Details

analyze227.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

sample31.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
0.0ms	6×	body	80	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5079	29

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.9b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.6b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.6b	(-.f64 (.f64 b b) (.f64 a a))
9.7b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
132×	`*-un-lft-identity_binary64`
100×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`
46×	`difference-of-squares_binary64`
19×	`associate-r_binary64` `div-inv_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
4×	`associate-/r*_binary64` `sub-neg_binary64` `associate-/r/_binary64`
3×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-sub_binary64` `frac-times_binary64`
2×	`diff-log_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
46.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
36.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
22.0ms	(-.f64 (.f64 b b) (.f64 a a))
56.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

simplify108.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5686	6717

prune934.0ms

Filtered

198 candidates to 242 candidates (-22.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	231	11	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	233	11	244

Merged error: 0.0b

Counts

244 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
0.3b	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

280×	`times-frac_binary64`
233×	`add-sqr-sqrt_binary64`
214×	`*-un-lft-identity_binary64`
122×	`add-cube-cbrt_binary64`
72×	`associate-r_binary64`
64×	`add-exp-log_binary64`
50×	`add-cbrt-cube_binary64`
45×	`difference-of-squares_binary64`
41×	`distribute-lft-out--_binary64`
37×	`associate-l_binary64`
24×	`prod-exp_binary64`
22×	`div-inv_binary64`
19×	`div-exp_binary64`
17×	`cbrt-unprod_binary64`
16×	`cbrt-undiv_binary64` `frac-times_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
10×	`associate-r/_binary64` `associate-l/_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`frac-sub_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `rec-exp_binary64`
3×	`distribute-lft-out_binary64` `unswap-sqr_binary64`
2×	`*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 307

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
8.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
32.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
50.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
34.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
51.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
33.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))

simplify129.0ms

Algorithm

egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5140	8195

prune1.1s

Filtered

224 candidates to 319 candidates (-42.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	313	6	319
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	321	9	330

Merged error: 0.0b

Counts

330 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(/.f64 (/.f64 (*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 a b)) (-.f64 b a))
0.2b	(/.f64 (*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 a b))
0.4b	(*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac_binary64`
116×	`add-sqr-sqrt_binary64`
111×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
29×	`difference-of-squares_binary64`
25×	`distribute-lft-out--_binary64`
19×	`associate-r_binary64`
17×	`div-inv_binary64`
16×	`associate-/r/_binary64`
13×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
11×	`associate-/l*_binary64`
9×	`associate-/r*_binary64`
8×	`associate-/l/_binary64` `distribute-lft-out_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64`
5×	`frac-sub_binary64`
3×	`sub-neg_binary64`
2×	`unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `*-commutative_binary64`

Counts

4 → 204

Calls

4 calls:

16.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
26.0ms	(/.f64 (/.f64 (*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 a b)) (-.f64 b a))
22.0ms	(/.f64 (*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 a b))
30.0ms	(*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
46.0ms	(/.f64 (/.f64 (*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 a b)) (-.f64 b a))
50.0ms	(/.f64 (*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 a b))
26.0ms	(*.f64 (/.f64 PI.f64 2) (-.f64 (/.f64 1 a) (/.f64 1 b)))

simplify97.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5081	6073

prune689.0ms

Filtered

154 candidates to 216 candidates (-40.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	216	9	225

Merged error: 0.0b

Counts

225 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(/.f64 (*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 b a)) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 b a))
0.2b	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
0.3b	(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 b a)) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

272×	`times-frac_binary64`
227×	`add-sqr-sqrt_binary64`
206×	`*-un-lft-identity_binary64`
116×	`add-cube-cbrt_binary64`
71×	`associate-l_binary64`
45×	`difference-of-squares_binary64`
41×	`distribute-lft-out--_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`div-inv_binary64`
19×	`associate-r_binary64`
14×	`associate-/l*_binary64`
13×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`associate-/r*_binary64`
8×	`associate-/l/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `prod-exp_binary64` `frac-times_binary64`
5×	`frac-sub_binary64`
3×	`sub-neg_binary64` `unswap-sqr_binary64`
2×	`distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 281

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
31.0ms	(/.f64 (*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 b a)) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 b a))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
49.0ms	(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 b a)) (-.f64 (/.f64 1 a) (/.f64 1 b)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
51.0ms	(/.f64 (*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 b a)) (-.f64 (/.f64 1 a) (/.f64 1 b))) (+.f64 b a))
31.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
37.0ms	(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 b a)) (-.f64 (/.f64 1 a) (/.f64 1 b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5003	7146

prune1.1s

Filtered

215 candidates to 293 candidates (-36.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	293	9	302

Merged error: 0.0b

Counts

302 → 9

regimes213.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms

sample679.0ms

Algorithm

intervals

Results

466.0ms	8000×	body	80	valid
22.0ms	378×	body	80	invalid

Details

analyze227.0ms

sample31.0ms

simplify52.0ms

prune19.0ms

localize21.0ms

rewrite85.0ms

series124.0ms

simplify108.0ms

prune934.0ms

localize23.0ms

rewrite125.0ms

series127.0ms

simplify129.0ms

prune1.1s

localize21.0ms

rewrite104.0ms

series132.0ms

simplify97.0ms

prune689.0ms

localize20.0ms

rewrite118.0ms

series128.0ms

simplify112.0ms

prune1.1s

regimes213.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample679.0ms

Profiling