Details

sample17.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	91×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 22.3b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

20.8b

(sqrt (+ (* x x) y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

4.0ms

(sqrt (+ (* x x) y))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(sqrt (+ (* x x) y))

simplify139.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	116	95
1	334	90
2	997	89
3	3969	87
4	5002	87

prune40.0ms

Filtered

18 candidates to 15 candidates (83.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Merged error: 0b

Counts

19 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow (sqrt (+ (* x x) y)) 3)
20.8b	(sqrt (+ (* x x) y))
37.8b	(cbrt (pow (sqrt (+ (* x x) y)) 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
15×	`add-sqr-sqrt` `sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `cube-div` `add-cbrt-cube`
3×	`pow-unpow` `pow-pow` `flip3-+` `flip-+` `add-log-exp`
2×	`cube-mult` `cbrt-div` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 78

Calls

3 calls:

6.0ms	(pow (sqrt (+ (* x x) y)) 3)
4.0ms	(sqrt (+ (* x x) y))
7.0ms	(cbrt (pow (sqrt (+ (* x x) y)) 3))

series127.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(pow (sqrt (+ (* x x) y)) 3)
45.0ms	(sqrt (+ (* x x) y))
40.0ms	(cbrt (pow (sqrt (+ (* x x) y)) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	276	487
1	952	459
2	5001	446

prune119.0ms

Filtered

87 candidates to 48 candidates (55.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0b

Counts

91 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 1/2 (/ y x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

7.0ms

(* 1/2 (/ y x))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(* 1/2 (/ y x))

simplify64.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	164	128
1	727	118
2	2966	118
3	5001	118

prune44.0ms

Filtered

35 candidates to 24 candidates (68.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	35	4	39

Merged error: 0b

Counts

39 → 4

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 1/2 (/ y x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

7.0ms

(* 1/2 (/ y x))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(* 1/2 (/ y x))

simplify64.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	164	128
1	727	118
2	2966	118
3	5001	118

prune44.0ms

Filtered

35 candidates to 24 candidates (68.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	35	4	39

Merged error: 0b

Counts

39 → 4

regimes148.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.5b

bsearch43.0ms

Steps

Iters	Range		Point
4	4.5418805312590315e+84	8.493915305067446e+84	8.26951437345956e+84
10	-4.1653256596649633e+164	-6.188077678441323e+152	-1.334087264880127e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	10
1	29	10
2	31	10
3	31	10

end0.0ms

sample436.0ms

Algorithm

intervals

Results

207.0ms	8000×	body	80	valid
62.0ms	2695×	body	80	nan

Details

sample17.0ms

simplify4.0ms

prune2.0ms

localize7.0ms

rewrite5.0ms

series40.0ms

simplify139.0ms

prune40.0ms

localize8.0ms

rewrite20.0ms

series127.0ms

simplify43.0ms

prune119.0ms

localize5.0ms

rewrite9.0ms

series21.0ms

simplify64.0ms

prune44.0ms

localize9.0ms

rewrite8.0ms

series17.0ms

simplify64.0ms

prune44.0ms

regimes148.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

sample436.0ms

Profiling