Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample35.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	59×	body	1024	valid
7.0ms	135×	body	128	valid
6.0ms	42×	body	512	valid
2.0ms	8×	body	2048	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify159.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune3.0ms (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

Merged error: 30.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

3.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`sqrt-prod_binary64_13052` `add-sqr-sqrt_binary64_13058`
10×	`*-un-lft-identity_binary64_13036`
6×	`cancel-sign-sub-inv_binary64_13002`
4×	`difference-of-squares_binary64_13005`
3×	`add-log-exp_binary64_13075` `distribute-lft-out--_binary64_12988` `add-cube-cbrt_binary64_13071`
1×	`flip--_binary64_13011` `sub-neg_binary64_13029` `flip3--_binary64_13040` `pow1_binary64_13097` `add-cbrt-cube_binary64_13072` `diff-log_binary64_13128` `distribute-lft-out_binary64_12987` `add-exp-log_binary64_13074`

Counts

1 → 24

Calls

1 calls:

15.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series67.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

67.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4981	542
1	4981	542

prune48.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.1b

Counts

28 → 2

Compiler

Compiled 417 to 273 computations (34.5% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_13036`
20×	`sqrt-prod_binary64_13052` `distribute-lft-out_binary64_12987`
18×	`times-frac_binary64_13042`
13×	`add-sqr-sqrt_binary64_13058` `add-cube-cbrt_binary64_13071`
6×	`associate-/r*_binary64_12980` `add-exp-log_binary64_13074`
4×	`add-log-exp_binary64_13075` `add-cbrt-cube_binary64_13072`
3×	`pow1_binary64_13097` `associate-/l*_binary64_12981`
2×	`associate-/r/_binary64_12982` `div-exp_binary64_13087` `flip3-+_binary64_13039` `flip-+_binary64_13010`
1×	`inv-pow_binary64_13121` `clear-num_binary64_13035` `cbrt-undiv_binary64_13070` `div-inv_binary64_13033` `pow-flip_binary64_13110` `rec-exp_binary64_13086` `1-exp_binary64_13080` `frac-2neg_binary64_13047` `sum-log_binary64_13127` `+-commutative_binary64_12966`

Counts

2 → 59

Calls

2 calls:

25.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series94.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
40.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify119.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4980	1269
1	4980	1269

prune144.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	59	8	67

Merged error: 0.0b

Counts

67 → 8

Compiler

Compiled 1191 to 853 computations (28.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

rewrite268.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_13036`
700×	`sqrt-prod_binary64_13052`
594×	`times-frac_binary64_13042`
280×	`distribute-lft-out_binary64_12987`
254×	`add-sqr-sqrt_binary64_13058`
252×	`add-cube-cbrt_binary64_13071`
36×	`associate-/l*_binary64_12981`
28×	`sqrt-div_binary64_13053`
24×	`associate-/r/_binary64_12982`
18×	`associate-/r*_binary64_12980`
17×	`add-exp-log_binary64_13074`
14×	`flip3-+_binary64_13039` `flip-+_binary64_13010`
12×	`div-inv_binary64_13033`
11×	`add-cbrt-cube_binary64_13072`
8×	`div-exp_binary64_13087` `pow1_binary64_13097`
4×	`cbrt-undiv_binary64_13070` `add-log-exp_binary64_13075`
3×	`pow1/2_binary64_13116` `pow-flip_binary64_13110` `sqrt-pow1_binary64_13054`
2×	`clear-num_binary64_13035` `rem-sqrt-square_binary64_13049` `rec-exp_binary64_13086` `1-exp_binary64_13080` `frac-2neg_binary64_13047`
1×	`inv-pow_binary64_13121` `associate-/l/_binary64_12983`

Counts

4 → 453

Calls

4 calls:

65.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
23.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
23.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
17.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series276.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
74.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
61.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
60.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

simplify420.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4903	17091
1	4903	17091

prune1.7s (19.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	460	5	465
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	464	9	473

Merged error: 0.0b

Counts

473 → 9

Compiler

Compiled 12931 to 9513 computations (26.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite236.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_13036`
290×	`sqrt-prod_binary64_13052`
172×	`times-frac_binary64_13042`
144×	`add-sqr-sqrt_binary64_13058`
116×	`distribute-lft-out_binary64_12987`
88×	`add-cube-cbrt_binary64_13071`
43×	`swap-sqr_binary64_13003`
31×	`pow1_binary64_13097`
27×	`associate-r_binary64_12976` `associate-l_binary64_12977` `sqrt-pow1_binary64_13054`
16×	`unswap-sqr_binary64_13004`
14×	`associate-/r/_binary64_12982` `add-exp-log_binary64_13074`
12×	`associate-/r*_binary64_12980`
11×	`inv-pow_binary64_13121` `pow-flip_binary64_13110`
10×	`add-cbrt-cube_binary64_13072`
9×	`div-inv_binary64_13033` `rem-sqrt-square_binary64_13049` `pow1/2_binary64_13116` `pow-prod-up_binary64_13106`
7×	`flip3-+_binary64_13039` `flip-+_binary64_13010`
6×	`associate-/l*_binary64_12981`
5×	`sqrt-div_binary64_13053` `pow-sqr_binary64_13009` `pow-prod-down_binary64_13107`
4×	`add-log-exp_binary64_13075` `div-exp_binary64_13087`
3×	`sqr-abs_binary64_13051`
2×	`clear-num_binary64_13035` `cbrt-undiv_binary64_13070` `rec-exp_binary64_13086` `1-exp_binary64_13080` `frac-2neg_binary64_13047`
1×	`pow2_binary64_13117` `rem-square-sqrt_binary64_13048` `associate-l/_binary64_12979` `sqrt-unprod_binary64_13056` `prod-exp_binary64_13085` `pow-plus_binary64_13099` `associate-r/_binary64_12978` `*-commutative_binary64_12967` `frac-times_binary64_13046` `cbrt-unprod_binary64_13069`

Counts

4 → 281

Calls

4 calls:

86.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
29.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
22.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
22.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series271.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
64.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
63.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
56.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify200.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5033	6769

prune808.0ms (9.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	294	8	302

Merged error: 0b

Counts

302 → 8

Compiler

Compiled 7328 to 5349 computations (27% saved)

regimes341.0ms (3.9%)

Compiler: Compiled 2392 to 1926 computations (19.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample3.3s (37.7%)

Algorithm

1×

intervals

Results

397.0ms	1933×	body	1024	valid
229.0ms	4316×	body	128	valid
155.0ms	1029×	body	512	valid
58.0ms	230×	body	2048	valid
48.0ms	492×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 1199 to 967 computations (19.3% saved)

Details

analyze4.0ms (0%)

sample35.0ms (0.4%)

simplify159.0ms (1.8%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite18.0ms (0.2%)

series67.0ms (0.8%)

simplify76.0ms (0.9%)

prune48.0ms (0.6%)

localize12.0ms (0.1%)

rewrite50.0ms (0.6%)

series94.0ms (1.1%)

simplify119.0ms (1.4%)

prune144.0ms (1.7%)

localize26.0ms (0.3%)

rewrite268.0ms (3.1%)

series276.0ms (3.2%)

simplify420.0ms (4.9%)

prune1.7s (19.4%)

localize20.0ms (0.2%)

rewrite236.0ms (2.7%)

series271.0ms (3.1%)

simplify200.0ms (2.3%)

prune808.0ms (9.4%)

regimes341.0ms (3.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (37.7%)

Profiling