Details

analyze273.0ms (3.5%)

Algorithm

1×

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

Compiler

Compiled 32 to 28 computations (12.5% saved)

sample125.0ms (1.6%)

Algorithm

1×

intervals

Results

44.0ms	140×	body	512	valid
30.0ms	299×	body	128	nan
23.0ms	57×	body	1024	valid
6.0ms	32×	body	256	valid
3.0ms	27×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify216.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5203	50

prune4.0ms (0.1%)

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: 4.5b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
2.4b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.6b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_6164`
32×	`*-un-lft-identity_binary64_6143` `sqrt-prod_binary64_6158`
16×	`difference-of-squares_binary64_6112`
12×	`distribute-lft-out--_binary64_6097` `add-log-exp_binary64_6179`
4×	`sub-neg_binary64_6136` `distribute-lft-out_binary64_6096` `add-exp-log_binary64_6178` `add-cube-cbrt_binary64_6175` `add-cbrt-cube_binary64_6176` `flip3--_binary64_6147` `flip--_binary64_6118` `diff-log_binary64_6232` `pow1_binary64_6201`

Counts

4 → 72

Calls

4 calls:

12.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series283.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
72.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
71.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
66.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5002	2087

prune192.0ms (2.4%)

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: 0.4b

Counts

85 → 6

Compiler

Compiled 3698 to 2417 computations (34.6% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
2.4b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.6b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_6143`
40×	`sqrt-prod_binary64_6158`
39×	`add-sqr-sqrt_binary64_6164`
19×	`distribute-lft-out_binary64_6096`
18×	`times-frac_binary64_6149`
15×	`add-cube-cbrt_binary64_6175`
12×	`difference-of-squares_binary64_6112`
10×	`add-log-exp_binary64_6179`
9×	`distribute-lft-out--_binary64_6097`
8×	`add-exp-log_binary64_6178`
6×	`associate-/r*_binary64_6089` `add-cbrt-cube_binary64_6176`
5×	`pow1_binary64_6201`
3×	`associate-/l*_binary64_6090` `sub-neg_binary64_6136` `flip3--_binary64_6147` `flip--_binary64_6118` `diff-log_binary64_6232`
2×	`div-exp_binary64_6191` `associate-/r/_binary64_6091`
1×	`frac-2neg_binary64_6154` `div-inv_binary64_6140` `1-exp_binary64_6184` `cbrt-undiv_binary64_6174` `clear-num_binary64_6142` `inv-pow_binary64_6225` `rec-exp_binary64_6190` `flip3-+_binary64_6146` `pow-flip_binary64_6214` `flip-+_binary64_6117`

Counts

4 → 99

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
9.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series261.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
69.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
68.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
54.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4872	2518
1	4872	2518

prune247.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	111	6	117

Merged error: 0.3b

Counts

117 → 6

Compiler

Compiled 4891 to 3255 computations (33.4% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
2.4b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64_6143`
48×	`sqrt-prod_binary64_6158`
42×	`add-sqr-sqrt_binary64_6164`
36×	`times-frac_binary64_6149`
34×	`distribute-lft-out_binary64_6096`
26×	`add-cube-cbrt_binary64_6175`
12×	`associate-/r*_binary64_6089` `add-exp-log_binary64_6178`
8×	`difference-of-squares_binary64_6112` `add-log-exp_binary64_6179` `add-cbrt-cube_binary64_6176`
6×	`distribute-lft-out--_binary64_6097` `associate-/l*_binary64_6090` `pow1_binary64_6201`
4×	`div-exp_binary64_6191` `associate-/r/_binary64_6091`
2×	`sub-neg_binary64_6136` `frac-2neg_binary64_6154` `div-inv_binary64_6140` `1-exp_binary64_6184` `cbrt-undiv_binary64_6174` `clear-num_binary64_6142` `inv-pow_binary64_6225` `rec-exp_binary64_6190` `flip3-+_binary64_6146` `flip3--_binary64_6147` `pow-flip_binary64_6214` `flip--_binary64_6118` `flip-+_binary64_6117` `diff-log_binary64_6232`

Counts

4 → 126

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
11.0ms	(/.f64 1 (+.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 z 1)) (sqrt.f64 z))

series257.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
67.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
59.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
53.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4894	2981
1	4894	2981

prune346.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Merged error: 0.0b

Counts

144 → 6

Compiler

Compiled 6196 to 4213 computations (32% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite69.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`*-un-lft-identity_binary64_6143`
56×	`sqrt-prod_binary64_6158`
54×	`times-frac_binary64_6149`
49×	`distribute-lft-out_binary64_6096`
45×	`add-sqr-sqrt_binary64_6164`
37×	`add-cube-cbrt_binary64_6175`
18×	`associate-/r*_binary64_6089`
16×	`add-exp-log_binary64_6178`
10×	`add-cbrt-cube_binary64_6176`
9×	`associate-/l*_binary64_6090`
7×	`pow1_binary64_6201`
6×	`add-log-exp_binary64_6179` `div-exp_binary64_6191` `associate-/r/_binary64_6091`
4×	`difference-of-squares_binary64_6112`
3×	`distribute-lft-out--_binary64_6097` `frac-2neg_binary64_6154` `div-inv_binary64_6140` `1-exp_binary64_6184` `cbrt-undiv_binary64_6174` `clear-num_binary64_6142` `inv-pow_binary64_6225` `rec-exp_binary64_6190` `flip3-+_binary64_6146` `pow-flip_binary64_6214` `flip-+_binary64_6117`
1×	`sub-neg_binary64_6136` `flip3--_binary64_6147` `flip--_binary64_6118` `diff-log_binary64_6232`

Counts

4 → 153

Calls

4 calls:

14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series256.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
65.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
58.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5612	3411

prune430.0ms (5.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Merged error: 0.0b

Counts

171 → 7

Compiler

Compiled 7336 to 5048 computations (31.2% saved)

regimes286.0ms (3.6%)

Compiler: Compiled 3700 to 3182 computations (14% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	76
1	50	76

end0.0ms (0%)

sample4.1s (52.1%)

Algorithm

1×

intervals

Results

1.3s	4344×	body	512	valid
968.0ms	9604×	body	128	nan
706.0ms	1733×	body	1024	valid
208.0ms	1041×	body	256	valid
87.0ms	881×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 443 to 380 computations (14.2% saved)

Details

analyze273.0ms (3.5%)

sample125.0ms (1.6%)

simplify216.0ms (2.7%)

prune4.0ms (0.1%)

localize22.0ms (0.3%)

rewrite50.0ms (0.6%)

series283.0ms (3.6%)

simplify47.0ms (0.6%)

prune192.0ms (2.4%)

localize24.0ms (0.3%)

rewrite57.0ms (0.7%)

series261.0ms (3.3%)

simplify89.0ms (1.1%)

prune247.0ms (3.1%)

localize29.0ms (0.4%)

rewrite60.0ms (0.8%)

series257.0ms (3.3%)

simplify57.0ms (0.7%)

prune346.0ms (4.4%)

localize26.0ms (0.3%)

rewrite69.0ms (0.9%)

series256.0ms (3.2%)

simplify75.0ms (0.9%)

prune430.0ms (5.4%)

regimes286.0ms (3.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.1s (52.1%)

Profiling