Details

sample85.0ms

Algorithm

intervals

Results

29.0ms	79×	body	1280	valid
16.0ms	65×	body	640	valid
14.0ms	233×	body	80	valid
7.0ms	39×	body	320	valid
2.0ms	18×	body	160	valid

simplify17.0ms

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

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.5b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

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

series367.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
125.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
59.0ms	(/ (cos th) (sqrt 2.0))
67.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (42.0ms)

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

prune667.0ms

Filtered

180 candidates to 116 candidates (64.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	12	182

Merged error: 0b

Counts

182 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 a2))
0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite32.0ms

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:

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

series332.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos th) (* a2 a2))
110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
112.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (45.0ms)

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

prune299.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	145	11	156

Merged error: 0b

Counts

156 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) a2) a2)
0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (* (* (cos th) a2) a2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

5.0ms	(* (* (cos th) a2) a2)
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
7.0ms	(/ (* (* (cos th) a2) a2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series331.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* (cos th) a2) a2)
112.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
112.0ms	(/ (* (* (cos th) a2) a2) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	514	978
1	2569	857
2	5001	844

prune296.0ms

Filtered

143 candidates to 89 candidates (62.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Merged error: 0b

Counts

154 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (pow a2 2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
121×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
53×	`associate-r`
41×	`unpow-prod-down`
33×	`add-exp-log`
25×	`associate-l` `add-cbrt-cube`
15×	`unpow2` `sqr-pow`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1` `associate-/l*`
10×	`prod-exp`
9×	`div-exp`
8×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 240

Calls

4 calls:

16.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
6.0ms	(/ (pow a2 2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series352.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
113.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
65.0ms	(/ (pow a2 2) (sqrt 2.0))
59.0ms	(/ (cos th) (sqrt 2.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	693	1786
1	3017	1552
2	5001	1540

prune478.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	253	10	263

Merged error: 0b

Counts

263 → 10

regimes317.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	11
1	17	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

963.0ms	2562×	body	1280	valid
540.0ms	2079×	body	640	valid
506.0ms	7993×	body	80	valid
206.0ms	1065×	body	320	valid
71.0ms	537×	body	160	valid

Details

sample85.0ms

simplify17.0ms

prune8.0ms

localize17.0ms

rewrite34.0ms

series367.0ms

simplify55.0ms

prune667.0ms

localize13.0ms

rewrite32.0ms

series332.0ms

simplify56.0ms

prune299.0ms

localize13.0ms

rewrite30.0ms

series331.0ms

simplify67.0ms

prune296.0ms

localize14.0ms

rewrite49.0ms

series352.0ms

simplify89.0ms

prune478.0ms

regimes317.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

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