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

sample21.0ms

Algorithm

intervals

Results

6.0ms	47×	body	1280	valid
4.0ms	46×	body	640	valid
4.0ms	135×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	12×	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

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: 28.7b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 18

Calls

1 calls:

8.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify39.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5323	324

prune43.0ms

Filtered

15 candidates to 21 candidates (-40.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	2	22

Merged error: 0.1b

Counts

22 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

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

series18.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5645	850

prune105.0ms

Filtered

43 candidates to 61 candidates (-41.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
27.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
26.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
19.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify122.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4952	11205
1	4952	11205

prune559.0ms

Filtered

152 candidates to 457 candidates (-200.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	454	3	457
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	455	7	462

Merged error: 0b

Counts

462 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)))
0.2b	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))
0.4b	(pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

1822×	`*-un-lft-identity`
1674×	`times-frac`
1600×	`sqrt-prod`
840×	`cbrt-prod`
702×	`add-sqr-sqrt` `add-cube-cbrt`
640×	`distribute-lft-out`
324×	`unpow-prod-down` `cube-prod`
90×	`associate-/l*`
36×	`cube-mult` `unpow3` `associate-/r*` `sqr-pow`
28×	`sqrt-div`
26×	`cube-div`
24×	`cbrt-div` `associate-/r/`
14×	`flip3-+` `flip-+`
12×	`add-exp-log` `div-inv`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 1096

Calls

4 calls:

20.0ms	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)))
45.0ms	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms	(cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))
12.0ms	(pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)

series75.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)))
20.0ms	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms	(cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))
21.0ms	(pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)

simplify308.0ms

Algorithm

egg-herbie

Counts

1108 → 1108

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	5147	26780

prune954.0ms

Filtered

229 candidates to 1108 candidates (-383.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1107	1	1108
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	1109	6	1115

Merged error: 0b

Counts

1115 → 6

regimes43.0ms

Accuracy

0% (0.1b 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	9	9
1	9	9

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

sample606.0ms

Algorithm

intervals

Results

213.0ms	1737×	body	1280	valid
127.0ms	1278×	body	640	valid
108.0ms	4079×	body	80	valid
44.0ms	586×	body	320	valid
18.0ms	320×	body	160	valid
0.0ms	4×	body	80	nan

Details

analyze2.0ms

sample21.0ms

simplify3.0ms

prune2.0ms

localize5.0ms

rewrite8.0ms

series10.0ms

simplify39.0ms

prune43.0ms

localize6.0ms

rewrite19.0ms

series18.0ms

simplify43.0ms

prune105.0ms

localize12.0ms

rewrite93.0ms

series67.0ms

simplify122.0ms

prune559.0ms

localize16.0ms

rewrite216.0ms

series75.0ms

simplify308.0ms

prune954.0ms

regimes43.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0ms

sample606.0ms

Profiling