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

sample265.0ms

Algorithm

intervals

Results

193.0ms	101×	body	2560	valid
52.0ms	85×	body	1280	valid
7.0ms	43×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	19×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	3×	body	80	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	6	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))
2.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite20.0ms

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:

6.0ms	(/ 1.0 (tan x))
12.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series27.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(/ 1.0 (tan x))
17.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6640	555

prune77.0ms

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

localize11.0ms

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))

rewrite19.0ms

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:

7.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
5.0ms	(* 0.022222222222222223 (pow x 3))

series13.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4928	705
1	4928	705

prune138.0ms

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: 0.2b

Counts

79 → 5

localize15.0ms

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)))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

rewrite37.0ms

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:

15.0ms	(* (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)))))
6.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
8.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
6.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (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)))))
20.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
18.0ms	(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))))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5488	3067

prune565.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	92	12	104

Merged error: 0.2b

Counts

104 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

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))))
22.0ms	(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))))

simplify41.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5106	1852

prune604.0ms

Filtered

60 candidates to 64 candidates (-6.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	62	14	76

Merged error: 0.1b

Counts

76 → 14

regimes134.0ms

Accuracy

0% (0.1b 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

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

sample7.2s

Algorithm

intervals

Results

5.4s	3235×	body	2560	valid
1.3s	2427×	body	1280	valid
239.0ms	1276×	body	640	valid
128.0ms	8000×	pre	80	true
80.0ms	690×	body	320	valid
24.0ms	308×	body	160	valid
3.0ms	64×	body	80	valid

Details

analyze5.0ms

sample265.0ms

simplify2.0ms

prune2.0ms

localize5.0ms

rewrite20.0ms

series27.0ms

simplify52.0ms

prune77.0ms

localize11.0ms

rewrite19.0ms

series13.0ms

simplify44.0ms

prune138.0ms

localize15.0ms

rewrite37.0ms

series79.0ms

simplify53.0ms

prune565.0ms

localize22.0ms

rewrite26.0ms

series78.0ms

simplify41.0ms

prune604.0ms

regimes134.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample7.2s

Profiling