Details

analyze116.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

prune5.0ms

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: 19.8b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

18.5b

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

rewrite7.0ms

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:

6.0ms

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

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify54.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4926	159
1	4926	159

prune31.0ms

Filtered

15 candidates to 18 candidates (-20.0%)

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)
18.5b	(sqrt (+ (* x x) y))
35.6b	(cbrt (pow (sqrt (+ (* x x) y)) 3))

rewrite18.0ms

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

series18.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4937	843
1	4937	843

prune78.0ms

Filtered

50 candidates to 87 candidates (-74.0%)

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

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (/ 1/2 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

(* y (/ 1/2 x))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* y (/ 1/2 x))

simplify50.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4960	229
1	4960	229

prune37.0ms

Filtered

24 candidates to 35 candidates (-45.8%)

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

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (/ -1/2 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

(* y (/ -1/2 x))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* y (/ -1/2 x))

simplify62.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5360	230

prune35.0ms

Filtered

24 candidates to 35 candidates (-45.8%)

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

regimes307.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 22.1b

bsearch24.0ms

Steps

Iters	Range		Point
8	1.4725895273564852e+112	5.644838682764314e+115	4.8205033805583175e+115
10	-2.516589151443666e+163	-5.233887043482204e+153	-1.3351570324639047e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms

sample334.0ms

Algorithm

intervals

Results

200.0ms	8000×	body	80	valid
3.0ms	143×	body	80	nan

Details

analyze116.0ms

sample23.0ms

simplify4.0ms

prune5.0ms

localize7.0ms

rewrite7.0ms

series9.0ms

simplify54.0ms

prune31.0ms

localize8.0ms

rewrite18.0ms

series18.0ms

simplify58.0ms

prune78.0ms

localize4.0ms

rewrite8.0ms

series3.0ms

simplify50.0ms

prune37.0ms

localize4.0ms

rewrite8.0ms

series3.0ms

simplify62.0ms

prune35.0ms

regimes307.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample334.0ms

Profiling