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	53×	body	1280	valid
4.0ms	136×	body	80	valid
4.0ms	37×	body	640	valid
1.0ms	20×	body	320	valid
0.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 28.5b

Counts

2 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite9.0ms

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))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify116.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (21.0ms)

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

prune44.0ms

Filtered

15 candidates to 22 candidates (-46.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Merged error: 0.1b

Counts

23 → 3

localize8.0ms

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)))

rewrite23.0ms

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:

7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series15.0ms

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

prune129.0ms

Filtered

44 candidates to 70 candidates (-59.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 0.0b

Counts

73 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite113.0ms

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:

13.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
16.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(/ (+ 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)))))

simplify166.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (124.0ms)

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

prune579.0ms

Filtered

150 candidates to 328 candidates (-118.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	324	4	328
Fresh	4	2	6
Picked	0	1	1
Done	1	1	2
Total	329	8	337

Merged error: 0.0b

Counts

337 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))))

rewrite69.0ms

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:

13.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
27.0ms	(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms	(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))))

simplify131.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	952	2243
1	4549	2057
2	5002	1968

prune361.0ms

Filtered

97 candidates to 159 candidates (-63.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	159	8	167

Merged error: 0b

Counts

167 → 8

regimes59.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

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

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

sample638.0ms

Algorithm

intervals

Results

229.0ms	1729×	body	1280	valid
132.0ms	1306×	body	640	valid
115.0ms	4029×	body	80	valid
46.0ms	610×	body	320	valid
17.0ms	326×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms

sample21.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite9.0ms

series10.0ms

simplify116.0ms

prune44.0ms

localize8.0ms

rewrite23.0ms

series15.0ms

simplify59.0ms

prune129.0ms

localize11.0ms

rewrite113.0ms

series56.0ms

simplify166.0ms

prune579.0ms

localize14.0ms

rewrite69.0ms

series51.0ms

simplify131.0ms

prune361.0ms

regimes59.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.0ms

sample638.0ms

Profiling