Details

analyze947.0ms (8.3%)

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)

sample129.0ms (1.1%)

Algorithm

1×

intervals

Results

48.0ms	191×	body	128	valid
36.0ms	30×	body	1024	valid
18.0ms	21×	body	512	valid
7.0ms	14×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify61.0ms (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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(/.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))))))
1.6b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.1b	(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)))))

rewrite168.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 113

Calls

4 calls:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(/.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))))))
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 kx) 2)

Compiler

Compiled 4229 to 3201 computations (24.3% saved)

series527.0ms (4.6%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

242.0ms	(/.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))))))
162.0ms	(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)))))
84.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 5281 to 4376 computations (17.1% saved)

simplify178.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

376×	`distribute-rgt-in_binary64`
364×	`distribute-lft-in_binary64`
350×	`times-frac_binary64`
300×	`unswap-sqr_binary64`
163×	`associate-l_binary64`

Counts

167 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	6270
1	671	5923
2	2020	5585
3	4808	5585
4	5066	5585

prune135.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	2	141

Error

0.0b

Counts

141 → 2

Alt Table

Status	Error	Program
	0.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))))
▶	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))))

Status

Error

Program

0.5b

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

▶

0.0b

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

Compiler

Compiled 3578 to 2668 computations (25.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))
0.4b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))
2.1b	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))
11.1b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))))

rewrite213.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

69×	`add-cbrt-cube_binary64`
69×	`add-exp-log_binary64`
32×	`cbrt-unprod_binary64`
32×	`prod-exp_binary64`
29×	`*-un-lft-identity_binary64`

Counts

4 → 142

Calls

4 calls:

17.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))
12.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))
5.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))))

Compiler

Compiled 6458 to 4535 computations (29.8% saved)

series600.0ms (5.3%)

Error

0.0b

Counts

4 → 65

Calls

4 calls:

248.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))
163.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))))
83.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om)))
71.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))

Compiler

Compiled 6136 to 5048 computations (17.7% saved)

simplify224.0ms (2%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-/r/_binary64`
345×	`associate-r_binary64`
290×	`associate-l_binary64`
218×	`*-commutative_binary64`
196×	`associate-/l/_binary64`

Counts

207 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	336	8653
1	839	7811
2	2985	7447
3	4621	7445
4	4987	7445

prune138.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	182	2	184

Error

0.0b

Counts

184 → 2

Alt Table

Status	Error	Program
▶	0.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))))

Status

Error

Program

▶

0.5b

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

✓

0.0b

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

Compiler

Compiled 4417 to 3026 computations (31.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
1.6b	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
3.0b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
11.1b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

rewrite835.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
39×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64`
25×	`log-pow_binary64`

Counts

4 → 129

Calls

4 calls:

14.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
7.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
5.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

Compiler

Compiled 5472 to 4213 computations (23% saved)

series850.0ms (7.4%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

364.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
211.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
156.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
83.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 6668 to 5567 computations (16.5% saved)

simplify210.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

403×	`times-frac_binary64`
387×	`associate-/l*_binary64`
334×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`
151×	`unswap-sqr_binary64`

Counts

195 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	8029
1	627	7593
2	1754	7148
3	4764	7148
4	4962	7148

prune222.0ms (1.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	177	2	179

Error

0.0b

Counts

179 → 2

Alt Table

Status	Error	Program
	0.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (/.f64 (.f64 2 l) Om))))))))

Status

Error

Program

0.5b

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

0.0b

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

Compiler

Compiled 4981 to 3731 computations (25.1% saved)

regimes2.2s (19.6%)

Accuracy

Total 0.0b remaining (0.3%)

Threshold costs 0.0b (0.3%)

Compiler

Compiled 56382 to 47518 computations (15.7% saved)

simplify3.0ms (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

end8.0ms (0.1%)

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

sample3.7s (32.1%)

Algorithm

1×

intervals

Results

1.6s	6377×	body	128	valid
929.0ms	763×	body	1024	valid
463.0ms	533×	body	512	valid
175.0ms	327×	body	256	valid

Compiler

Compiled 135 to 115 computations (14.8% saved)

Details

analyze947.0ms (8.3%)

sample129.0ms (1.1%)

simplify61.0ms (0.5%)

prune4.0ms (0%)

localize20.0ms (0.2%)

rewrite168.0ms (1.5%)

series527.0ms (4.6%)

simplify178.0ms (1.6%)

prune135.0ms (1.2%)

localize18.0ms (0.2%)

rewrite213.0ms (1.9%)

series600.0ms (5.3%)

simplify224.0ms (2%)

prune138.0ms (1.2%)

localize24.0ms (0.2%)

rewrite835.0ms (7.3%)

series850.0ms (7.4%)

simplify210.0ms (1.8%)

prune222.0ms (1.9%)

regimes2.2s (19.6%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample3.7s (32.1%)

Profiling