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

sample26.0ms

Algorithm

intervals

Results

8.0ms	68×	body	1280	valid
4.0ms	15×	body	160	valid
3.0ms	36×	body	640	valid
3.0ms	115×	body	80	valid
2.0ms	22×	body	320	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 33.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

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))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune70.0ms

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

rewrite26.0ms

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))
8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series19.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(/ 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	5038	1051

prune141.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	1	1	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 (sqrt (+ 1.0 x)))
0.1b	(sqrt (sqrt (+ 1.0 x)))
0.2b	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ 1.0 x)))
4.0ms	(sqrt (sqrt (+ 1.0 x)))
16.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
16.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ 1.0 x)))
7.0ms	(sqrt (sqrt (+ 1.0 x)))
193.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
4.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify63.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4941	1700
1	4941	1700

prune232.0ms

Filtered

91 candidates to 173 candidates (-90.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	174	8	182

Merged error: 0.0b

Counts

182 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:

11.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
40.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(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)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4952	4249
1	4952	4249

prune439.0ms

Filtered

142 candidates to 262 candidates (-84.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	262	8	270

Merged error: 0.0b

Counts

270 → 8

regimes97.0ms

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

sample609.0ms

Algorithm

intervals

Results

221.0ms	1755×	body	1280	valid
123.0ms	1224×	body	640	valid
110.0ms	4079×	body	80	valid
47.0ms	624×	body	320	valid
15.0ms	318×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms

sample26.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite12.0ms

series14.0ms

simplify44.0ms

prune70.0ms

localize6.0ms

rewrite26.0ms

series19.0ms

simplify25.0ms

prune141.0ms

localize9.0ms

rewrite47.0ms

series210.0ms

simplify63.0ms

prune232.0ms

localize9.0ms

rewrite88.0ms

series54.0ms

simplify83.0ms

prune439.0ms

regimes97.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample609.0ms

Profiling