Details

analyze255.0ms

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
12.5%	87.4%	0.1%	5
15.6%	84.3%	0.1%	6
32.8%	67.1%	0.1%	7
38.2%	61.6%	0.1%	8
46%	53.8%	0.1%	9
62.6%	37.3%	0.1%	10
67.2%	32.7%	0.1%	11
71.1%	28.8%	0.1%	12
81.6%	18.2%	0.1%	13
84.1%	15.7%	0.1%	14

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify138.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	3018	9
1	3018	9

prune2.0ms

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 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 76

Calls

2 calls:

7.0ms	(-.f64 1 (/.f64 y z))
12.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series18.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(-.f64 1 (/.f64 y z))
14.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5309	1116

prune50.0ms

Filtered

49 candidates to 82 candidates (-67.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	6	83

Merged error: 5.0b

Counts

83 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
0.4b	(/.f64 1 (-.f64 1 (/.f64 y z)))
5.8b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64`
32×	`difference-of-squares_binary64`
30×	`associate-r_binary64`
29×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-l_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

3 → 127

Calls

3 calls:

7.0ms	(-.f64 1 (/.f64 y z))
9.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))
19.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

series23.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(-.f64 1 (/.f64 y z))
6.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))
14.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

simplify51.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5619	1454

prune60.0ms

Filtered

83 candidates to 136 candidates (-63.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Merged error: 5.0b

Counts

142 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
0.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
6.2b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

318×	`times-frac_binary64`
284×	`add-sqr-sqrt_binary64`
278×	`*-un-lft-identity_binary64`
108×	`add-cube-cbrt_binary64`
88×	`difference-of-squares_binary64`
42×	`associate-/r*_binary64`
41×	`distribute-lft-out_binary64`
22×	`distribute-lft-out--_binary64`
16×	`add-exp-log_binary64`
11×	`associate-/r/_binary64` `associate-/l*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
6×	`div-inv_binary64`
5×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

3 → 253

Calls

3 calls:

9.0ms	(-.f64 1 (/.f64 y z))
17.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
12.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series32.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(-.f64 1 (/.f64 y z))
18.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
10.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

simplify85.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5523	4377

prune95.0ms

Filtered

130 candidates to 262 candidates (-101.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	262	6	268

Merged error: 5.0b

Counts

268 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
0.0b	(/.f64 1 (+.f64 y x))
0.2b	(/.f64 1 (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 y x))))
6.2b	(*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 y x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log_binary64`
47×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64` `div-exp_binary64`
18×	`associate-r_binary64`
16×	`prod-exp_binary64`
10×	`pow1_binary64` `1-exp_binary64` `associate-/r/_binary64` `rec-exp_binary64`
8×	`associate-l_binary64` `difference-of-squares_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
5×	`associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
4×	`cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64` `pow-flip_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-*r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `*-commutative_binary64`

Counts

4 → 147

Calls

4 calls:

8.0ms	(-.f64 1 (/.f64 y z))
6.0ms	(/.f64 1 (+.f64 y x))
17.0ms	(/.f64 1 (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 y x))))
19.0ms	(*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 y x)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(-.f64 1 (/.f64 y z))
8.0ms	(/.f64 1 (+.f64 y x))
18.0ms	(/.f64 1 (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 y x))))
11.0ms	(*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 y x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5062	1445

prune57.0ms

Filtered

88 candidates to 159 candidates (-80.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	159	6	165

Merged error: 4.9b

Counts

165 → 6

regimes155.0ms

Accuracy

0% (1.9b remaining)

Error of 7.4b against oracle of 5.5b and baseline of 7.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	26	9

end0.0ms

sample400.0ms

Algorithm

intervals

Results

235.0ms	7998×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid

Details

analyze255.0ms

sample15.0ms

simplify138.0ms

prune2.0ms

localize6.0ms

rewrite22.0ms

series18.0ms

simplify44.0ms

prune50.0ms

localize7.0ms

rewrite41.0ms

series23.0ms

simplify51.0ms

prune60.0ms

localize7.0ms

rewrite53.0ms

series32.0ms

simplify85.0ms

prune95.0ms

localize11.0ms

rewrite55.0ms

series40.0ms

simplify60.0ms

prune57.0ms

regimes155.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample400.0ms

Profiling