Details

analyze79.0ms

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

sample18.0ms

Algorithm

intervals

Results

6.0ms	200×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	13×	body	160	valid

simplify157.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	5619	11

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 22.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) y)
3.8b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
8.7b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-/r_binary64` `difference-of-squares_binary64` `times-frac_binary64` `associate-l/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

3 → 64

Calls

3 calls:

7.0ms	(*.f64 (-.f64 1 x) y)
8.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

series23.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(*.f64 (-.f64 1 x) y)
11.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
8.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

simplify42.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5649	730

prune104.0ms

Filtered

53 candidates to 73 candidates (-37.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Merged error: 0.3b

Counts

74 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 1 y) y)
0.3b	(/.f64 (-.f64 1 x) (/.f64 (+.f64 1 y) y))
3.8b	(-.f64 1 (/.f64 (-.f64 1 x) (/.f64 (+.f64 1 y) y)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac_binary64`
191×	`*-un-lft-identity_binary64`
151×	`add-sqr-sqrt_binary64`
85×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`
25×	`distribute-lft-out_binary64`
19×	`associate-/r*_binary64`
18×	`distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
9×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`flip3--_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate--r-_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

3 → 188

Calls

3 calls:

6.0ms	(/.f64 (+.f64 1 y) y)
13.0ms	(/.f64 (-.f64 1 x) (/.f64 (+.f64 1 y) y))
36.0ms	(-.f64 1 (/.f64 (-.f64 1 x) (/.f64 (+.f64 1 y) y)))

series26.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/.f64 (+.f64 1 y) y)
7.0ms	(/.f64 (-.f64 1 x) (/.f64 (+.f64 1 y) y))
11.0ms	(-.f64 1 (/.f64 (-.f64 1 x) (/.f64 (+.f64 1 y) y)))

simplify65.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5235	3078

prune165.0ms

Filtered

118 candidates to 197 candidates (-66.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	197	5	202

Merged error: 0.3b

Counts

202 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y))))
0.1b	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y)))
0.1b	(/.f64 y (sqrt.f64 (+.f64 1 y)))
5.0b	(-.f64 1 (*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

161×	`*-un-lft-identity_binary64`
151×	`add-sqr-sqrt_binary64`
138×	`times-frac_binary64`
86×	`sqrt-prod_binary64`
76×	`add-cube-cbrt_binary64`
48×	`associate-l_binary64`
30×	`difference-of-squares_binary64`
27×	`associate-r_binary64`
20×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`distribute-lft-out--_binary64`
14×	`associate-/r*_binary64`
9×	`unswap-sqr_binary64` `associate-/l*_binary64`
8×	`associate-/r/_binary64` `sqrt-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `div-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 232

Calls

4 calls:

39.0ms	(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y))))
10.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y)))
6.0ms	(/.f64 y (sqrt.f64 (+.f64 1 y)))
4.0ms	(-.f64 1 (*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y))))
9.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y)))
8.0ms	(/.f64 y (sqrt.f64 (+.f64 1 y)))
11.0ms	(-.f64 1 (*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5113	3486

prune236.0ms

Filtered

144 candidates to 244 candidates (-69.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	244	5	249

Merged error: 0.3b

Counts

249 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

8.7b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
8.7b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
8.7b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
11.8b	(/.f64 (-.f64 1 (.f64 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)) (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)))) (+.f64 1 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-/r*_binary64`
12×	`distribute-lft-out_binary64`
10×	`difference-of-squares_binary64`
8×	`associate-/l/_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-*l/_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`
1×	`div-sub_binary64`

Counts

4 → 127

Calls

4 calls:

10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
13.0ms	(/.f64 (-.f64 1 (.f64 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)) (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)))) (+.f64 1 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
7.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
7.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 1 y))
82.0ms	(/.f64 (-.f64 1 (.f64 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)) (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y)))) (+.f64 1 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 1 y))))

simplify60.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5973	2539

prune198.0ms

Filtered

101 candidates to 139 candidates (-37.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	139	5	144

Merged error: 0.3b

Counts

144 → 5

regimes167.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 13.9b

bsearch30.0ms

Steps

Iters	Range		Point
7	7004858.354069281	570932256.8256192	153067620.3959889
10	-1063262642075101.2	-20041.8651071721	-198093045.25882047

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	29
1	116	29

end0.0ms

sample519.0ms

Algorithm

intervals

Results

189.0ms	6152×	body	80	valid
82.0ms	696×	body	640	valid
52.0ms	350×	body	1280	valid
44.0ms	495×	body	320	valid
18.0ms	307×	body	160	valid

Details

analyze79.0ms

sample18.0ms

simplify157.0ms

prune5.0ms

localize11.0ms

rewrite27.0ms

series23.0ms

simplify42.0ms

prune104.0ms

localize7.0ms

rewrite65.0ms

series26.0ms

simplify65.0ms

prune165.0ms

localize9.0ms

rewrite71.0ms

series35.0ms

simplify54.0ms

prune236.0ms

localize11.0ms

rewrite48.0ms

series102.0ms

simplify60.0ms

prune198.0ms

regimes167.0ms

bsearch30.0ms

simplify3.0ms

end0.0ms

sample519.0ms

Profiling