Details

analyze68.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	201×	body	128	valid
2.0ms	20×	body	1024	valid
1.0ms	16×	body	512	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 23 to 23 computations (0% saved)

simplify271.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	4852	16
1	4852	16

prune3.0ms (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

Error

22.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) y)
3.7b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
8.3b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_16787`
17×	`add-sqr-sqrt_binary64_16809`
10×	`cancel-sign-sub-inv_binary64_16753` `add-exp-log_binary64_16825` `add-cbrt-cube_binary64_16823`
9×	`add-cube-cbrt_binary64_16822`
8×	`times-frac_binary64_16793`
6×	`associate-l_binary64_16728`
5×	`add-log-exp_binary64_16826` `pow1_binary64_16848`
4×	`difference-of-squares_binary64_16756` `associate-/r_binary64_16731` `associate-/r/_binary64_16733` `associate-l/_binary64_16730`
3×	`associate-r_binary64_16727` `flip3--_binary64_16791` `distribute-lft-out_binary64_16738` `flip--_binary64_16762`
2×	`cbrt-undiv_binary64_16821` `cbrt-unprod_binary64_16820` `prod-exp_binary64_16836` `div-exp_binary64_16838` `distribute-lft-out--_binary64_16739` `associate-/l/_binary64_16734` `flip-+_binary64_16761` `div-inv_binary64_16784` `flip3-+_binary64_16790`
1×	`diff-log_binary64_16879` `sub-neg_binary64_16780` `associate-/l_binary64_16732` `clear-num_binary64_16786` `-commutative_binary64_16718` `unswap-sqr_binary64_16755` `frac-2neg_binary64_16798` `pow-prod-down_binary64_16858`

Counts

3 → 74

Calls

3 calls:

11.0ms	(*.f64 (-.f64 1 x) y)
10.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
9.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

series92.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
27.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
19.0ms	(*.f64 (-.f64 1 x) y)

simplify62.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5643	1232

prune96.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Error

0.2b

Counts

84 → 3

Compiler

Compiled 1334 to 952 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 1 y))
0.0b	(*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y)))
3.7b	(-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y))))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_16787`
29×	`add-sqr-sqrt_binary64_16809`
25×	`times-frac_binary64_16793`
21×	`add-cube-cbrt_binary64_16822`
18×	`associate-r_binary64_16727`
10×	`add-exp-log_binary64_16825` `add-cbrt-cube_binary64_16823`
7×	`distribute-lft-out_binary64_16738`
6×	`associate-l_binary64_16728`
5×	`add-log-exp_binary64_16826` `pow1_binary64_16848`
4×	`associate-/r*_binary64_16731` `associate-/r/_binary64_16733`
3×	`associate-/l*_binary64_16732` `flip3--_binary64_16791` `flip--_binary64_16762`
2×	`cbrt-undiv_binary64_16821` `cbrt-unprod_binary64_16820` `difference-of-squares_binary64_16756` `prod-exp_binary64_16836` `div-exp_binary64_16838` `flip-+_binary64_16761` `frac-times_binary64_16797` `unswap-sqr_binary64_16755` `associate-*l/_binary64_16730` `div-inv_binary64_16784` `flip3-+_binary64_16790`
1×	`diff-log_binary64_16879` `cancel-sign-sub-inv_binary64_16753` `sub-neg_binary64_16780` `clear-num_binary64_16786` `-commutative_binary64_16718` `associate-r/_binary64_16729` `distribute-lft-out--_binary64_16739` `frac-2neg_binary64_16798` `pow-prod-down_binary64_16858`

Counts

3 → 89

Calls

3 calls:

14.0ms	(*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y)))
8.0ms	(/.f64 y (+.f64 1 y))
4.0ms	(-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y))))

series88.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y))))
26.0ms	(*.f64 (-.f64 1 x) (/.f64 y (+.f64 1 y)))
12.0ms	(/.f64 y (+.f64 1 y))

simplify86.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4971	1527
1	4971	1527

prune86.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Error

0.2b

Counts

101 → 3

Compiler

Compiled 1703 to 1212 computations (28.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y)))
0.1b	(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y))))
0.1b	(/.f64 y (sqrt.f64 (+.f64 1 y)))
5.5b	(-.f64 1 (*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y)))))

rewrite93.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

161×	`*-un-lft-identity_binary64_16787`
151×	`add-sqr-sqrt_binary64_16809`
138×	`times-frac_binary64_16793`
86×	`sqrt-prod_binary64_16803`
76×	`add-cube-cbrt_binary64_16822`
48×	`associate-l_binary64_16728`
30×	`difference-of-squares_binary64_16756`
27×	`associate-r_binary64_16727`
20×	`distribute-lft-out_binary64_16738` `add-exp-log_binary64_16825` `add-cbrt-cube_binary64_16823`
15×	`distribute-lft-out--_binary64_16739`
14×	`associate-/r*_binary64_16731`
9×	`associate-/l*_binary64_16732` `unswap-sqr_binary64_16755`
8×	`sqrt-div_binary64_16804` `associate-/r/_binary64_16733`
6×	`cbrt-undiv_binary64_16821` `add-log-exp_binary64_16826` `pow1_binary64_16848` `div-exp_binary64_16838`
4×	`cbrt-unprod_binary64_16820` `prod-exp_binary64_16836` `flip-+_binary64_16761` `div-inv_binary64_16784` `flip3-+_binary64_16790`
2×	`clear-num_binary64_16786` `flip3--_binary64_16791` `associate-/l/_binary64_16734` `flip--_binary64_16762` `frac-2neg_binary64_16798`
1×	`diff-log_binary64_16879` `div-sub_binary64_16792` `cancel-sign-sub-inv_binary64_16753` `sub-neg_binary64_16780` `-commutative_binary64_16718` `associate-r/_binary64_16729` `frac-times_binary64_16797` `associate-*l/_binary64_16730` `pow-prod-down_binary64_16858`

Counts

4 → 233

Calls

4 calls:

45.0ms	(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y))))
11.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y)))
7.0ms	(/.f64 y (sqrt.f64 (+.f64 1 y)))
4.0ms	(-.f64 1 (*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y)))))

series143.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(-.f64 1 (*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y)))))
34.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y)))
33.0ms	(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 y))) (/.f64 y (sqrt.f64 (+.f64 1 y))))
25.0ms	(/.f64 y (sqrt.f64 (+.f64 1 y)))

simplify104.0ms (3%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5171	5462

prune399.0ms (11.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	245	3	248

Error

0.2b

Counts

248 → 3

Compiler

Compiled 6106 to 4602 computations (24.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (/.f64 1 y))
0.0b	(-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_16787`
14×	`add-sqr-sqrt_binary64_16809`
13×	`cancel-sign-sub-inv_binary64_16753`
10×	`times-frac_binary64_16793`
9×	`add-log-exp_binary64_16826` `add-cube-cbrt_binary64_16822`
4×	`distribute-lft-out_binary64_16738`
3×	`distribute-lft-out--_binary64_16739` `div-inv_binary64_16784`
2×	`diff-log_binary64_16879` `pow1_binary64_16848` `sum-log_binary64_16878` `difference-of-squares_binary64_16756` `flip-+_binary64_16761` `frac-sub_binary64_16796` `add-exp-log_binary64_16825` `add-cbrt-cube_binary64_16823` `flip3-+_binary64_16790`
1×	`sub-neg_binary64_16780` `flip3--_binary64_16791` `associate--l+_binary64_16724` `+-commutative_binary64_16717` `flip--_binary64_16762`

Counts

2 → 46

Calls

2 calls:

15.0ms	(-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))
6.0ms	(+.f64 x (/.f64 1 y))

series29.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))
12.0ms	(+.f64 x (/.f64 1 y))

simplify91.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4918	736
1	4918	736

prune37.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	50	5	55

Error

0.2b

Counts

55 → 5

Compiler

Compiled 718 to 374 computations (47.9% saved)

regimes411.0ms (11.9%)

Accuracy

Total 0.0b remaining (21.2%)

Threshold costs 0.0b (21.2%)

Compiler

Compiled 3005 to 2432 computations (19.1% saved)

bsearch39.0ms (1.1%)

Steps

Iters	Range		Point
9	14706542.462942973	6452450467848536.0	87364310.78362173
10	-783123910.1095239	-0.01005018946655823	-30425717.663810726

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	270	58
1	270	58

end0.0ms (0%)

sample1.1s (32.1%)

Algorithm

1×

intervals

Results

204.0ms	6242×	body	128	valid
68.0ms	605×	body	1024	valid
60.0ms	675×	body	512	valid
28.0ms	471×	body	256	valid
1.0ms	7×	body	2048	valid

Compiler

Compiled 679 to 542 computations (20.2% saved)

Details

analyze68.0ms (2%)

sample21.0ms (0.6%)

simplify271.0ms (7.8%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite36.0ms (1%)

series92.0ms (2.6%)

simplify62.0ms (1.8%)

prune96.0ms (2.8%)

localize7.0ms (0.2%)

rewrite33.0ms (0.9%)

series88.0ms (2.5%)

simplify86.0ms (2.5%)

prune86.0ms (2.5%)

localize9.0ms (0.3%)

rewrite93.0ms (2.7%)

series143.0ms (4.1%)

simplify104.0ms (3%)

prune399.0ms (11.5%)

localize6.0ms (0.2%)

rewrite25.0ms (0.7%)

series29.0ms (0.8%)

simplify91.0ms (2.6%)

prune37.0ms (1.1%)

regimes411.0ms (11.9%)

bsearch39.0ms (1.1%)

simplify9.0ms (0.3%)

end0.0ms (0%)

sample1.1s (32.1%)

Profiling