Details

sample76.0ms

Algorithm

intervals

Results

26.0ms	83×	body	1280	valid
15.0ms	70×	body	640	valid
12.0ms	245×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	19×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (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))

rewrite40.0ms

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

series347.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
56.0ms	(/ (cos th) (sqrt 2.0))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

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

prune494.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) a1)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 165

Calls

4 calls:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
12.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
101.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
57.0ms	(/ (cos th) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	444	1207
1	1802	1104
2	5001	1084

prune493.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (/ a1 (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b	(/ a1 (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`sqrt-prod`
25×	`add-exp-log` `associate-l` `add-cbrt-cube`
23×	`associate-r`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 165

Calls

4 calls:

9.0ms	(* (cos th) (/ a1 (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ a1 (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series332.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cos th) (/ a1 (sqrt 2.0)))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
58.0ms	(/ a1 (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	516	1140
1	2223	1043
2	5001	1018

prune474.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
640×	`add-sqr-sqrt`
593×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube`
13×	`unswap-sqr`
8×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 739

Calls

4 calls:

50.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
21.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series326.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify142.0ms

Algorithm

egg-herbie

Counts

751 → 751

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1319	9484
1	4967	8360
2	5001	8360

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes260.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	15
1	19	15

end0.0ms

sample2.4s

Algorithm

intervals

Results

818.0ms	2508×	body	1280	valid
598.0ms	8067×	body	80	valid
447.0ms	2039×	body	640	valid
175.0ms	1110×	body	320	valid
57.0ms	547×	body	160	valid