Details

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0.219727%

Results

167.0ms	57×	body	2560	valid
47.0ms	82×	body	1280	valid
16.0ms	65×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	12×	body	80	valid

simplify364.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

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: 33.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (sin x))
1.4b	(- x (tan x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series38.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
20.0ms	(- x (tan x))

simplify148.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune105.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 0.1b

Counts

90 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
13.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`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×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
6.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series15.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
6.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	316
2	5001	313

prune114.0ms

Filtered

46 candidates to 75 candidates (-63.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	74	5	79

Merged error: 0.1b

Counts

79 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

13.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.4b	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.4b	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.4b	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `sum-log` `associate--r+`

Counts

4 → 53

Calls

4 calls:

6.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
6.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
6.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
6.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
17.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
14.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
16.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))

simplify101.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	227	901
1	723	833
2	3160	827
3	5001	827

prune322.0ms

Filtered

56 candidates to 65 candidates (-16.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	65	5	70

Merged error: 0.1b

Counts

70 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b	(- x (tan x))
1.4b	(- x (tan x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
26.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series61.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (sin x) (- x (tan x)))
30.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	870
2	5001	870

prune85.0ms

Filtered

80 candidates to 106 candidates (-32.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	107	4	111

Merged error: 0.1b

Counts

111 → 4

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.5b

bsearch44.0ms

Steps

Iters	Range		Point
8	0.018355360142520552	391.0994193283684	0.03436993896801193
9	-0.11178818041521428	-1.1746611908901782e-08	-0.02909113960781213

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample11.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0.219727%

Results

3.9s	1575×	body	2560	valid
1.6s	2760×	body	1280	valid
491.0ms	1849×	body	640	valid
174.0ms	976×	body	320	valid
58.0ms	468×	body	160	valid
28.0ms	372×	body	80	valid

Details

sample4.9s

simplify364.0ms

prune4.0ms

localize10.0ms

rewrite20.0ms

series38.0ms

simplify148.0ms

prune105.0ms

localize9.0ms

rewrite18.0ms

series15.0ms

simplify41.0ms

prune114.0ms

localize15.0ms

rewrite26.0ms

series51.0ms

simplify101.0ms

prune322.0ms

localize9.0ms

rewrite43.0ms

series61.0ms

simplify38.0ms

prune85.0ms

regimes49.0ms

bsearch44.0ms

simplify2.0ms

end0.0ms

sample11.0s

Profiling