Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.2%	87.6%	0.2%	13
21.8%	77.8%	0.4%	14

sample30.0ms

Algorithm

intervals

Results

8.0ms	209×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	34×	body	80	invalid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4892	13
1	4892	13

prune4.0ms

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: 26.7b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
2.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
18.1b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 79

Calls

3 calls:

10.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
13.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

series119.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
65.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
43.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6037	1081

prune145.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	13	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 4.3b

Counts

89 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
3.6b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
6.2b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 274

Calls

3 calls:

8.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
41.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
16.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
60.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
77.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5076	5455

prune219.0ms

Filtered

169 candidates to 283 candidates (-67.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	277	6	283
Fresh	7	5	12
Picked	0	1	1
Done	0	0	0
Total	284	12	296

Merged error: 4.0b

Counts

296 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 t x))
0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
3.2b	(/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x)))
3.9b	(+.f64 x (/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

1721×	`times-frac_binary64`
1222×	`*-un-lft-identity_binary64`
1220×	`add-sqr-sqrt_binary64`
556×	`add-cube-cbrt_binary64`
332×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
113×	`associate-/r/_binary64`
57×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
39×	`associate-/l*_binary64`
32×	`add-exp-log_binary64`
31×	`associate-/r*_binary64`
20×	`add-cbrt-cube_binary64`
19×	`div-exp_binary64`
10×	`cbrt-undiv_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `div-sub_binary64`
3×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 834

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 t x))
8.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
30.0ms	(/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x)))
127.0ms	(+.f64 x (/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (-.f64 t x))
11.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
71.0ms	(/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x)))
65.0ms	(+.f64 x (/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x))))

simplify163.0ms

Algorithm

egg-herbie

Counts

846 → 846

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5395	20770

prune459.0ms

Filtered

373 candidates to 846 candidates (-126.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	845	1	846
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	847	11	858

Merged error: 4.0b

Counts

858 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 a z))
0.3b	(*.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x))
5.6b	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x))))
6.2b	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
32×	`add-exp-log_binary64` `times-frac_binary64`
26×	`associate-l_binary64`
25×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`frac-times_binary64`
16×	`flip3--_binary64` `flip--_binary64`
13×	`associate-*r/_binary64` `prod-exp_binary64`
12×	`pow1_binary64`
10×	`sub-neg_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cbrt-unprod_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `div-exp_binary64` `associate-*l/_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `associate-+r+_binary64`
3×	`1-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 152

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 a z))
13.0ms	(*.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x))
5.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x))))
16.0ms	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (-.f64 a z))
40.0ms	(*.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x))
61.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x))))
72.0ms	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5795	1850

prune120.0ms

Filtered

110 candidates to 164 candidates (-49.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	164	11	175

Merged error: 4.0b

Counts

175 → 11

regimes662.0ms

Accuracy

40.3% (5.1b remaining)

Error of 8.3b against oracle of 3.2b and baseline of 11.7b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	61
1	88	61

end0.0ms

sample807.0ms

Algorithm

intervals

Results

260.0ms	6563×	body	80	valid
88.0ms	561×	body	640	valid
56.0ms	1223×	body	80	invalid
45.0ms	384×	body	320	valid
44.0ms	244×	body	1280	valid
18.0ms	236×	body	160	valid
3.0ms	12×	body	2560	valid

Details

analyze1.0s

sample30.0ms

simplify64.0ms

prune4.0ms

localize16.0ms

rewrite34.0ms

series119.0ms

simplify47.0ms

prune145.0ms

localize10.0ms

rewrite82.0ms

series152.0ms

simplify75.0ms

prune219.0ms

localize10.0ms

rewrite245.0ms

series151.0ms

simplify163.0ms

prune459.0ms

localize13.0ms

rewrite45.0ms

series177.0ms

simplify57.0ms

prune120.0ms

regimes662.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample807.0ms

Profiling