Details

analyze963.0ms (11.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample2.8s (33.9%)

Results

1.5s	10899×	body	128	invalid
1.2s	8256×	body	128	valid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify127.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
522×	`fma-def_binary64`
417×	`neg-sub0_binary64`
408×	`neg-mul-1_binary64`
378×	`prod-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	51	25
3	102	25
4	219	25
5	464	25
6	1225	25
7	2416	25
8	3703	25
9	4714	25
10	4874	25
11	4224	25
12	4608	25
13	4555	25
14	4942	25

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 77 to 57 computations (26% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

series449.0ms (5.4%)

Counts

3 → 64

Calls

3 calls:

418.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
29.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
3.0ms	(sqrt.f64 (exp.f64 t))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`associate-r_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

11.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
6.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
1.0ms	(sqrt.f64 (exp.f64 t))

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
658×	`fma-def_binary64`
291×	`associate-l_binary64`
267×	`associate-r_binary64`
256×	`distribute-rgt-in_binary64`

Counts

136 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3670
1	495	3220
2	1783	3055
3	4590	3055
4	5133	3055

prune130.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	123	8	131
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	9	132

Error

0.0b

Counts

132 → 9

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	33.7b	(.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (.f64 (cbrt.f64 (sqrt.f64 (.f64 z 2))) (cbrt.f64 (sqrt.f64 (.f64 z 2))))) (cbrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	34.0b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (cbrt.f64 (-.f64 (.f64 x 1/2) y))) (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	41.7b	(.f64 (/.f64 (.f64 (-.f64 (pow.f64 (.f64 x 1/2) 3) (pow.f64 y 3)) (sqrt.f64 (.f64 z 2))) (+.f64 (.f64 (.f64 x 1/2) (.f64 x 1/2)) (+.f64 (.f64 y y) (.f64 (.f64 x 1/2) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 3803 to 2258 computations (40.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.0b	(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.5b	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series621.0ms (7.5%)

Counts

3 → 60

Calls

3 calls:

465.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))

150.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

5.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`prod-exp_binary64`
19×	`add-cbrt-cube_binary64`
17×	`associate-r_binary64`

Counts

3 → 90

Calls

3 calls:

10.0ms

(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))

10.0ms

(*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

8.0ms

(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

simplify212.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-neg_binary64`
524×	`cancel-sign-sub-inv_binary64`
408×	`associate-l_binary64`
371×	`associate-r_binary64`
291×	`distribute-rgt-in_binary64`

Counts

150 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	4875
1	622	3816
2	2407	3714
3	4506	3712
4	4994	3712
5	4975	3712

prune172.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	170	7	177

Error

Counts

177 → 7

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	33.7b	(.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.6b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.7b	(.f64 (.f64 (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

Compiler

Compiled 4811 to 2768 computations (42.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.3b	(.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))
✓	0.5b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

series253.0ms (3%)

Counts

3 → 84

Calls

3 calls:

198.0ms

(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

31.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

23.0ms

(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`distribute-lft-in_binary64`
35×	`distribute-rgt-in_binary64`
34×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`

Counts

3 → 128

Calls

3 calls:

11.0ms

(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

9.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

8.0ms

(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))

simplify127.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-l_binary64`
565×	`associate-r_binary64`
488×	`distribute-rgt-in_binary64`
329×	`cancel-sign-sub-inv_binary64`
293×	`fma-neg_binary64`

Counts

212 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	5929
1	623	5031
2	2710	4816
3	4986	4816

prune162.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	213	6	219

Error

Counts

219 → 6

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.7b	(.f64 (.f64 (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

Compiler

Compiled 5887 to 2997 computations (49.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (exp.f64 t))
	0.3b	(.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

series67.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
30.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`distribute-lft-in_binary64`
112×	`distribute-rgt-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
36×	`prod-diff_binary64`
32×	`*-un-lft-identity_binary64`

Counts

2 → 143

Calls

2 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

simplify177.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

504×	`exp-prod_binary64`
397×	`distribute-rgt-in_binary64`
379×	`distribute-lft-in_binary64`
378×	`associate-l_binary64`
363×	`associate-r_binary64`

Counts

191 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	5492
1	372	4999
2	1453	4301
3	4109	4231
4	4924	4231
5	5160	4231

prune220.0ms (2.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	259	6	265

Error

Counts

265 → 6

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))) (sqrt.f64 z))
	0.7b	(.f64 (.f64 (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

Compiler

Compiled 8686 to 5038 computations (42% saved)

regimes1.4s (16.7%)

Accuracy

Total 0.3b remaining (92.6%)

Threshold costs 0.3b (92.6%)

Counts

86 → 1

Compiler

Compiled 30257 to 23007 computations (24% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	27	25
3	29	25
4	30	25
5	30	25

end118.0ms (1.4%)

Compiler: Compiled 180 to 137 computations (23.9% saved)

Details

analyze963.0ms (11.6%)

sample2.8s (33.9%)

simplify127.0ms (1.5%)

prune4.0ms (0%)

localize13.0ms (0.2%)

series449.0ms (5.4%)

rewrite22.0ms (0.3%)

simplify106.0ms (1.3%)

prune130.0ms (1.6%)

localize12.0ms (0.1%)

series621.0ms (7.5%)

rewrite35.0ms (0.4%)

simplify212.0ms (2.5%)

prune172.0ms (2.1%)

localize12.0ms (0.1%)

series253.0ms (3%)

rewrite40.0ms (0.5%)

simplify127.0ms (1.5%)

prune162.0ms (1.9%)

localize17.0ms (0.2%)

series67.0ms (0.8%)

rewrite43.0ms (0.5%)

simplify177.0ms (2.1%)

prune220.0ms (2.7%)

regimes1.4s (16.7%)

simplify3.0ms (0%)

end118.0ms (1.4%)

Profiling