Details

analyze53.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

sample15.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify215.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (212.0ms)

Iter	Nodes	Cost
0	2641	11
1	2641	11

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: 0.0b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (/.f64 y (+.f64 1.0 (/.f64 (*.f64 x y) 2.0))))
0.0b	(/.f64 (*.f64 x y) 2.0)
7.6b	(/.f64 y (+.f64 1.0 (/.f64 (*.f64 x y) 2.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

11.0ms	(-.f64 x (/.f64 y (+.f64 1.0 (/.f64 (*.f64 x y) 2.0))))
5.0ms	(/.f64 (*.f64 x y) 2.0)
7.0ms	(/.f64 y (+.f64 1.0 (/.f64 (*.f64 x y) 2.0)))

series32.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(-.f64 x (/.f64 y (+.f64 1.0 (/.f64 (*.f64 x y) 2.0))))
4.0ms	(/.f64 (*.f64 x y) 2.0)
18.0ms	(/.f64 y (+.f64 1.0 (/.f64 (*.f64 x y) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4969	946
1	4969	946

prune86.0ms

Filtered

60 candidates to 77 candidates (-28.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	3	78

Merged error: 0b

Counts

78 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (/.f64 1 (/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y)))
0.0b	(/.f64 (*.f64 y x) 2.0)
0.1b	(/.f64 1 (/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y))
7.5b	(/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac_binary64`
101×	`*-un-lft-identity_binary64`
78×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64` `add-exp-log_binary64`
16×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
10×	`div-exp_binary64`
8×	`associate-/l*_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64`
5×	`pow1_binary64` `difference-of-squares_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `inv-pow_binary64` `prod-exp_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 160

Calls

4 calls:

19.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y)))
5.0ms	(/.f64 (*.f64 y x) 2.0)
10.0ms	(/.f64 1 (/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y))
8.0ms	(/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y)

series39.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y)))
4.0ms	(/.f64 (*.f64 y x) 2.0)
16.0ms	(/.f64 1 (/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y))
9.0ms	(/.f64 (+.f64 1.0 (/.f64 (*.f64 y x) 2.0)) y)

simplify76.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5071	2527

prune129.0ms

Filtered

106 candidates to 172 candidates (-62.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Merged error: 0b

Counts

175 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 x (sqrt.f64 2.0)) (/.f64 y (sqrt.f64 2.0)))
0.5b	(/.f64 x (sqrt.f64 2.0))
0.5b	(/.f64 y (sqrt.f64 2.0))
7.6b	(/.f64 y (+.f64 1.0 (*.f64 (/.f64 x (sqrt.f64 2.0)) (/.f64 y (sqrt.f64 2.0)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt_binary64`
93×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`
22×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
15×	`associate-/r*_binary64`
9×	`unswap-sqr_binary64` `associate-/l*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 180

Calls

4 calls:

17.0ms	(*.f64 (/.f64 x (sqrt.f64 2.0)) (/.f64 y (sqrt.f64 2.0)))
4.0ms	(/.f64 x (sqrt.f64 2.0))
4.0ms	(/.f64 y (sqrt.f64 2.0))
6.0ms	(/.f64 y (+.f64 1.0 (*.f64 (/.f64 x (sqrt.f64 2.0)) (/.f64 y (sqrt.f64 2.0)))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(*.f64 (/.f64 x (sqrt.f64 2.0)) (/.f64 y (sqrt.f64 2.0)))
7.0ms	(/.f64 x (sqrt.f64 2.0))
7.0ms	(/.f64 y (sqrt.f64 2.0))
46.0ms	(/.f64 y (+.f64 1.0 (*.f64 (/.f64 x (sqrt.f64 2.0)) (/.f64 y (sqrt.f64 2.0)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5043	1843

prune160.0ms

Filtered

127 candidates to 192 candidates (-51.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	192	3	195

Merged error: 0b

Counts

195 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 y x) 2.0)
0.2b	(.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (*.f64 y x) 2.0))
5.0b	(/.f64 y (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (.f64 y x) 2.0))))
13.2b	(.f64 (/.f64 y (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (.f64 y x) 2.0)))) (-.f64 1.0 (/.f64 (.f64 x y) 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
25×	`associate-l_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`pow1_binary64`
12×	`associate-r_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64` `swap-sqr_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `flip--_binary64`
3×	`associate-*r/_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `distribute-lft-out--_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 155

Calls

4 calls:

5.0ms	(/.f64 (*.f64 y x) 2.0)
10.0ms	(.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (*.f64 y x) 2.0))
7.0ms	(/.f64 y (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (.f64 y x) 2.0))))
16.0ms	(.f64 (/.f64 y (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (.f64 y x) 2.0)))) (-.f64 1.0 (/.f64 (.f64 x y) 2.0)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 (*.f64 y x) 2.0)
9.0ms	(.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (*.f64 y x) 2.0))
18.0ms	(/.f64 y (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (.f64 y x) 2.0))))
33.0ms	(.f64 (/.f64 y (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 y x) 2.0) (/.f64 (.f64 y x) 2.0)))) (-.f64 1.0 (/.f64 (.f64 x y) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4968	2257
1	4968	2257

prune177.0ms

Filtered

119 candidates to 167 candidates (-40.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	167	3	170

Merged error: 0b

Counts

170 → 3

regimes66.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	13
1	34	13

end0.0ms

sample397.0ms

Algorithm

intervals

Results

264.0ms	7998×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid

Details

analyze53.0ms

sample15.0ms

simplify215.0ms

prune2.0ms

localize7.0ms

rewrite24.0ms

series32.0ms

simplify55.0ms

prune86.0ms

localize8.0ms

rewrite51.0ms

series39.0ms

simplify76.0ms

prune129.0ms

localize10.0ms

rewrite38.0ms

series78.0ms

simplify61.0ms

prune160.0ms

localize13.0ms

rewrite46.0ms

series64.0ms

simplify43.0ms

prune177.0ms

regimes66.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample397.0ms

Profiling