Details

analyze74.0ms

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

sample19.0ms

Algorithm

intervals

Results

6.0ms	195×	body	80	valid
2.0ms	18×	body	1280	valid
2.0ms	20×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	7×	body	160	valid

simplify297.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (294.0ms)

Iter	Nodes	Cost
0	5206	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: 21.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.7b	(-.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0)))
7.0b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

8.0ms	(-.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0)))
9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0))

series24.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(-.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0)))
9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5160	570

prune75.0ms

Filtered

36 candidates to 46 candidates (-27.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	41	5	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	5	47

Merged error: 0.1b

Counts

47 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 y (+.f64 1.0 y))
2.7b	(-.f64 1.0 (*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`pow1_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(/.f64 y (+.f64 1.0 y))
4.0ms	(-.f64 1.0 (*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y))))

series18.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/.f64 y (+.f64 1.0 y))
15.0ms	(-.f64 1.0 (*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y))))

simplify53.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5225	537

prune57.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Merged error: 0.1b

Counts

55 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y)))
0.1b	(*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y))))
0.1b	(/.f64 y (sqrt.f64 (+.f64 1.0 y)))
6.1b	(-.f64 1.0 (*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity_binary64`
132×	`add-sqr-sqrt_binary64`
124×	`times-frac_binary64`
78×	`sqrt-prod_binary64`
72×	`add-cube-cbrt_binary64`
41×	`associate-l_binary64`
27×	`associate-r_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`distribute-lft-out_binary64`
15×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
14×	`associate-/r*_binary64`
9×	`unswap-sqr_binary64`
8×	`associate-/r/_binary64` `associate-/l*_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 → 217

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y)))
32.0ms	(*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y))))
6.0ms	(/.f64 y (sqrt.f64 (+.f64 1.0 y)))
4.0ms	(-.f64 1.0 (*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y)))
8.0ms	(*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y))))
11.0ms	(/.f64 y (sqrt.f64 (+.f64 1.0 y)))
15.0ms	(-.f64 1.0 (*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4963	3359
1	4963	3359

prune226.0ms

Filtered

139 candidates to 229 candidates (-64.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	229	5	234

Merged error: 0.1b

Counts

234 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

7.0b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.0b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.0b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.3b	(/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)) (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)))) (+.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`associate-/r*_binary64`
11×	`distribute-lft-out_binary64`
8×	`associate-/l/_binary64` `associate-/r/_binary64`
7×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`associate-*l/_binary64`
5×	`difference-of-squares_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 → 122

Calls

4 calls:

10.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
10.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
14.0ms	(/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)) (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)))) (+.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
10.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
8.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
105.0ms	(/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)) (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)))) (+.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))))

simplify60.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4962	2310
1	4962	2310

prune203.0ms

Filtered

101 candidates to 134 candidates (-32.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	134	5	139

Merged error: 0.1b

Counts

139 → 5

regimes163.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.9b

bsearch29.0ms

Steps

Iters	Range		Point
9	117042592.7078196	448751684616435.8	217289467.81919855
9	-145556152964612.3	-90384.7951388277	-130646298.08262084

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	305	29
1	305	29

end0.0ms

sample504.0ms

Algorithm

intervals

Results

178.0ms	6022×	body	80	valid
79.0ms	742×	body	640	valid
60.0ms	402×	body	1280	valid
41.0ms	501×	body	320	valid
18.0ms	333×	body	160	valid

Details

analyze74.0ms

sample19.0ms

simplify297.0ms

prune5.0ms

localize6.0ms

rewrite19.0ms

series24.0ms

simplify47.0ms

prune75.0ms

localize6.0ms

rewrite10.0ms

series18.0ms

simplify53.0ms

prune57.0ms

localize9.0ms

rewrite63.0ms

series45.0ms

simplify82.0ms

prune226.0ms

localize11.0ms

rewrite46.0ms

series131.0ms

simplify60.0ms

prune203.0ms

regimes163.0ms

bsearch29.0ms

simplify8.0ms

end0.0ms

sample504.0ms

Profiling