Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify299.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (289.0ms)

Iter	Nodes	Cost
0	4988	37
1	4988	37

prune7.0ms (0.1%)

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: 1.1b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
7.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
11.2b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite93.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`flip3-+_binary64` `flip-+_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r/_binary64`
16×	`frac-times_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
13×	`pow1_binary64`
11×	`swap-sqr_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
9×	`associate-l_binary64`
8×	`associate-*r/_binary64`
7×	`associate-/l/_binary64`
6×	`associate-/r*_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 158

Calls

4 calls:

28.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series63.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
22.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
13.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
5.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5332	3970

prune369.0ms (6.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	160	10	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Merged error: 0.0b

Counts

172 → 11

Compiler

Compiled 5391 to 3501 computations (35.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
7.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite163.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

769×	`*-un-lft-identity_binary64`
364×	`times-frac_binary64`
331×	`distribute-lft-out_binary64`
224×	`sqrt-prod_binary64`
206×	`add-sqr-sqrt_binary64`
131×	`add-cube-cbrt_binary64`
127×	`swap-sqr_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
45×	`associate-l_binary64`
42×	`associate-r_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
16×	`pow1_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-/l/_binary64` `associate-*r/_binary64`
12×	`associate-/r/_binary64`
11×	`associate-*l/_binary64`
10×	`associate-/r*_binary64` `unswap-sqr_binary64`
8×	`associate-/l*_binary64`
6×	`div-inv_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 388

Calls

4 calls:

49.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
37.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
31.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
16.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series74.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
22.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
18.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

simplify160.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

400 → 400

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5255	11912

prune793.0ms (14.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	398	2	400
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	401	10	411

Merged error: 0.0b

Counts

411 → 10

Compiler

Compiled 14191 to 9572 computations (32.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.1b	(.f64 (.f64 (+.f64 alpha 1) (*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
7.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite173.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

781×	`*-un-lft-identity_binary64`
374×	`times-frac_binary64`
334×	`distribute-lft-out_binary64`
224×	`sqrt-prod_binary64`
213×	`add-sqr-sqrt_binary64`
142×	`add-exp-log_binary64`
138×	`add-cube-cbrt_binary64`
127×	`swap-sqr_binary64`
92×	`add-cbrt-cube_binary64`
73×	`prod-exp_binary64`
63×	`associate-r_binary64`
46×	`associate-l_binary64`
43×	`cbrt-unprod_binary64`
39×	`frac-times_binary64`
37×	`div-exp_binary64`
27×	`associate-*l/_binary64`
25×	`pow1_binary64`
23×	`cbrt-undiv_binary64`
20×	`associate-*r/_binary64`
19×	`flip3-+_binary64` `flip-+_binary64`
12×	`associate-/r/_binary64`
10×	`pow-prod-down_binary64` `unswap-sqr_binary64`
7×	`associate-/l*_binary64`
6×	`1-exp_binary64` `rec-exp_binary64` `div-inv_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l/_binary64` `sqrt-div_binary64`
1×	`pow-prod-up_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 435

Calls

4 calls:

47.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
45.0ms	(.f64 (.f64 (+.f64 alpha 1) (*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
35.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series76.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
24.0ms	(.f64 (.f64 (+.f64 alpha 1) (*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
12.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

simplify178.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

447 → 447

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5074	13790

prune1.0s (18.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	445	2	447
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	447	10	457

Merged error: 0b

Counts

457 → 10

Compiler

Compiled 16200 to 11192 computations (30.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
0.0b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 beta alpha) 2))
0.1b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))

rewrite98.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64`
80×	`add-exp-log_binary64`
68×	`times-frac_binary64`
57×	`distribute-lft-out_binary64`
52×	`add-cbrt-cube_binary64`
51×	`add-sqr-sqrt_binary64`
47×	`associate-r_binary64`
39×	`add-cube-cbrt_binary64`
30×	`div-exp_binary64`
28×	`prod-exp_binary64`
18×	`cbrt-undiv_binary64`
16×	`cbrt-unprod_binary64`
15×	`associate-l_binary64`
10×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `flip-+_binary64`
8×	`pow1_binary64`
7×	`associate-/l/_binary64`
5×	`unswap-sqr_binary64` `associate-/l_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`associate-*r/_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`un-div-inv_binary64`

Counts

4 → 201

Calls

4 calls:

35.0ms	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
22.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 beta alpha) 2))
21.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series67.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
21.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 beta alpha) 2))
15.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
6.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4971	5695
1	4971	5695

prune232.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	213	10	223

Merged error: 0b

Counts

223 → 10

Compiler

Compiled 6963 to 4542 computations (34.8% saved)

regimes88.0ms (1.6%)

Compiler: Compiled 670 to 502 computations (25.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	27	40

end0.0ms (0%)

sample1.3s (24%)

Algorithm

1×

intervals

Results

469.0ms	8000×	body	80	valid
124.0ms	8000×	pre	80	true

Compiler

Compiled 402 to 298 computations (25.9% saved)

Details

analyze4.0ms (0.1%)

sample25.0ms (0.5%)

simplify299.0ms (5.4%)

prune7.0ms (0.1%)

localize16.0ms (0.3%)

rewrite93.0ms (1.7%)

series63.0ms (1.1%)

simplify83.0ms (1.5%)

prune369.0ms (6.7%)

localize14.0ms (0.2%)

rewrite163.0ms (2.9%)

series74.0ms (1.3%)

simplify160.0ms (2.9%)

prune793.0ms (14.3%)

localize16.0ms (0.3%)

rewrite173.0ms (3.1%)

series76.0ms (1.4%)

simplify178.0ms (3.2%)

prune1.0s (18.2%)

localize16.0ms (0.3%)

rewrite98.0ms (1.8%)

series67.0ms (1.2%)

simplify93.0ms (1.7%)

prune232.0ms (4.2%)

regimes88.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (24%)

Profiling