Details

analyze678.0ms

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample20.0ms

Algorithm

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

simplify256.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

Iter	Nodes	Cost
0	5125	22

prune1.0ms

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: 26.3b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 b c) (.f64 a d))
25.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(-.f64 (.f64 b c) (.f64 a d))
9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

series272.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(-.f64 (.f64 b c) (.f64 a d))
195.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify43.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4974	1263
1	4974	1263

prune53.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Merged error: 25.5b

Counts

50 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
15.1b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac_binary64`
164×	`add-sqr-sqrt_binary64`
162×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
156×	`sqrt-prod_binary64`
27×	`associate-/l*_binary64`
22×	`sqrt-div_binary64`
18×	`associate-/r/_binary64`
12×	`associate-/r*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64` `div-sub_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `flip--_binary64`

Counts

4 → 266

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
14.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
250.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
56.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
50.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify175.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4980	13644
1	4980	13644

prune168.0ms

Filtered

151 candidates to 278 candidates (-84.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	274	4	278
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	275	8	283

Merged error: 24.0b

Counts

283 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
15.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
28.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`
27×	`associate-/r*_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
9×	`associate-/l*_binary64`
7×	`pow1_binary64`
6×	`div-inv_binary64` `sqrt-div_binary64`
5×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 191

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
13.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
153.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
43.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify133.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4957	7416
1	4957	7416

prune137.0ms

Filtered

123 candidates to 203 candidates (-65.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	203	8	211

Merged error: 24.0b

Counts

211 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d))))
7.3b	(sqrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d))))
25.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
25.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
6×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
4×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

4 → 118

Calls

4 calls:

9.0ms	(sqrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d))))
8.0ms	(sqrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d))))
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

series828.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(sqrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d))))
228.0ms	(sqrt.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d))))
176.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
188.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5530	3990

prune107.0ms

Filtered

108 candidates to 130 candidates (-20.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	130	8	138

Merged error: 24.0b

Counts

138 → 8

regimes113.0ms

Accuracy

-4.2% (3.1b remaining)

Error of 26.0b against oracle of 22.9b and baseline of 25.9b

bsearch34.0ms

Steps

Iters	Range		Point
9	7.893330328097678e+146	1.623166018444903e+152	3.40778976921943e+151
4	6.280097503922549e+93	1.1231299536994925e+94	1.0135236429461193e+94

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	72
1	63	72

end0.0ms

sample570.0ms

Algorithm

intervals

Results

337.0ms	8000×	body	128	valid
19.0ms	482×	body	128	invalid

Details

analyze678.0ms

sample20.0ms

simplify256.0ms

prune1.0ms

localize10.0ms

rewrite17.0ms

series272.0ms

simplify43.0ms

prune53.0ms

localize13.0ms

rewrite92.0ms

series559.0ms

simplify175.0ms

prune168.0ms

localize14.0ms

rewrite68.0ms

series459.0ms

simplify133.0ms

prune137.0ms

localize15.0ms

rewrite55.0ms

series828.0ms

simplify65.0ms

prune107.0ms

regimes113.0ms

bsearch34.0ms

simplify3.0ms

end0.0ms

sample570.0ms

Profiling