Details

analyze2.0ms

Algorithm: search

sample21.0ms

Algorithm

intervals

Results

6.0ms	51×	body	1280	valid
4.0ms	141×	body	80	valid
3.0ms	34×	body	640	valid
1.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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: 27.2b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (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 → 19

Calls

1 calls:

8.0ms

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

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify118.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	203	216
1	808	206
2	4153	197
3	5001	197

prune42.0ms

Filtered

15 candidates to 22 candidates (-46.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	2	23

Merged error: 0.2b

Counts

23 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

9.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series14.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	435	698
1	1872	651
2	5001	615

prune118.0ms

Filtered

44 candidates to 70 candidates (-59.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	65	7	72

Merged error: 0.0b

Counts

72 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`associate-/l/` `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 → 316

Calls

4 calls:

12.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify162.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	827	3981
1	4531	3471
2	5001	3422

prune554.0ms

Filtered

152 candidates to 328 candidates (-115.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	322	6	328
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	326	9	335

Merged error: 0.0b

Counts

335 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

142×	`*-un-lft-identity`
96×	`sqrt-prod`
61×	`distribute-lft-out`
58×	`times-frac`
36×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `sqrt-div` `associate-/r/`
5×	`flip3-+` `flip-+` `associate-/l*`
4×	`add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `div-inv` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`sqrt-undiv` `sqrt-unprod` `associate-*l/` `prod-exp` `cbrt-unprod`

Counts

4 → 147

Calls

4 calls:

11.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
7.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms	(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
14.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify130.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	952	2241
1	4576	2057
2	5002	1968

prune344.0ms

Filtered

97 candidates to 159 candidates (-63.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	159	9	168

Merged error: 0.0b

Counts

168 → 9

regimes61.0ms

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	12	6
1	16	6
2	16	6

end0.0ms

analyze2.0ms

Algorithm: search

sample585.0ms

Algorithm

intervals

Results

211.0ms	1756×	body	1280	valid
120.0ms	1234×	body	640	valid
111.0ms	4114×	body	80	valid
42.0ms	600×	body	320	valid
14.0ms	296×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms

sample21.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite8.0ms

series9.0ms

simplify118.0ms

prune42.0ms

localize7.0ms

rewrite24.0ms

series14.0ms

simplify59.0ms

prune118.0ms

localize10.0ms

rewrite107.0ms

series54.0ms

simplify162.0ms

prune554.0ms

localize12.0ms

rewrite65.0ms

series54.0ms

simplify130.0ms

prune344.0ms

regimes61.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0ms

sample585.0ms

Profiling