Details

sample428.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.611328%

Guaranteed chance to sample good point: 91.755583%

Results

11.0ms	256×	body	80	valid
1.0ms	26×	body	80	invalid

simplify11.0ms

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: 6.6b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.1b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.5b	(* y (+ 1.0 (* z z)))

rewrite15.0ms

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:

8.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms	(* y (+ 1.0 (* z z)))

series25.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (10.0ms)

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

prune173.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 5.5b

Counts

77 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
2.1b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
17.0b	(sqrt (+ 1.0 (* z z)))
17.0b	(sqrt (+ 1.0 (* z z)))

rewrite31.0ms

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:

9.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
13.0ms	(/ (/ 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)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
19.0ms	(/ (/ 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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (54.0ms)

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

prune195.0ms

Filtered

93 candidates to 129 candidates (-38.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	129	7	136

Merged error: 5.5b

Counts

136 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* y (sqrt (+ 1.0 (* z z)))))
0.9b	(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))))
17.0b	(sqrt (+ 1.0 (* z z)))
17.0b	(sqrt (+ 1.0 (* z z)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
97×	`add-sqr-sqrt`
93×	`add-exp-log`
84×	`associate-r`
79×	`add-cube-cbrt` `*-un-lft-identity`
47×	`sqrt-prod`
45×	`add-cbrt-cube`
37×	`div-exp`
33×	`prod-exp`
17×	`cbrt-undiv`
13×	`cbrt-unprod`
11×	`pow1`
10×	`sqrt-div`
9×	`associate-l` `div-inv`
8×	`rec-exp` `1-exp`
6×	`associate-/r/`
5×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `pow-prod-down`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `*-commutative` `inv-pow`

Counts

4 → 200

Calls

4 calls:

6.0ms	(/ 1 (* y (sqrt (+ 1.0 (* z z)))))
34.0ms	(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))))
2.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(sqrt (+ 1.0 (* z z)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (* y (sqrt (+ 1.0 (* z z)))))
15.0ms	(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))))
7.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1133	2402
1	5002	2122

prune320.0ms

Filtered

126 candidates to 212 candidates (-68.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	213	6	219

Merged error: 5.5b

Counts

219 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1.0 x) (sqrt (+ 1.0 (* z z))))
0.8b	(/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) (* y (sqrt (+ 1.0 (* z z)))))
17.0b	(sqrt (+ 1.0 (* z z)))
17.0b	(sqrt (+ 1.0 (* z z)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

489×	`times-frac`
223×	`add-sqr-sqrt`
221×	`add-cube-cbrt` `*-un-lft-identity`
126×	`sqrt-prod`
97×	`associate-/l*`
30×	`add-exp-log` `add-cbrt-cube`
23×	`div-inv`
15×	`cbrt-undiv` `div-exp`
12×	`sqrt-div`
8×	`associate-/r/`
7×	`associate-/r*`
6×	`pow1` `flip3-+` `flip-+`
4×	`add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num` `associate-/l/`

Counts

4 → 338

Calls

4 calls:

8.0ms	(/ (/ 1.0 x) (sqrt (+ 1.0 (* z z))))
23.0ms	(/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) (* y (sqrt (+ 1.0 (* z z)))))
2.0ms	(sqrt (+ 1.0 (* z z)))
3.0ms	(sqrt (+ 1.0 (* z z)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (/ 1.0 x) (sqrt (+ 1.0 (* z z))))
16.0ms	(/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

simplify130.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1153	4419
1	4729	4002
2	5002	4002

prune724.0ms

Filtered

245 candidates to 350 candidates (-42.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	350	6	356

Merged error: 5.5b

Counts

356 → 6

regimes430.0ms

Accuracy

0% (1.1b remaining)

Error of 5.9b against oracle of 4.8b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	10
1	13	10

end0.0ms

sample951.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 1.611328%

Guaranteed chance to sample good point: 91.755583%

Results

278.0ms	8000×	body	80	valid
18.0ms	463×	body	80	invalid

Details

sample428.0ms

simplify11.0ms

prune3.0ms

localize7.0ms

rewrite15.0ms

series25.0ms

simplify46.0ms

prune173.0ms

localize9.0ms

rewrite31.0ms

series35.0ms

simplify67.0ms

prune195.0ms

localize13.0ms

rewrite54.0ms

series39.0ms

simplify47.0ms

prune320.0ms

localize9.0ms

rewrite58.0ms

series38.0ms

simplify130.0ms

prune724.0ms

regimes430.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample951.0ms

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