Details

analyze806.0ms (4.7%)

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)

sample79.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	171×	body	128	valid
13.0ms	31×	body	2048	valid
7.0ms	14×	body	4096	valid
7.0ms	22×	body	1024	valid
3.0ms	11×	body	512	valid
2.0ms	25×	body	128	nan
1.0ms	7×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify311.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune8.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

34.4b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize33.0ms (0.2%)

Local error

Found 8 expressions with local error:

23.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.3b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite81.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 96

Calls

8 calls:

23.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
19.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
11.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

series1.2s (6.9%)

Counts

4 → 74

Calls

4 calls:

386.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
290.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
280.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
227.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1997 to 1629 computations (18.4% saved)

simplify146.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4939	3526
1	4939	3526

prune348.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	158	12	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	12	171

Error

5.9b

Counts

171 → 12

Compiler

Compiled 3232 to 706 computations (78.2% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

10.7b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
2.3b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
2.3b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.7b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
23.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite101.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 129

Calls

8 calls:

26.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
21.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series1.5s (8.7%)

Counts

4 → 78

Calls

4 calls:

487.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
468.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
298.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
254.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2735 to 1994 computations (27.1% saved)

simplify201.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4958	5432
1	4958	5432

prune299.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	211	8	219

Error

5.9b

Counts

219 → 8

Compiler

Compiled 4845 to 979 computations (79.8% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

23.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite67.0ms (0.4%)

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×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

8 calls:

25.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series1.2s (6.8%)

Counts

4 → 78

Calls

4 calls:

422.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
321.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
231.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
208.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2344 to 1899 computations (19% saved)

simplify132.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5228	3378

prune225.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	164	7	171

Error

5.9b

Counts

171 → 7

Compiler

Compiled 3328 to 1031 computations (69% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.3b	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
2.3b	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
2.5b	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
23.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite93.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`associate-r_binary64`
22×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`difference-of-squares_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `associate-l*_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
2×	`associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 99

Calls

8 calls:

29.0ms	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
24.0ms	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series1.4s (8.4%)

Counts

4 → 78

Calls

4 calls:

478.0ms	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
420.0ms	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
304.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
245.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2735 to 2029 computations (25.8% saved)

simplify168.0ms (1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4969	3752
1	4969	3752

prune232.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	176	8	184

Error

5.9b

Counts

184 → 8

Compiler

Compiled 3760 to 895 computations (76.2% saved)

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	1786	1226
1	1786	1226

regimes1.3s (7.3%)

Accuracy

Total 1.1b remaining (17.6%)

Threshold costs 0b (0%)

Compiler

Compiled 3321 to 2257 computations (32% saved)

bsearch153.0ms (0.9%)

Steps

Iters	Range	Point
12	5.319674851868761e+62	1.7193923204947955e+106	1.6550855570993975e+91
5	-1.8072510287730896e-293	-6.810377341466479e-294	-6.943016465332528e-294
8	-2.896882628819812e+127	-9.970494331055357e+124	-1.6307928858729175e+125

Iters

Range

Point

5.319674851868761e+62

1.7193923204947955e+106

1.6550855570993975e+91

-1.8072510287730896e-293

-6.810377341466479e-294

-6.943016465332528e-294

-2.896882628819812e+127

-9.970494331055357e+124

-1.6307928858729175e+125

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	81
1	101	81

end0.0ms (0%)

sample7.0s (40.7%)

Algorithm

1×

intervals

Results

422.0ms	1134×	body	2048	valid
404.0ms	5218×	body	128	valid
217.0ms	730×	body	1024	valid
172.0ms	373×	body	4096	valid
84.0ms	361×	body	512	valid
58.0ms	812×	body	128	nan
29.0ms	184×	body	256	valid
20.0ms	268×	body	128	invalid

Compiler

Compiled 2501 to 1670 computations (33.2% saved)

Pareto

-0.11988883678150636

Details

analyze806.0ms (4.7%)

sample79.0ms (0.5%)

simplify311.0ms (1.8%)

prune8.0ms (0%)

localize33.0ms (0.2%)

rewrite81.0ms (0.5%)

series1.2s (6.9%)

simplify146.0ms (0.8%)

prune348.0ms (2%)

localize20.0ms (0.1%)

rewrite101.0ms (0.6%)

series1.5s (8.7%)

simplify201.0ms (1.2%)

prune299.0ms (1.7%)

localize19.0ms (0.1%)

rewrite67.0ms (0.4%)

series1.2s (6.8%)

simplify132.0ms (0.8%)

prune225.0ms (1.3%)

localize26.0ms (0.1%)

rewrite93.0ms (0.5%)

series1.4s (8.4%)

simplify168.0ms (1%)

prune232.0ms (1.3%)

simplify107.0ms (0.6%)

regimes1.3s (7.3%)

bsearch153.0ms (0.9%)

simplify6.0ms (0%)

end0.0ms (0%)

sample7.0s (40.7%)

Profiling