Details

analyze267.0ms

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

sample139.0ms

Algorithm

intervals

Results

65.0ms	166×	body	640	valid
30.0ms	297×	body	80	nan
15.0ms	53×	body	320	valid
6.0ms	19×	body	160	valid
3.0ms	7×	body	1280	valid
1.0ms	11×	body	80	valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5039	31

prune6.0ms

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: 5.4b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.3b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite41.0ms

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:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
9.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series44.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
11.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
11.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
11.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify34.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5194	1304

prune121.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 0.8b

Counts

85 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.3b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
40×	`sqrt-prod_binary64`
39×	`add-sqr-sqrt_binary64`
19×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
9×	`distribute-lft-out--_binary64`
8×	`add-exp-log_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 99

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
11.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series41.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
11.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
11.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify37.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5116	1621

prune116.0ms

Filtered

70 candidates to 111 candidates (-58.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Merged error: 0.5b

Counts

118 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64`
48×	`sqrt-prod_binary64`
42×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
34×	`distribute-lft-out_binary64`
26×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64` `add-exp-log_binary64`
8×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
6×	`pow1_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
4×	`associate-/r/_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 126

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series42.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
11.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify66.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4886	1870
1	4886	1870

prune145.0ms

Filtered

77 candidates to 138 candidates (-79.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	137	7	144

Merged error: 0.0b

Counts

144 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

128×	`*-un-lft-identity_binary64`
56×	`sqrt-prod_binary64`
54×	`times-frac_binary64`
49×	`distribute-lft-out_binary64`
45×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64` `div-exp_binary64`
4×	`difference-of-squares_binary64`
3×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-flip_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 153

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series37.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
9.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
12.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

simplify44.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4962	2143
1	4962	2143

prune146.0ms

Filtered

86 candidates to 165 candidates (-91.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	166	6	172

Merged error: 0.0b

Counts

172 → 6

regimes459.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	39
1	40	39

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	5295×	body	640	valid
973.0ms	9852×	body	80	nan
436.0ms	1496×	body	320	valid
86.0ms	430×	body	160	valid
83.0ms	165×	body	1280	valid
62.0ms	614×	body	80	valid

Details

analyze267.0ms

sample139.0ms

simplify49.0ms

prune6.0ms

localize21.0ms

rewrite41.0ms

series44.0ms

simplify34.0ms

prune121.0ms

localize22.0ms

rewrite43.0ms

series41.0ms

simplify37.0ms

prune116.0ms

localize27.0ms

rewrite44.0ms

series42.0ms

simplify66.0ms

prune145.0ms

localize26.0ms

rewrite51.0ms

series37.0ms

simplify44.0ms

prune146.0ms

regimes459.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.2s

Profiling