Details

analyze3.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.07323%

Guaranteed chance to sample good point: 99.993895%

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	3
1	10	3
2	10	3

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: 30.6b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

29.6b

(sqrt (* (* 2.0 x) x))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
3×	`sqrt-pow1` `pow-prod-down`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/2` `sqrt-prod` `add-cbrt-cube` `add-log-exp`

Counts

1 → 12

Calls

1 calls:

3.0ms

(sqrt (* (* 2.0 x) x))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(sqrt (* (* 2.0 x) x))

simplify98.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	33	45
1	60	43
2	86	43
3	100	43
4	119	43
5	173	43
6	600	43
7	1831	43
8	5001	43

prune35.0ms

Filtered

11 candidates to 15 candidates (-36.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Merged error: 0.2b

Counts

16 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* (* 2.0 x) x)))
0.5b	(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
29.6b	(sqrt (* (* 2.0 x) x))
29.6b	(sqrt (* (* 2.0 x) x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

158×	`pow1`
154×	`sqrt-pow1`
82×	`pow-prod-down`
33×	`sqrt-prod`
26×	`add-sqr-sqrt`
24×	`pow1/2`
21×	`pow-prod-up`
13×	`add-cube-cbrt` `*-un-lft-identity` `pow-sqr`
9×	`swap-sqr`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

4.0ms	(sqrt (sqrt (* (* 2.0 x) x)))
15.0ms	(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
3.0ms	(sqrt (* (* 2.0 x) x))
4.0ms	(sqrt (* (* 2.0 x) x))

series19.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (sqrt (* (* 2.0 x) x)))
4.0ms	(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
4.0ms	(sqrt (* (* 2.0 x) x))
7.0ms	(sqrt (* (* 2.0 x) x))

simplify40.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	213	559
1	889	517
2	5001	478

prune132.0ms

Filtered

61 candidates to 142 candidates (-132.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	142	5	147

Merged error: 0.2b

Counts

147 → 5

localize4.0ms

Local error

Found 1 expressions with local error:

0.5b	(* (sqrt 2.0) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-l`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

4.0ms

(* (sqrt 2.0) x)

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(* (sqrt 2.0) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	64	84
1	224	80
2	521	80
3	809	80
4	1933	80
5	5001	80

prune37.0ms

Filtered

15 candidates to 25 candidates (-66.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	23	7	30

Merged error: 0.1b

Counts

30 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cbrt (sqrt 2.0)) x)
0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`associate-l`
9×	`pow-prod-down` `prod-exp` `add-cbrt-cube` `cbrt-unprod`
8×	`cbrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `sqrt-prod`
3×	`unswap-sqr`
2×	`*-commutative` `add-log-exp`

Counts

2 → 48

Calls

2 calls:

5.0ms	(* (cbrt (sqrt 2.0)) x)
11.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) x))

series32.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(* (cbrt (sqrt 2.0)) x)
4.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) x))

simplify126.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	155	394
1	670	289
2	4049	252
3	5002	240

prune89.0ms

Filtered

32 candidates to 54 candidates (-68.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	3	3
Picked	0	1	1
Done	1	2	3
Total	53	8	61

Merged error: 0.1b

Counts

61 → 8

Details

analyze3.0ms

sample10.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite4.0ms

series4.0ms

simplify98.0ms

prune35.0ms

localize7.0ms

rewrite33.0ms

series19.0ms

simplify40.0ms

prune132.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify55.0ms

prune37.0ms

localize8.0ms

rewrite17.0ms

series32.0ms

simplify126.0ms

prune89.0ms

regimes205.0ms

bsearch2.0ms

Profiling