Details

analyze1.1s

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	96.7%	3.3%	9
16.4%	74.9%	8.7%	10
17.6%	71.8%	10.7%	11
26.3%	59.5%	14.2%	12
30.7%	45.7%	23.5%	13
31.7%	43.5%	24.7%	14

sample42.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
9.0ms	125×	body	80	invalid

simplify441.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5486	25

prune27.0ms

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: 6.2b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
5.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
5.3b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
8.6b	(.f64 r (.f64 w w))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

109×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
44×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64`
18×	`difference-of-squares_binary64`
17×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`div-inv_binary64`
9×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `associate-*r/_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 177

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
21.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
8.0ms	(.f64 r (.f64 w w))

series68.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
15.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
23.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
17.0ms	(.f64 r (.f64 w w))

simplify48.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4971	2755
1	4971	2755

prune255.0ms

Filtered

128 candidates to 189 candidates (-47.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	182	7	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	7	191

Merged error: 2.1b

Counts

191 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (*.f64 r r))
1.4b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
5.3b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
45×	`add-cube-cbrt_binary64`
35×	`associate-r_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
18×	`difference-of-squares_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r_binary64` `associate-/l_binary64`
11×	`div-inv_binary64`
9×	`distribute-lft-out--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 179

Calls

4 calls:

5.0ms	(/.f64 2 (*.f64 r r))
10.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
21.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 2 (*.f64 r r))
14.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
15.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
25.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))

simplify51.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5516	2821

prune276.0ms

Filtered

137 candidates to 191 candidates (-39.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	188	10	198

Merged error: 0.0b

Counts

198 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (-.f64 1 v))
0.7b	(/.f64 2 (*.f64 r r))
2.1b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

205×	`times-frac_binary64`
146×	`add-sqr-sqrt_binary64`
144×	`*-un-lft-identity_binary64`
105×	`add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
32×	`associate-/r*_binary64` `add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
26×	`difference-of-squares_binary64`
14×	`cbrt-div_binary64`
13×	`associate-r_binary64` `distribute-lft-out--_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
9×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
7×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
6×	`pow1_binary64` `associate-/l*_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 220

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 1 v))
5.0ms	(/.f64 2 (*.f64 r r))
12.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
20.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cbrt.f64 (-.f64 1 v))
3.0ms	(/.f64 2 (*.f64 r r))
20.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
30.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4936	3683
1	4936	3683

prune455.0ms

Filtered

174 candidates to 232 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	232	10	242

Merged error: 0.0b

Counts

242 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
1.2b	(/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w)))
1.6b	(.f64 (.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (.f64 r w)))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
6.0b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

737×	`times-frac_binary64`
465×	`add-sqr-sqrt_binary64`
461×	`*-un-lft-identity_binary64`
423×	`cbrt-prod_binary64`
344×	`add-cube-cbrt_binary64`
337×	`add-exp-log_binary64`
208×	`add-cbrt-cube_binary64`
201×	`associate-r_binary64`
145×	`cbrt-unprod_binary64` `prod-exp_binary64`
129×	`cbrt-undiv_binary64` `div-exp_binary64`
78×	`difference-of-squares_binary64`
39×	`distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
20×	`div-inv_binary64`
11×	`pow1_binary64` `frac-times_binary64` `associate-*l/_binary64`
7×	`associate-/l*_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-r/_binary64` `associate-/r/_binary64` `associate-l*_binary64`
2×	`unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 616

Calls

4 calls:

18.0ms	(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
17.0ms	(/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w)))
60.0ms	(.f64 (.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (.f64 r w)))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
22.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
56.0ms	(/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w)))
28.0ms	(.f64 (.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (.f64 r w)))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
67.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))))

simplify131.0ms

Algorithm

egg-herbie

Counts

628 → 628

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5390	17422

prune2.2s

Filtered

470 candidates to 628 candidates (-33.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	628	0	628
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	628	10	638

Merged error: 0.0b

Counts

638 → 10

regimes285.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	36
1	129	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

540.0ms	8000×	body	80	valid
324.0ms	4863×	body	80	invalid

Details

analyze1.1s

sample42.0ms

simplify441.0ms

prune27.0ms

localize18.0ms

rewrite66.0ms

series68.0ms

simplify48.0ms

prune255.0ms

localize16.0ms

rewrite55.0ms

series57.0ms

simplify51.0ms

prune276.0ms

localize21.0ms

rewrite56.0ms

series59.0ms

simplify74.0ms

prune455.0ms

localize24.0ms

rewrite167.0ms

series188.0ms

simplify131.0ms

prune2.2s

regimes285.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling