Details

analyze995.0ms (7.1%)

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
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample120.0ms (0.9%)

Algorithm

1×

intervals

Results

45.0ms	204×	body	128	valid
38.0ms	26×	body	1024	valid
13.0ms	17×	body	512	valid
4.0ms	9×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
437×	`associate-r_binary64`
407×	`distribute-rgt-out_binary64`
369×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	39
2	107	39
3	429	39
4	2037	39
5	4850	39
6	4809	39
7	5523	39

prune4.0ms (0%)

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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))

Compiler

Compiled 87 to 75 computations (13.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
2.9b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.9b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite139.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 90

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
2.0ms	(pow.f64 (sin.f64 ky) 2)
2.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3007 to 2262 computations (24.8% saved)

series414.0ms (2.9%)

Error

0.2b

Counts

4 → 40

Calls

4 calls:

190.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
145.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 kx) 2)
13.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3692 to 3071 computations (16.8% saved)

simplify248.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

352×	`distribute-rgt-in_binary64`
338×	`distribute-lft-in_binary64`
324×	`unswap-sqr_binary64`
319×	`times-frac_binary64`
171×	`associate-r_binary64`

Counts

130 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	4162
1	684	3954
2	1985	3562
3	4804	3562
4	4969	3562

prune153.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	2	107

Error

0.0b

Counts

107 → 2

Alt Table

Status	Error	Program
▶	28.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
✓	0.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))

Status

Error

Program

▶

28.6b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (*.f64 l (sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))

✓

0.8b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))

Compiler

Compiled 2185 to 1608 computations (26.4% saved)

localize57.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.9b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
2.9b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
29.6b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
30.0b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite586.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

51×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`

Counts

4 → 144

Calls

4 calls:

81.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
65.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
11.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
9.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 8249 to 5463 computations (33.8% saved)

series609.0ms (4.3%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

244.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
205.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
52.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
51.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 4785 to 3462 computations (27.6% saved)

simplify295.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

887×	`times-frac_binary64`
800×	`associate-/l*_binary64`
272×	`associate-/r/_binary64`
194×	`associate-/l/_binary64`
122×	`*-commutative_binary64`

Counts

181 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	6208
1	789	5780
2	2013	5698
3	5446	5698

prune224.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	130	2	132

Error

0.0b

Counts

132 → 2

Alt Table

Status	Error	Program
✓	28.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
✓	0.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))

Status

Error

Program

✓

28.6b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (*.f64 l (sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (*.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))

✓

0.8b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))

Compiler

Compiled 4822 to 3131 computations (35.1% saved)

regimes3.9s (28%)

Accuracy

Total 0.6b remaining (79.2%)

Threshold costs 0.6b (79.2%)

Compiler

Compiled 57048 to 45644 computations (20% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	30	45
2	29	45

end15.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 99 to 81 computations (18.2% saved)

sample6.2s (43.9%)

Algorithm

1×

intervals

Results

2.7s	6423×	body	128	valid
1.5s	719×	body	1024	valid
855.0ms	557×	body	512	valid
268.0ms	301×	body	256	valid

Compiler

Compiled 154 to 126 computations (18.2% saved)

Details

analyze995.0ms (7.1%)

sample120.0ms (0.9%)

simplify67.0ms (0.5%)

prune4.0ms (0%)

localize22.0ms (0.2%)

rewrite139.0ms (1%)

series414.0ms (2.9%)

simplify248.0ms (1.8%)

prune153.0ms (1.1%)

localize57.0ms (0.4%)

rewrite586.0ms (4.2%)

series609.0ms (4.3%)

simplify295.0ms (2.1%)

prune224.0ms (1.6%)

regimes3.9s (28%)

simplify6.0ms (0%)

end15.0ms (0.1%)

sample6.2s (43.9%)

Profiling