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

6.0ms	50×	body	1280	valid
5.0ms	48×	body	640	valid
3.0ms	126×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

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: 31.2b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

1.7b	(- (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 → 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))

simplify28.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5102	335

prune44.0ms

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

rewrite18.0ms

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:

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

simplify23.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5138	866

prune108.0ms

Filtered

43 candidates to 61 candidates (-41.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 0.0b

Counts

63 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
0.3b	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
74×	`*-un-lft-identity`
32×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `add-log-exp` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
11.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
20.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
20.0ms	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
6.0ms	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5254	2070

prune237.0ms

Filtered

84 candidates to 147 candidates (-75.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	146	7	153

Merged error: 0.0b

Counts

153 → 7

localize13.0ms

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))))

rewrite90.0ms

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:

8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
11.0ms	(/ 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))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
18.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
25.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify121.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5073	11200

prune556.0ms

Filtered

152 candidates to 457 candidates (-200.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	453	4	457
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	456	8	464

Merged error: 0b

Counts

464 → 8

regimes59.0ms

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

sample597.0ms

Algorithm

intervals

Results

207.0ms	1650×	body	1280	valid
123.0ms	1254×	body	640	valid
112.0ms	4160×	body	80	valid
46.0ms	615×	body	320	valid
15.0ms	321×	body	160	valid
0.0ms	4×	body	80	nan

Details

analyze2.0ms

sample22.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite9.0ms

series10.0ms

simplify28.0ms

prune44.0ms

localize6.0ms

rewrite18.0ms

series18.0ms

simplify23.0ms

prune108.0ms

localize9.0ms

rewrite64.0ms

series36.0ms

simplify50.0ms

prune237.0ms

localize13.0ms

rewrite90.0ms

series64.0ms

simplify121.0ms

prune556.0ms

regimes59.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample597.0ms

Profiling