Details

analyze263.0ms

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
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

sample157.0ms

Algorithm

intervals

Results

66.0ms	163×	body	640	valid
31.0ms	324×	body	80	nan
16.0ms	54×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	21×	body	80	valid
2.0ms	4×	body	1280	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5040	31

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 5.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (sqrt.f64 (+.f64 t 1.0)) (sqrt.f64 t))
2.7b	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
4.2b	(-.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
16×	`difference-of-squares_binary64`
12×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 t 1.0)) (sqrt.f64 t))
8.0ms	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
8.0ms	(-.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z))

series232.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (+.f64 t 1.0)) (sqrt.f64 t))
194.0ms	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
12.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
13.0ms	(-.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z))

simplify47.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4985	1360
1	4985	1360

prune157.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	6	85

Merged error: 0.8b

Counts

85 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
2.2b	(-.f64 (sqrt.f64 (+.f64 t 1.0)) (sqrt.f64 t))
2.7b	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
44×	`sqrt-prod_binary64`
40×	`add-sqr-sqrt_binary64`
30×	`distribute-lft-out_binary64`
24×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `associate-/l*_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 t 1.0)) (sqrt.f64 t))
8.0ms	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

series54.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
16.0ms	(-.f64 (sqrt.f64 (+.f64 t 1.0)) (sqrt.f64 t))
13.0ms	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
13.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

simplify39.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4957	1837
1	4957	1837

prune184.0ms

Filtered

78 candidates to 116 candidates (-48.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	117	5	122

Merged error: 0.6b

Counts

122 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 t)) (sqrt.f64 t)))
0.2b	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
2.7b	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64`
52×	`sqrt-prod_binary64`
45×	`distribute-lft-out_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
7×	`associate-/l*_binary64`
6×	`distribute-lft-out--_binary64`
4×	`pow1_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

4 → 127

Calls

4 calls:

10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 t)) (sqrt.f64 t)))
15.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 t)) (sqrt.f64 t)))
12.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
13.0ms	(-.f64 (sqrt.f64 (+.f64 y 1.0)) (sqrt.f64 y))
13.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

simplify60.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5564	2128

prune236.0ms

Filtered

89 candidates to 139 candidates (-56.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Merged error: 0.4b

Counts

144 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 t)) (sqrt.f64 t)))
0.2b	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 y)) (sqrt.f64 y)))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity_binary64`
60×	`distribute-lft-out_binary64` `times-frac_binary64` `sqrt-prod_binary64`
46×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `difference-of-squares_binary64` `flip-+_binary64`
3×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 150

Calls

4 calls:

10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 t)) (sqrt.f64 t)))
13.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 y)) (sqrt.f64 y)))
12.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

series58.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 t)) (sqrt.f64 t)))
16.0ms	(/.f64 (+.f64 1.0 0) (+.f64 (sqrt.f64 (+.f64 z 1.0)) (sqrt.f64 z)))
14.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 y)) (sqrt.f64 y)))
13.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

simplify66.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5886	2423

prune249.0ms

Filtered

100 candidates to 162 candidates (-62.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	161	7	168

Merged error: 0.0b

Counts

168 → 7

regimes900.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	39
1	42	39

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	5246×	body	640	valid
965.0ms	9607×	body	80	nan
481.0ms	1590×	body	320	valid
90.0ms	456×	body	160	valid
71.0ms	131×	body	1280	valid
59.0ms	577×	body	80	valid

Details

analyze263.0ms

sample157.0ms

simplify45.0ms

prune8.0ms

localize24.0ms

rewrite35.0ms

series232.0ms

simplify47.0ms

prune157.0ms

localize27.0ms

rewrite42.0ms

series54.0ms

simplify39.0ms

prune184.0ms

localize25.0ms

rewrite46.0ms

series50.0ms

simplify60.0ms

prune236.0ms

localize27.0ms

rewrite51.0ms

series58.0ms

simplify66.0ms

prune249.0ms

regimes900.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.2s

Profiling