Details

analyze230.0ms

Algorithm: search

sample17.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
0.0ms	11×	body	80	invalid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	5
1	37	5
2	61	5
3	91	5
4	115	5
5	121	5
6	121	5

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: 5.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

3.2b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.3b	(* y (+ 1.0 (* z z)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `unswap-sqr`

Counts

2 → 70

Calls

2 calls:

7.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms	(* y (+ 1.0 (* z z)))

series28.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
9.0ms	(* y (+ 1.0 (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	409	511
1	1963	443
2	5001	443

prune120.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 4.3b

Counts

77 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.2b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
13.6b	(sqrt (+ 1.0 (* z z)))
13.6b	(sqrt (+ 1.0 (* z z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
8×	`frac-times` `associate-/r/`
6×	`associate-r`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

11.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
12.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
2.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(sqrt (+ 1.0 (* z z)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
16.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
3.0ms	(sqrt (+ 1.0 (* z z)))

simplify66.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	610	1242
1	2886	1023
2	5002	1005

prune194.0ms

Filtered

93 candidates to 129 candidates (-38.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	129	8	137

Merged error: 4.3b

Counts

137 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
2.8b	(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
13.6b	(sqrt (+ 1.0 (* z z)))
13.6b	(sqrt (+ 1.0 (* z z)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

299×	`times-frac`
118×	`add-sqr-sqrt`
116×	`add-cube-cbrt` `*-un-lft-identity`
66×	`sqrt-prod`
34×	`add-exp-log` `add-cbrt-cube`
32×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/` `div-inv`
17×	`cbrt-undiv` `div-exp`
16×	`associate-*r/`
11×	`flip3-+` `flip-+`
7×	`associate-/r*`
6×	`pow1`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

14.0ms	(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
8.0ms	(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
2.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(sqrt (+ 1.0 (* z z)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
27.0ms	(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

simplify104.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	963	3413
1	4085	3172
2	5002	3077

prune424.0ms

Filtered

175 candidates to 252 candidates (-44.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	253	7	260

Merged error: 4.3b

Counts

260 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (/ 1.0 (* (* y (sqrt (+ 1.0 (* z z)))) x)) (sqrt (+ 1.0 (* z z))))
2.7b	(* (* y (sqrt (+ 1.0 (* z z)))) x)
13.6b	(sqrt (+ 1.0 (* z z)))
13.6b	(sqrt (+ 1.0 (* z z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
43×	`add-sqr-sqrt`
41×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqrt-prod`
23×	`add-exp-log` `add-cbrt-cube`
22×	`sqrt-div`
16×	`associate-r/` `associate-l/` `associate-/r/`
11×	`pow1` `flip3-+` `flip-+`
9×	`associate-/l*`
8×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `associate-/r*` `cbrt-unprod`
4×	`add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

12.0ms	(/ (/ 1.0 (* (* y (sqrt (+ 1.0 (* z z)))) x)) (sqrt (+ 1.0 (* z z))))
6.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) x)
2.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(sqrt (+ 1.0 (* z z)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (/ 1.0 (* (* y (sqrt (+ 1.0 (* z z)))) x)) (sqrt (+ 1.0 (* z z))))
13.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) x)
5.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

simplify78.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	650	1944
1	3056	1804
2	5001	1737

prune236.0ms

Filtered

107 candidates to 152 candidates (-42.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	152	7	159

Merged error: 4.3b

Counts

159 → 7

regimes441.0ms

Accuracy

0% (1.5b remaining)

Error of 6.3b against oracle of 4.8b and baseline of 6.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

analyze229.0ms

Algorithm: search

sample448.0ms

Algorithm

intervals

Results

276.0ms	8000×	body	80	valid
14.0ms	417×	body	80	invalid

Details

analyze230.0ms

sample17.0ms

simplify12.0ms

prune3.0ms

localize8.0ms

rewrite14.0ms

series28.0ms

simplify47.0ms

prune120.0ms

localize9.0ms

rewrite32.0ms

series32.0ms

simplify66.0ms

prune194.0ms

localize9.0ms

rewrite38.0ms

series51.0ms

simplify104.0ms

prune424.0ms

localize10.0ms

rewrite28.0ms

series39.0ms

simplify78.0ms

prune236.0ms

regimes441.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze229.0ms

sample448.0ms

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