Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

sample238.0ms

Algorithm

intervals

Results

162.0ms	99×	body	2560	valid
54.0ms	95×	body	1280	valid
7.0ms	34×	body	640	valid
5.0ms	256×	pre	80	true
2.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	220	8
1	220	8

prune2.0ms

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: 59.7b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 49

Calls

2 calls:

3.0ms	(/ 1.0 (tan x))
13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series28.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ 1.0 (tan x))
18.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4916	556
1	4916	556

prune81.0ms

Filtered

45 candidates to 55 candidates (-22.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	1	56

Merged error: 0.3b

Counts

56 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.0b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series16.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
7.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4943	707
1	4943	707

prune121.0ms

Filtered

49 candidates to 78 candidates (-59.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	5	79

Merged error: 0.3b

Counts

79 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

20.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
19.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
19.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
19.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify39.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4987	3186
1	4987	3186

prune575.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	90	14	104

Merged error: 0.1b

Counts

104 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
14×	`cbrt-div`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 61

Calls

4 calls:

7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
8.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
8.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
8.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
22.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
22.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
24.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))

simplify32.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5554	2389

prune707.0ms

Filtered

69 candidates to 73 candidates (-5.8%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	70	17	87

Merged error: 0.1b

Counts

87 → 17

regimes156.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.2s

Algorithm

intervals

Results

5.2s	3241×	body	2560	valid
1.3s	2526×	body	1280	valid
235.0ms	1271×	body	640	valid
129.0ms	8000×	pre	80	true
65.0ms	579×	body	320	valid
26.0ms	320×	body	160	valid
3.0ms	63×	body	80	valid

Details

analyze4.0ms

sample238.0ms

simplify10.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series28.0ms

simplify46.0ms

prune81.0ms

localize9.0ms

rewrite20.0ms

series16.0ms

simplify52.0ms

prune121.0ms

localize14.0ms

rewrite43.0ms

series80.0ms

simplify39.0ms

prune575.0ms

localize20.0ms

rewrite33.0ms

series89.0ms

simplify32.0ms

prune707.0ms

regimes156.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.2s

Profiling