Details

analyze1.0s (5.8%)

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)

sample128.0ms (0.7%)

Algorithm

1×

intervals

Results

54.0ms	203×	body	128	valid
29.0ms	25×	body	1024	valid
13.0ms	16×	body	512	valid
6.0ms	12×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
575×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
437×	`associate-r_binary64`
369×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	37
2	113	37
3	465	37
4	2149	37
5	4982	37
6	4847	37
7	4964	37

prune5.0ms (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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 113 to 95 computations (15.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 2 l) Om)
✓	0.2b	(pow.f64 (sin.f64 ky) 2)
✓	2.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	7.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64`

Counts

4 → 68

Calls

4 calls:

3.0ms	(/.f64 (*.f64 2 l) Om)
2.0ms	(pow.f64 (sin.f64 ky) 2)
1.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
0.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

series478.0ms (2.7%)

Counts

4 → 124

Calls

4 calls:

262.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
184.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
26.0ms	(/.f64 (*.f64 2 l) Om)
6.0ms	(pow.f64 (sin.f64 ky) 2)

simplify181.0ms (1%)

Algorithm

1×	egg-herbie

Rules

493×	`cancel-sign-sub-inv_binary64`
308×	`unswap-sqr_binary64`
223×	`fma-neg_binary64`
219×	`associate-r_binary64`
203×	`fma-def_binary64`

Counts

192 → 332

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	7969
1	1001	7256
2	3784	7229
3	5308	7229

prune257.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	329	3	332
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	329	4	333

Error

0.0b

Counts

333 → 4

Alt Table

Status	Error	Program
	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
▶	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))

Compiler

Compiled 8294 to 5907 computations (28.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.9b	(cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
	7.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
	7.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
	7.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 16

Calls

1 calls:

1.0ms

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

series3.9s (22%)

Counts

1 → 48

Calls

1 calls:

3.9s	(cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))

simplify145.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
373×	`unswap-sqr_binary64`
367×	`cancel-sign-sub-inv_binary64`
186×	`associate-r_binary64`
155×	`*-commutative_binary64`

Counts

64 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	6012
1	809	5739
2	3140	5627
3	5179	5627

prune780.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	955	0	955
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	955	4	959

Error

0.0b

Counts

959 → 4

Alt Table

Status	Error	Program
	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
▶	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))

Compiler

Compiled 33358 to 23718 computations (28.9% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune5.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
✓	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))

Compiler

Compiled 157 to 127 computations (19.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))
✓	0.4b	(.f64 (.f64 2 l) (sin.f64 kx))
✓	1.1b	(/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om)
✓	5.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

4 → 142

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
4.0ms	(.f64 (.f64 2 l) (sin.f64 kx))
4.0ms	(/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))
2.0ms	(/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om)

series1.9s (10.8%)

Counts

4 → 156

Calls

4 calls:

855.0ms	(/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))
547.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
464.0ms	(/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om)
38.0ms	(.f64 (.f64 2 l) (sin.f64 kx))

simplify210.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

394×	`times-frac_binary64`
366×	`associate-/r*_binary64`
327×	`associate-*r/_binary64`
327×	`associate-/l*_binary64`
298×	`fma-def_binary64`

Counts

298 → 554

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	591	12558
1	1732	11524
2	5262	11524

prune444.0ms (2.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	552	2	554
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	552	6	558

Error

Counts

558 → 6

Alt Table

Status	Error	Program
	45.6b	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
✓	33.2b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (/.f64 (hypot.f64 (.f64 (.f64 2 l) (sin.f64 kx)) (.f64 (.f64 2 l) (sin.f64 ky))) Om))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))))
	34.2b	(-.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 Om (*.f64 (sqrt.f64 1/2) l)) (sqrt.f64 (/.f64 1/4 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
✓	24.7b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 13954 to 8601 computations (38.4% saved)

regimes941.0ms (5.3%)

Accuracy

Total 1.1b remaining (97.4%)

Threshold costs 0b (0%)

Compiler

Compiled 24124 to 19470 computations (19.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	37
1	26	37
2	25	37

end8.0ms (0%)

Remove: (sort kx ky)
Compiler: Compiled 84 to 72 computations (14.3% saved)

sample7.1s (40.1%)

Algorithm

1×

intervals

Results

3.1s	6392×	body	128	valid
1.8s	722×	body	1024	valid
926.0ms	550×	body	512	valid
361.0ms	336×	body	256	valid

Compiler

Compiled 252 to 210 computations (16.7% saved)

Details

analyze1.0s (5.8%)

sample128.0ms (0.7%)

simplify63.0ms (0.4%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite9.0ms (0.1%)

series478.0ms (2.7%)

simplify181.0ms (1%)

prune257.0ms (1.5%)

localize27.0ms (0.2%)

rewrite2.0ms (0%)

series3.9s (22%)

simplify145.0ms (0.8%)

prune780.0ms (4.4%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite33.0ms (0.2%)

series1.9s (10.8%)

simplify210.0ms (1.2%)

prune444.0ms (2.5%)

regimes941.0ms (5.3%)

simplify3.0ms (0%)

end8.0ms (0%)

sample7.1s (40.1%)

Profiling