Details

analyze607.0ms (7%)

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample43.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	35×	body	2048	valid
7.0ms	160×	body	128	valid
7.0ms	16×	body	4096	valid
4.0ms	24×	body	1024	valid
2.0ms	14×	body	512	valid
1.0ms	15×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify169.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

37.0b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

8 calls:

12.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

series559.0ms (6.4%)

Counts

4 → 68

Calls

4 calls:

183.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
133.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
119.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1712 to 1386 computations (19% saved)

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5209	3070

prune232.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	141	13	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	13	155

Error

6.6b

Counts

155 → 13

Compiler

Compiled 2901 to 652 computations (77.5% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.1b	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
124×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
71×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
24×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 164

Calls

8 calls:

14.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series542.0ms (6.2%)

Counts

4 → 68

Calls

4 calls:

183.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
123.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
115.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1864 to 1538 computations (17.5% saved)

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5045	6061

prune182.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	234	11	245

Error

6.5b

Counts

245 → 11

Compiler

Compiled 5299 to 1216 computations (77.1% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.1b	(/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite113.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

789×	`times-frac_binary64`
494×	`add-sqr-sqrt_binary64`
407×	`*-un-lft-identity_binary64`
321×	`add-cube-cbrt_binary64`
86×	`difference-of-squares_binary64`
46×	`sqrt-prod_binary64`
44×	`add-exp-log_binary64`
43×	`distribute-lft-out--_binary64`
40×	`div-inv_binary64`
32×	`div-exp_binary64`
29×	`associate-/r/_binary64`
24×	`associate-/r*_binary64`
17×	`flip3--_binary64` `flip--_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
5×	`pow1_binary64`
4×	`cancel-sign-sub-inv_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 425

Calls

8 calls:

26.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series556.0ms (6.4%)

Counts

4 → 68

Calls

4 calls:

184.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
126.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
120.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2016 to 1690 computations (16.2% saved)

simplify219.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

493 → 493

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4984	18731
1	4984	18731

prune527.0ms (6.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	492	1	493
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	492	12	504

Error

6.5b

Counts

504 → 12

Compiler

Compiled 13869 to 3740 computations (73% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
0.0b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.0b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
25.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 64

Calls

8 calls:

11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series510.0ms (5.9%)

Counts

4 → 66

Calls

4 calls:

131.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
129.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
124.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3176 to 2224 computations (30% saved)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5493	2328

prune112.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	130	12	142

Error

6.5b

Counts

142 → 12

Compiler

Compiled 3860 to 651 computations (83.1% saved)

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	441	1836
1	441	1836

regimes1.1s (12.1%)

Compiler: Compiled 3558 to 2124 computations (40.3% saved)

bsearch32.0ms (0.4%)

Steps

Iters	Range		Point
2	3.259171884535959e-89	3.7213833768997876e-89	3.6636069403543086e-89
6	-5.045126685015859e+86	-1.1486306167505172e+86	-3.451742738610391e+86

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes166.0ms (1.9%)

Compiler: Compiled 375 to 402 computations (-7.2% saved)

bsearch38.0ms (0.4%)

Steps

Iters	Range		Point
2	3.259171884535959e-89	3.7213833768997876e-89	3.432501194172394e-89
10	-8.062592021620835e-40	-6.956855420995776e-50	-2.4088045938895408e-49

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes147.0ms (1.7%)

Compiler: Compiled 255 to 288 computations (-12.9% saved)

bsearch30.0ms (0.3%)

Steps

Iters	Range		Point
2	3.259171884535959e-89	3.7213833768997876e-89	3.432501194172394e-89
7	-5.37849589326646e-92	-9.87264692979017e-94	-1.9940217110596974e-92

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes109.0ms (1.3%)

Compiler: Compiled 234 to 267 computations (-14.1% saved)

bsearch40.0ms (0.5%)

Steps

Iters	Range		Point
11	-3.4039374770558263e-299	9.819302712786404e-286	3.9601360834155e-310

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes96.0ms (1.1%)

Compiler: Compiled 162 to 207 computations (-27.8% saved)

bsearch32.0ms (0.4%)

Steps

Iters	Range		Point
10	1.6601534123058575e-267	4.370529579559701e-256	2.0239955054116272e-261

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.3%)

Compiler: Compiled 45 to 87 computations (-93.3% saved)

bsearch0.0ms (0%)

regimes29.0ms (0.3%)

Accuracy

Total 4.4b remaining (44.2%)

Threshold costs 0b (0%)

Compiler

Compiled 30 to 69 computations (-130% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 141 to 110 computations (22% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	206
1	91	206

end0.0ms (0%)

sample2.1s (24.1%)

Algorithm

1×

intervals

Results

255.0ms	1191×	body	2048	valid
242.0ms	5138×	body	128	valid
118.0ms	721×	body	1024	valid
102.0ms	394×	body	4096	valid
47.0ms	365×	body	512	valid
31.0ms	762×	body	128	nan
16.0ms	191×	body	256	valid
11.0ms	247×	body	128	invalid

Compiler

Compiled 1339 to 826 computations (38.3% saved)

Pareto

0.6309636770209591

Details

analyze607.0ms (7%)

sample43.0ms (0.5%)

simplify169.0ms (1.9%)

prune8.0ms (0.1%)

localize11.0ms (0.1%)

rewrite46.0ms (0.5%)

series559.0ms (6.4%)

simplify54.0ms (0.6%)

prune232.0ms (2.7%)

localize10.0ms (0.1%)

rewrite52.0ms (0.6%)

series542.0ms (6.2%)

simplify80.0ms (0.9%)

prune182.0ms (2.1%)

localize11.0ms (0.1%)

rewrite113.0ms (1.3%)

series556.0ms (6.4%)

simplify219.0ms (2.5%)

prune527.0ms (6.1%)

localize12.0ms (0.1%)

rewrite33.0ms (0.4%)

series510.0ms (5.9%)

simplify64.0ms (0.7%)

prune112.0ms (1.3%)

simplify30.0ms (0.4%)

regimes1.1s (12.1%)

bsearch32.0ms (0.4%)

regimes166.0ms (1.9%)

bsearch38.0ms (0.4%)

regimes147.0ms (1.7%)

bsearch30.0ms (0.3%)

regimes109.0ms (1.3%)

bsearch40.0ms (0.5%)

regimes96.0ms (1.1%)

bsearch32.0ms (0.4%)

regimes30.0ms (0.3%)

bsearch0.0ms (0%)

regimes29.0ms (0.3%)

bsearch8.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.1s (24.1%)

Profiling