Details

analyze1.3s

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

sample36.0ms

Algorithm

intervals

Results

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

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

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

localize9.0ms

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))

series117.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
59.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
45.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	6037	1081

prune140.0ms

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

localize9.0ms

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)))

rewrite90.0ms

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:

9.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
41.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
19.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
58.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
73.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5076	5455

prune213.0ms

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

localize11.0ms

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))))

rewrite262.0ms

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))
33.0ms	(/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x)))
137.0ms	(+.f64 x (/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (-.f64 t x))
11.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
72.0ms	(/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x)))
66.0ms	(+.f64 x (/.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (/.f64 1 (-.f64 t x))))

simplify176.0ms

Algorithm

egg-herbie

Counts

846 → 846

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5395	20770

prune462.0ms

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

localize10.0ms

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)))

rewrite47.0ms

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))))
17.0ms	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x)))

series182.0ms

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))))
74.0ms	(.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 a z)) (-.f64 t x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5795	1850

prune111.0ms

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

regimes592.0ms

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 (2.0ms)

Iter	Nodes	Cost
0	88	61
1	88	61

end0.0ms

sample805.0ms

Algorithm

intervals

Results

261.0ms	6563×	body	80	valid
85.0ms	561×	body	640	valid
49.0ms	1223×	body	80	invalid
46.0ms	244×	body	1280	valid
41.0ms	384×	body	320	valid
17.0ms	236×	body	160	valid
3.0ms	12×	body	2560	valid

Details

analyze1.3s

sample36.0ms

simplify68.0ms

prune4.0ms

localize9.0ms

rewrite34.0ms

series117.0ms

simplify49.0ms

prune140.0ms

localize9.0ms

rewrite90.0ms

series146.0ms

simplify78.0ms

prune213.0ms

localize11.0ms

rewrite262.0ms

series155.0ms

simplify176.0ms

prune462.0ms

localize10.0ms

rewrite47.0ms

series182.0ms

simplify59.0ms

prune111.0ms

regimes592.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample805.0ms

Profiling