Details

analyze5.0ms

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

sample221.0ms

Algorithm

intervals

Results

162.0ms	101×	body	2560	valid
38.0ms	78×	body	1280	valid
8.0ms	46×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	3×	body	80	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

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: 59.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.2b	(- (/ 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)))

series33.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(/ 1.0 (tan x))
19.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4916	556
1	4916	556

prune84.0ms

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: 0.4b

Counts

56 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
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))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
6.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series26.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
6.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4959	885
1	4959	885

prune144.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	5	93

Merged error: 0.2b

Counts

93 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

rewrite28.0ms

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:

12.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
59.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

simplify49.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4987	2218
1	4987	2218

prune455.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	89	10	99
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	90	14	104

Merged error: 0.1b

Counts

104 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
0.7b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
21.0ms	(cbrt x)
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
59.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

simplify34.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4962	792
1	4962	792

prune279.0ms

Filtered

48 candidates to 60 candidates (-25.0%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	59	15	74

Merged error: 0.1b

Counts

74 → 15

regimes113.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b 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	3191×	body	2560	valid
1.3s	2566×	body	1280	valid
220.0ms	1198×	body	640	valid
132.0ms	8000×	pre	80	true
79.0ms	671×	body	320	valid
27.0ms	327×	body	160	valid
2.0ms	47×	body	80	valid

Details

analyze5.0ms

sample221.0ms

simplify9.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series33.0ms

simplify45.0ms

prune84.0ms

localize10.0ms

rewrite27.0ms

series26.0ms

simplify60.0ms

prune144.0ms

localize15.0ms

rewrite28.0ms

series238.0ms

simplify49.0ms

prune455.0ms

localize34.0ms

rewrite12.0ms

series160.0ms

simplify34.0ms

prune279.0ms

regimes113.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.2s

Profiling