Details

sample95.0ms

Algorithm

intervals

Results

36.0ms	93×	body	1280	valid
19.0ms	76×	body	640	valid
14.0ms	237×	body	80	valid
6.0ms	36×	body	320	valid
3.0ms	25×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))
8.0ms	(/ (cos th) (sqrt 2.0))

series349.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
59.0ms	(/ (cos th) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	504	1284
1	2009	1156
2	5001	1136

prune457.0ms

Filtered

180 candidates to 116 candidates (64.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	167	13	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	13	181

Merged error: 0.0b

Counts

181 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-*l/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (cos th) (* a1 a1))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series333.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos th) (* a1 a1))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
110.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	501	987
1	2139	864
2	5002	850

prune312.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	146	11	157

Merged error: 0.0b

Counts

157 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 a2))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-*l/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (cos th) (* a2 a2))
8.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))

series530.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos th) (* a2 a2))
111.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
310.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	501	987
1	2125	864
2	5002	850

prune295.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	146	9	155

Merged error: 0.0b

Counts

155 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

256×	`sqrt-prod`
254×	`times-frac`
125×	`add-sqr-sqrt`
120×	`add-cube-cbrt` `*-un-lft-identity`
41×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
17×	`associate-/l*`
14×	`div-inv`
13×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

9.0ms	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2.0)))
15.0ms	(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
11.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt 2.0))

series445.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2.0)))
117.0ms	(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
108.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	914	3480
1	4153	2999
2	5002	2994

prune484.0ms

Filtered

289 candidates to 140 candidates (48.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	290	8	298

Merged error: 0b

Counts

298 → 8

regimes253.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	11
1	16	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

932.0ms	2498×	body	1280	valid
520.0ms	2036×	body	640	valid
494.0ms	8059×	body	80	valid
192.0ms	1055×	body	320	valid
67.0ms	538×	body	160	valid

Details

sample95.0ms

simplify16.0ms

prune6.0ms

localize12.0ms

rewrite39.0ms

series349.0ms

simplify55.0ms

prune457.0ms

localize13.0ms

rewrite33.0ms

series333.0ms

simplify53.0ms

prune312.0ms

localize13.0ms

rewrite33.0ms

series530.0ms

simplify54.0ms

prune295.0ms

localize20.0ms

rewrite54.0ms

series445.0ms

simplify106.0ms

prune484.0ms

regimes253.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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