Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	pre	128	true
9.0ms	256×	body	128	valid

simplify163.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4898	22
1	4898	22

prune1.0ms

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: 20.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
20.6b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`pow1_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
15.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+.f64 (.f64 x x) (.f64 y y))
92.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

simplify35.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5123	969

prune44.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 0.4b

Counts

49 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
0.0b	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
19.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
19.8b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
90×	`times-frac_binary64`
55×	`add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`
36×	`associate-l_binary64`
30×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`distribute-lft-out_binary64`
10×	`sqrt-div_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 175

Calls

4 calls:

44.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
11.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
113.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
51.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
62.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify104.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4985	5627
1	4985	5627

prune115.0ms

Filtered

119 candidates to 187 candidates (-57.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	187	6	193

Merged error: 0.4b

Counts

193 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(/.f64 (-.f64 x y) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y)))
19.9b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac_binary64`
161×	`*-un-lft-identity_binary64`
117×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64` `distribute-lft-out_binary64`
19×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
15×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-/l*_binary64` `div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 177

Calls

3 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
16.0ms	(/.f64 (-.f64 x y) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y)))
9.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y))

series204.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+.f64 (.f64 x x) (.f64 y y))
91.0ms	(/.f64 (-.f64 x y) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y)))
77.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y))

simplify100.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5201	6506

prune101.0ms

Filtered

123 candidates to 186 candidates (-51.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	186	6	192

Merged error: 0.4b

Counts

192 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
20.6b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
22×	`associate-/r*_binary64`
17×	`difference-of-squares_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
6×	`flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`cbrt-undiv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 152

Calls

4 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))
14.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
11.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+.f64 (.f64 x x) (.f64 y y))
45.0ms	(-.f64 (.f64 x x) (.f64 y y))
67.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
71.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5128	5148

prune103.0ms

Filtered

114 candidates to 164 candidates (-43.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	164	6	170

Merged error: 0.4b

Counts

170 → 6

regimes64.0ms

Accuracy

76.7% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 20.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	50
1	27	50

end0.0ms

sample565.0ms

Algorithm

intervals

Results

282.0ms	8000×	body	128	valid
145.0ms	8000×	pre	128	true

Details

analyze12.0ms

sample24.0ms

simplify163.0ms

prune1.0ms

localize9.0ms

rewrite23.0ms

series132.0ms

simplify35.0ms

prune44.0ms

localize11.0ms

rewrite92.0ms

series316.0ms

simplify104.0ms

prune115.0ms

localize9.0ms

rewrite57.0ms

series204.0ms

simplify100.0ms

prune101.0ms

localize10.0ms

rewrite51.0ms

series227.0ms

simplify86.0ms

prune103.0ms

regimes64.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample565.0ms

Profiling