Details

analyze327.0ms

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	69×	body	80	nan
1.0ms	28×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

prune3.0ms

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: 27.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (sqrt (- (* y y) (* z z))))
2.8b	(- (* y y) (* z z))
27.1b	(sqrt (- (* y y) (* z z)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-l` `flip--` `difference-of-squares`
2×	`associate-*r/` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 53

Calls

3 calls:

7.0ms	(* x (sqrt (- (* y y) (* z z))))
3.0ms	(- (* y y) (* z z))
3.0ms	(sqrt (- (* y y) (* z z)))

series31.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* x (sqrt (- (* y y) (* z z))))
6.0ms	(- (* y y) (* z z))
8.0ms	(sqrt (- (* y y) (* z z)))

simplify49.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4944	609
1	4944	609

prune77.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	4	63

Merged error: 0.3b

Counts

63 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* y y) (* z z))
2.8b	(- (* y y) (* z z))
27.1b	(sqrt (- (* y y) (* z z)))
27.1b	(sqrt (- (* y y) (* z z)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 56

Calls

4 calls:

5.0ms	(- (* y y) (* z z))
3.0ms	(- (* y y) (* z z))
4.0ms	(sqrt (- (* y y) (* z z)))
4.0ms	(sqrt (- (* y y) (* z z)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* y y) (* z z))
9.0ms	(- (* y y) (* z z))
11.0ms	(sqrt (- (* y y) (* z z)))
12.0ms	(sqrt (- (* y y) (* z z)))

simplify40.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5467	632

prune145.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	68	4	72

Merged error: 0.3b

Counts

72 → 4

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Merged error: 0.3b

Counts

4 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
0.0b	(sqrt (+ y z))
0.0b	(sqrt (- y z))
0.2b	(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-div`
25×	`add-sqr-sqrt`
22×	`sqrt-prod`
19×	`*-un-lft-identity`
15×	`pow1`
12×	`associate-*r/`
11×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
10×	`associate-l`
9×	`associate-r`
8×	`frac-times`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow-prod-down`
4×	`sqrt-pow1` `pow1/2` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `*-commutative` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`sqrt-unprod`

Counts

4 → 100

Calls

4 calls:

11.0ms	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
3.0ms	(sqrt (+ y z))
3.0ms	(sqrt (- y z))
11.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
6.0ms	(sqrt (+ y z))
9.0ms	(sqrt (- y z))
13.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

simplify27.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5029	1223

prune94.0ms

Filtered

83 candidates to 112 candidates (-34.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	112	4	116

Merged error: 0.3b

Counts

116 → 4

Details

analyze327.0ms

sample22.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite15.0ms

series31.0ms

simplify49.0ms

prune77.0ms

localize9.0ms

rewrite17.0ms

series42.0ms

simplify40.0ms

prune145.0ms

localize2.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune6.0ms

localize8.0ms

rewrite34.0ms

series51.0ms

simplify27.0ms

prune94.0ms

regimes400.0ms

bsearch38.0ms

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