1.0ms	5×	body	320	invalid
0.0ms	1×	body	160	invalid

Details

analyze231.0ms

sample83.0ms

simplify44.0ms

prune11.0ms

localize19.0ms

rewrite47.0ms

series71.0ms

simplify121.0ms

prune340.0ms

localize9.0ms

rewrite24.0ms

series13.0ms

simplify50.0ms

prune134.0ms

localize6.0ms

rewrite10.0ms

series7.0ms

simplify49.0ms

prune51.0ms

localize16.0ms

rewrite10.0ms

series32.0ms

simplify66.0ms

prune227.0ms

regimes135.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling