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
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

sample18.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan
0.0ms	3×	body	80	invalid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	1582	12
1	1582	12

prune6.0ms

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: 0.3b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
21×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
14×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
7×	`prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `pow-flip_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 93

Calls

4 calls:

8.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
5.0ms	(/.f64 1 (*.f64 x 9))
15.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))

series26.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))
14.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4973	853
1	4973	853

prune134.0ms

Filtered

65 candidates to 105 candidates (-61.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	93	12	105
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	94	13	107

Merged error: 0.0b

Counts

107 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
14×	`associate-r_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64` `div-exp_binary64`
5×	`div-inv_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64` `cbrt-undiv_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 135

Calls

4 calls:

26.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
37.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
12.0ms	(/.f64 (/.f64 1 x) 9)
9.0ms	(*.f64 3 (sqrt.f64 x))

series42.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
23.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
4.0ms	(/.f64 (/.f64 1 x) 9)
8.0ms	(*.f64 3 (sqrt.f64 x))

simplify94.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5024	1352

prune135.0ms

Filtered

94 candidates to 147 candidates (-56.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	10	11
Picked	1	0	1
Done	1	0	1
Total	149	11	160

Merged error: 0.0b

Counts

160 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
37×	`add-exp-log_binary64`
34×	`sqrt-prod_binary64`
25×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
14×	`associate-r_binary64` `div-exp_binary64`
13×	`pow1_binary64`
8×	`prod-exp_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64`
6×	`cbrt-unprod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64` `div-inv_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `pow-flip_binary64`
2×	`sub-neg_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `flip--_binary64`

Counts

4 → 164

Calls

4 calls:

20.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (sqrt.f64 x))
13.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

series54.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
8.0ms	(*.f64 3 (sqrt.f64 x))
14.0ms	(/.f64 1 (sqrt.f64 x))
7.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

simplify41.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4957	1539
1	4957	1539

prune124.0ms

Filtered

103 candidates to 176 candidates (-70.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	175	12	187

Merged error: 0.0b

Counts

187 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sqrt.f64 x) 3) y)
0.3b	(*.f64 (sqrt.f64 x) 3)
0.4b	(*.f64 (sqrt.f64 x) (+.f64 -3 (/.f64 1/3 x)))
0.4b	(/.f64 1/3 x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64` `associate-l_binary64`
10×	`associate-r_binary64`
9×	`times-frac_binary64`
8×	`sqrt-prod_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-*r/_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 94

Calls

4 calls:

11.0ms	(.f64 (.f64 (sqrt.f64 x) 3) y)
9.0ms	(*.f64 (sqrt.f64 x) 3)
18.0ms	(*.f64 (sqrt.f64 x) (+.f64 -3 (/.f64 1/3 x)))
6.0ms	(/.f64 1/3 x)

series31.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 x) 3) y)
5.0ms	(*.f64 (sqrt.f64 x) 3)
8.0ms	(*.f64 (sqrt.f64 x) (+.f64 -3 (/.f64 1/3 x)))
2.0ms	(/.f64 1/3 x)

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4943	885
1	4943	885

prune66.0ms

Filtered

77 candidates to 106 candidates (-37.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

regimes100.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	19
1	18	19

end0.0ms

sample512.0ms

Algorithm

intervals

Results

350.0ms	8000×	body	80	valid
6.0ms	144×	body	80	nan
3.0ms	70×	body	80	invalid

Details

analyze53.0ms

sample18.0ms

simplify113.0ms

prune6.0ms

localize9.0ms

rewrite36.0ms

series26.0ms

simplify55.0ms

prune134.0ms

localize15.0ms

rewrite93.0ms

series42.0ms

simplify94.0ms

prune135.0ms

localize10.0ms

rewrite54.0ms

series54.0ms

simplify41.0ms

prune124.0ms

localize16.0ms

rewrite46.0ms

series31.0ms

simplify56.0ms

prune66.0ms

regimes100.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample512.0ms

Profiling