Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample22.0ms

Algorithm

intervals

Results

7.0ms	54×	body	1280	valid
4.0ms	47×	body	640	valid
3.0ms	122×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	9×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune3.0ms

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: 32.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify40.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5374	504

prune69.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify25.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5251	1049

prune143.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 0.0b

Counts

83 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

9.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
36.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
16.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5020	4266

prune439.0ms

Filtered

140 candidates to 262 candidates (-87.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	261	10	271

Merged error: 0.0b

Counts

271 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
82×	`sqrt-prod`
46×	`times-frac`
40×	`distribute-lft-out`
34×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `sqrt-div` `associate-/r/`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `div-inv`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`sqrt-undiv` `sqrt-unprod` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

7.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
11.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
22.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
20.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
12.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify41.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4963	2717
1	4963	2717

prune298.0ms

Filtered

93 candidates to 144 candidates (-54.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	3	4	7
Picked	0	1	1
Done	1	1	2
Total	146	8	154

Merged error: 0.0b

Counts

154 → 8

regimes52.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	15	22

end0.0ms

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample608.0ms

Algorithm

intervals

Results

224.0ms	1770×	body	1280	valid
126.0ms	1232×	body	640	valid
105.0ms	4038×	body	80	valid
46.0ms	635×	body	320	valid
16.0ms	325×	body	160	valid
0.0ms	2×	body	80	nan

Details

analyze2.0ms

sample22.0ms

simplify3.0ms

prune3.0ms

localize5.0ms

rewrite11.0ms

series13.0ms

simplify40.0ms

prune69.0ms

localize6.0ms

rewrite21.0ms

series18.0ms

simplify25.0ms

prune143.0ms

localize9.0ms

rewrite79.0ms

series53.0ms

simplify55.0ms

prune439.0ms

localize12.0ms

rewrite55.0ms

series54.0ms

simplify41.0ms

prune298.0ms

regimes52.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0ms

sample608.0ms

Profiling