Details

analyze42.0ms

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

sample20.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	2×	body	80	invalid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	496	12
1	496	12

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
6×	`associate-r_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
5×	`prod-exp_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-undiv_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `1-exp_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`associate--l-_binary64` `inv-pow_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
5.0ms	(/.f64 1 (*.f64 x 9))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms	(*.f64 3 (sqrt.f64 x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
2.0ms	(/.f64 1 (*.f64 x 9))
11.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5013	912

prune143.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`
19×	`add-exp-log_binary64`
16×	`associate-/l*_binary64`
13×	`add-cbrt-cube_binary64`
10×	`div-inv_binary64`
8×	`add-log-exp_binary64`
7×	`associate-/r*_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`diff-log_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `inv-pow_binary64` `associate--l+_binary64`

Counts

3 → 164

Calls

3 calls:

42.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
6.0ms	(/.f64 1 (*.f64 x 9))
9.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

series28.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
2.0ms	(/.f64 1 (*.f64 x 9))
15.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

simplify89.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4929	2196
1	4929	2196

prune173.0ms

Filtered

111 candidates to 173 candidates (-55.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Merged error: 0.0b

Counts

182 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 (/.f64 y 3) (sqrt.f64 x)) (/.f64 1/9 x))
0.3b	(/.f64 1/9 x)
0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

152×	`times-frac_binary64`
94×	`*-un-lft-identity_binary64`
88×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
42×	`sqrt-prod_binary64`
16×	`associate-/l*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/r*_binary64` `div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `frac-add_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 153

Calls

3 calls:

60.0ms	(+.f64 (/.f64 (/.f64 y 3) (sqrt.f64 x)) (/.f64 1/9 x))
3.0ms	(/.f64 1/9 x)
9.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

series28.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+.f64 (/.f64 (/.f64 y 3) (sqrt.f64 x)) (/.f64 1/9 x))
2.0ms	(/.f64 1/9 x)
11.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

simplify97.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5123	1946

prune168.0ms

Filtered

113 candidates to 162 candidates (-43.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	161	8	169

Merged error: 0b

Counts

169 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 x) 9)
0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

27.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
7.0ms	(/.f64 (/.f64 1 x) 9)
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms	(*.f64 3 (sqrt.f64 x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
2.0ms	(/.f64 (/.f64 1 x) 9)
11.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))

simplify77.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4913	1418
1	4913	1418

prune133.0ms

Filtered

102 candidates to 146 candidates (-43.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	146	8	154

Merged error: 0b

Counts

154 → 8

regimes112.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	12
1	59	12

end0.0ms

sample500.0ms

Algorithm

intervals

Results

354.0ms	8000×	body	80	valid
4.0ms	91×	body	80	invalid

Details

analyze42.0ms

sample20.0ms

simplify28.0ms

prune13.0ms

localize10.0ms

rewrite35.0ms

series29.0ms

simplify56.0ms

prune143.0ms

localize13.0ms

rewrite66.0ms

series28.0ms

simplify89.0ms

prune173.0ms

localize9.0ms

rewrite81.0ms

series28.0ms

simplify97.0ms

prune168.0ms

localize10.0ms

rewrite56.0ms

series29.0ms

simplify77.0ms

prune133.0ms

regimes112.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample500.0ms

Profiling