Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample11.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	6
1	10	6

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 30.3b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

29.1b

(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))

simplify108.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4675	80
1	4675	80

prune40.0ms

Filtered

11 candidates to 15 candidates (-36.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	9	6	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	9	7	16

Merged error: 0.2b

Counts

16 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (* 2.0 (* x x))))
0.5b	(* (sqrt (sqrt (* 2.0 (* x x)))) (sqrt (sqrt (* 2.0 (* x x)))))
29.1b	(sqrt (* 2.0 (* x x)))
29.1b	(sqrt (* 2.0 (* x x)))

rewrite35.0ms

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:

5.0ms	(sqrt (sqrt (* 2.0 (* x x))))
16.0ms	(* (sqrt (sqrt (* 2.0 (* x x)))) (sqrt (sqrt (* 2.0 (* x x)))))
4.0ms	(sqrt (* 2.0 (* x x)))
4.0ms	(sqrt (* 2.0 (* x x)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(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)))
4.0ms	(sqrt (* 2.0 (* x x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4936	775
1	4936	775

prune171.0ms

Filtered

66 candidates to 142 candidates (-115.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	140	9	149

Merged error: 0.1b

Counts

149 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (fabs (* x (sqrt 2.0))))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (fabs (* x (sqrt 2.0)))) (sqrt (fabs x))))
0.4b	(* (sqrt (fabs (* x (sqrt 2.0)))) (sqrt (fabs x)))
0.5b	(* x (sqrt 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`sqrt-prod`
19×	`pow1`
18×	`associate-l`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
11×	`pow-prod-down`
6×	`sqrt-pow1` `pow1/2` `unswap-sqr`
5×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`sqrt-unprod` `*-commutative`
1×	`rem-sqrt-square`

Counts

4 → 92

Calls

4 calls:

1.0ms	(sqrt (fabs (* x (sqrt 2.0))))
9.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (fabs (* x (sqrt 2.0)))) (sqrt (fabs x))))
6.0ms	(* (sqrt (fabs (* x (sqrt 2.0)))) (sqrt (fabs x)))
5.0ms	(* x (sqrt 2.0))

series25.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (fabs (* x (sqrt 2.0))))
11.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (fabs (* x (sqrt 2.0)))) (sqrt (fabs x))))
7.0ms	(* (sqrt (fabs (* x (sqrt 2.0)))) (sqrt (fabs x)))
4.0ms	(* x (sqrt 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4965	1063
1	4965	1063

prune195.0ms

Filtered

61 candidates to 104 candidates (-70.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	103	10	113

Merged error: 0.0b

Counts

113 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (fabs (* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))) (sqrt (fabs x))))
0.3b	(* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.4b	(* (sqrt (fabs (* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))) (sqrt (fabs x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
25×	`add-exp-log`
24×	`add-sqr-sqrt`
22×	`sqrt-prod`
19×	`associate-l` `pow-prod-down`
18×	`add-cbrt-cube`
17×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`prod-exp` `cbrt-unprod`
6×	`cbrt-prod`
5×	`sqrt-pow1` `pow1/2` `unswap-sqr`
4×	`*-commutative` `add-log-exp`
3×	`sqrt-unprod`

Counts

4 → 103

Calls

4 calls:

8.0ms	(* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
9.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (fabs (* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))) (sqrt (fabs x))))
14.0ms	(* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
6.0ms	(* (sqrt (fabs (* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))) (sqrt (fabs x)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
11.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (fabs (* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))) (sqrt (fabs x))))
4.0ms	(* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
7.0ms	(* (sqrt (fabs (* (* x (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))) (sqrt (fabs x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5058	1107

prune201.0ms

Filtered

70 candidates to 115 candidates (-64.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	116	9	125

Merged error: 0.0b

Counts

125 → 9

regimes155.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	18	23

end0.0ms

sample260.0ms

Algorithm

intervals

Results

177.0ms	8000×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze3.0ms

sample11.0ms

simplify2.0ms

prune4.0ms

localize4.0ms

rewrite4.0ms

series4.0ms

simplify108.0ms

prune40.0ms

localize7.0ms

rewrite35.0ms

series20.0ms

simplify43.0ms

prune171.0ms

localize11.0ms

rewrite24.0ms

series25.0ms

simplify56.0ms

prune195.0ms

localize14.0ms

rewrite40.0ms

series55.0ms

simplify60.0ms

prune201.0ms

regimes155.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample260.0ms

Profiling