Details

analyze8.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample64.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
3.0ms	260×	pre	80	true
1.0ms	4×	body	80	invalid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5216	49

prune18.0ms

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: 1.2b

Counts

2 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.1b	(pow (exp (fabs x)) (fabs x))
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.4b	(pow (/ 1.0 (fabs x)) 7)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `sqr-pow`
2×	`div-exp` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 89

Calls

4 calls:

1.0ms	(sqrt PI)
3.0ms	(pow (exp (fabs x)) (fabs x))
5.0ms	(pow (/ 1.0 (fabs x)) 5)
5.0ms	(pow (/ 1.0 (fabs x)) 7)

series57.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(sqrt PI)
28.0ms	(pow (exp (fabs x)) (fabs x))
15.0ms	(pow (/ 1.0 (fabs x)) 5)
15.0ms	(pow (/ 1.0 (fabs x)) 7)

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4987	897
1	4987	897

prune356.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	15	99
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	16	101

Merged error: 0.5b

Counts

101 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.1b	(pow (exp (fabs x)) (fabs x))
1.1b	(pow (/ 1.0 (fabs x)) 5)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
29×	`unpow-prod-down`
27×	`times-frac`
13×	`cube-prod`
10×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `div-inv` `sqr-pow`
2×	`div-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3`

Counts

4 → 107

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
3.0ms	(pow (exp (fabs x)) (fabs x))
5.0ms	(pow (/ 1.0 (fabs x)) 5)

series51.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
30.0ms	(pow (exp (fabs x)) (fabs x))
12.0ms	(pow (/ 1.0 (fabs x)) 5)

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5099	967

prune331.0ms

Filtered

70 candidates to 117 candidates (-67.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	115	18	133

Merged error: 0.4b

Counts

133 → 18

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (exp (fabs x)) (fabs x)) (+ (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3)) (+ (* (/ 3.0 4.0) (/ 1.0 (pow (fabs x) 5))) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 7)))))))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.1b	(pow (exp (fabs x)) (fabs x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

95×	`frac-add`
66×	`associate-*r/`
32×	`add-sqr-sqrt`
29×	`frac-times` `associate-*l/`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
23×	`cube-div`
20×	`unpow-prod-down`
18×	`times-frac`
13×	`cube-prod`
11×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
6×	`pow-unpow`
5×	`pow-pow` `flip3-+` `flip-+`
4×	`associate-r` `pow-exp` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `exp-prod` `prod-exp` `sqrt-prod` `unswap-sqr`
2×	`div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `div-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 144

Calls

4 calls:

31.0ms	(* (pow (exp (fabs x)) (fabs x)) (+ (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3)) (+ (* (/ 3.0 4.0) (/ 1.0 (pow (fabs x) 5))) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 7)))))))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
3.0ms	(pow (exp (fabs x)) (fabs x))

series135.0ms

Counts

4 → 10

Calls

4 calls:

92.0ms	(* (pow (exp (fabs x)) (fabs x)) (+ (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3)) (+ (* (/ 3.0 4.0) (/ 1.0 (pow (fabs x) 5))) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 7)))))))
9.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
33.0ms	(pow (exp (fabs x)) (fabs x))

simplify51.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5099	5055

prune740.0ms

Filtered

110 candidates to 154 candidates (-40.0%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	7	10	17
Picked	0	1	1
Done	0	0	0
Total	152	20	172

Merged error: 0.4b

Counts

172 → 20

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.1b	(pow (exp (fabs x)) (fabs x))
1.1b	(pow (/ 1.0 (fabs x)) 5)
4.9b	(log (exp (pow (/ 1.0 (fabs x)) 3)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

35×	`exp-prod`
33×	`add-sqr-sqrt` `log-pow`
32×	`add-cube-cbrt` `*-un-lft-identity`
29×	`unpow-prod-down`
27×	`times-frac`
13×	`cube-prod`
8×	`pow1`
7×	`add-exp-log`
6×	`pow-unpow`
5×	`pow-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`log-prod` `pow-exp` `sqrt-prod` `div-inv` `sqr-pow`
2×	`pow-to-exp`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `div-exp` `rem-log-exp`

Counts

4 → 105

Calls

4 calls:

1.0ms	(sqrt PI)
3.0ms	(pow (exp (fabs x)) (fabs x))
4.0ms	(pow (/ 1.0 (fabs x)) 5)
8.0ms	(log (exp (pow (/ 1.0 (fabs x)) 3)))

series48.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(sqrt PI)
27.0ms	(pow (exp (fabs x)) (fabs x))
12.0ms	(pow (/ 1.0 (fabs x)) 5)
9.0ms	(log (exp (pow (/ 1.0 (fabs x)) 3)))

simplify47.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4983	820
1	4983	820

prune274.0ms

Filtered

76 candidates to 115 candidates (-51.3%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	2	16	18
Picked	0	1	1
Done	0	1	1
Total	111	24	135

Merged error: 0.3b

Counts

135 → 24

regimes531.0ms

Accuracy

0% (0.9b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	49
1	41	49

end0.0ms

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample1.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
95.0ms	8129×	pre	80	true
25.0ms	129×	body	80	invalid

Details

analyze8.0ms

sample64.0ms

simplify20.0ms

prune18.0ms

localize33.0ms

rewrite17.0ms

series57.0ms

simplify50.0ms

prune356.0ms

localize34.0ms

rewrite17.0ms

series51.0ms

simplify45.0ms

prune331.0ms

localize37.0ms

rewrite46.0ms

series135.0ms

simplify51.0ms

prune740.0ms

localize38.0ms

rewrite22.0ms

series48.0ms

simplify47.0ms

prune274.0ms

regimes531.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze7.0ms

sample1.8s

Profiling