Details

analyze40.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

sample23.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
0.0ms	2×	body	80	invalid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	799	14
1	799	14

prune3.0ms

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: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (.f64 x 9.0))) (/.f64 y (.f64 3.0 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3.0 (sqrt.f64 x)))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.3b	(/.f64 1.0 (*.f64 x 9.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
2×	`associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

11.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (.f64 x 9.0))) (/.f64 y (.f64 3.0 (sqrt.f64 x))))
5.0ms	(/.f64 y (*.f64 3.0 (sqrt.f64 x)))
5.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))

series31.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (.f64 x 9.0))) (/.f64 y (.f64 3.0 (sqrt.f64 x))))
12.0ms	(/.f64 y (*.f64 3.0 (sqrt.f64 x)))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4981	999
1	4981	999

prune135.0ms

Filtered

71 candidates to 95 candidates (-33.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	86	9	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	9	96

Merged error: 0.0b

Counts

96 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y 3.0) (sqrt.f64 x)))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(/.f64 (/.f64 y 3.0) (sqrt.f64 x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`
16×	`associate-/l*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`div-inv_binary64`
8×	`add-log-exp_binary64`
7×	`associate-/r*_binary64`
5×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64`
3×	`pow1_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate--l+_binary64`

Counts

3 → 156

Calls

3 calls:

30.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y 3.0) (sqrt.f64 x)))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))
7.0ms	(/.f64 (/.f64 y 3.0) (sqrt.f64 x))

series28.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y 3.0) (sqrt.f64 x)))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))
14.0ms	(/.f64 (/.f64 y 3.0) (sqrt.f64 x))

simplify70.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	2300
1	4965	2300

prune196.0ms

Filtered

112 candidates to 165 candidates (-47.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Merged error: 0.0b

Counts

174 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0))))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(/.f64 (sqrt.f64 x) (/.f64 y 3.0))
0.3b	(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

943×	`times-frac_binary64`
482×	`add-sqr-sqrt_binary64`
456×	`*-un-lft-identity_binary64`
443×	`add-cube-cbrt_binary64`
202×	`sqrt-prod_binary64`
97×	`associate-/r*_binary64`
40×	`div-inv_binary64`
35×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
12×	`associate-/l*_binary64`
11×	`cbrt-undiv_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
6×	`associate-/r/_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64`
3×	`diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate--l-_binary64` `cbrt-unprod_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `associate--l+_binary64`

Counts

4 → 524

Calls

4 calls:

80.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0))))
4.0ms	(/.f64 1.0 (*.f64 x 9.0))
8.0ms	(/.f64 (sqrt.f64 x) (/.f64 y 3.0))
37.0ms	(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0))))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))
15.0ms	(/.f64 (sqrt.f64 x) (/.f64 y 3.0))
15.0ms	(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4979	8274
1	4979	8274

prune475.0ms

Filtered

284 candidates to 536 candidates (-88.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	535	1	536
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	536	8	544

Merged error: 0.0b

Counts

544 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y (sqrt.f64 x)) 3.0))
0.3b	(/.f64 y (sqrt.f64 x))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(/.f64 (/.f64 y (sqrt.f64 x)) 3.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac_binary64`
109×	`add-sqr-sqrt_binary64`
101×	`*-un-lft-identity_binary64`
96×	`add-cube-cbrt_binary64`
49×	`sqrt-prod_binary64`
28×	`associate-/l*_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r*_binary64`
9×	`add-log-exp_binary64`
7×	`div-inv_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64` `difference-of-squares_binary64`
3×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate--l+_binary64`

Counts

4 → 188

Calls

4 calls:

28.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y (sqrt.f64 x)) 3.0))
6.0ms	(/.f64 y (sqrt.f64 x))
4.0ms	(/.f64 1.0 (*.f64 x 9.0))
8.0ms	(/.f64 (/.f64 y (sqrt.f64 x)) 3.0)

series36.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y (sqrt.f64 x)) 3.0))
9.0ms	(/.f64 y (sqrt.f64 x))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))
11.0ms	(/.f64 (/.f64 y (sqrt.f64 x)) 3.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4966	2505
1	4966	2505

prune168.0ms

Filtered

143 candidates to 200 candidates (-39.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Merged error: 0.0b

Counts

208 → 8

regimes95.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	14
1	52	14

end0.0ms

sample504.0ms

Algorithm

intervals

Results

357.0ms	8000×	body	80	valid
5.0ms	113×	body	80	invalid

Details

analyze40.0ms

sample23.0ms

simplify46.0ms

prune3.0ms

localize10.0ms

rewrite29.0ms

series31.0ms

simplify62.0ms

prune135.0ms

localize9.0ms

rewrite49.0ms

series28.0ms

simplify70.0ms

prune196.0ms

localize20.0ms

rewrite167.0ms

series43.0ms

simplify109.0ms

prune475.0ms

localize9.0ms

rewrite55.0ms

series36.0ms

simplify69.0ms

prune168.0ms

regimes95.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample504.0ms

Profiling