Details

analyze1.7s (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample305.0ms (2%)

Algorithm

1×

intervals

Results

171.0ms	164×	body	1024	valid
26.0ms	39×	body	512	valid
7.0ms	44×	body	128	valid
3.0ms	9×	body	256	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

645×	`associate-/r*_binary64`
634×	`sqr-pow_binary64`
394×	`associate-l_binary64`
373×	`cube-prod_binary64`
368×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	26	18
2	40	18
3	68	18
4	141	18
5	348	18
6	1055	18
7	1796	18
8	2484	18
9	2697	18
10	2968	18
11	3311	18
12	3705	18
13	4603	18
14	4799	18

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	6.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 ky)
✓	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.1b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

series355.0ms (2.4%)

Counts

4 → 88

Calls

4 calls:

199.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
125.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
30.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms	(sin.f64 ky)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
3.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	(sin.f64 ky)
0.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify215.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
308×	`fma-neg_binary64`
224×	`sub-neg_binary64`
206×	`fma-def_binary64`
164×	`*-commutative_binary64`

Counts

170 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	335	4685
1	930	4356
2	3235	4356
3	4863	4352
4	4990	4352
5	4997	4352
6	4999	4352
7	4954	4352

prune183.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	208	8	216
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	210	8	218

Error

0.0b

Counts

218 → 8

Alt Table

Status	Error	Program
	33.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	33.7b	(log.f64 (exp.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
▶	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (cbrt.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))) (cbrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	7.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	33.3b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))

Compiler

Compiled 5777 to 2198 computations (62% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.1b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	0.1b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))

series410.0ms (2.8%)

Counts

3 → 84

Calls

3 calls:

226.0ms

(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))

131.0ms

(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

52.0ms

(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
103×	`add-sqr-sqrt_binary64`
91×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

3 → 181

Calls

3 calls:

11.0ms

(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))

4.0ms

(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

2.0ms

(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

simplify166.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

453×	`cancel-sign-sub-inv_binary64`
248×	`associate-r_binary64`
232×	`fma-def_binary64`
219×	`sub-neg_binary64`
198×	`*-commutative_binary64`

Counts

265 → 342

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	7761
1	1001	7004
2	3670	6977
3	4959	6977

prune298.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	373	2	375
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	376	7	383

Error

0.0b

Counts

383 → 7

Alt Table

Status	Error	Program
	33.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.3b	(.f64 (/.f64 1 (.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky)))) (sin.f64 th))
	33.3b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	7.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
▶	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Compiler

Compiled 10651 to 3880 computations (63.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 ky)
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
	0.1b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	0.1b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series203.0ms (1.4%)

Counts

1 → 36

Calls

1 calls:

202.0ms

(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

1 → 72

Calls

1 calls:

5.0ms

(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

simplify125.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

939×	`times-frac_binary64`
436×	`fma-def_binary64`
325×	`fma-neg_binary64`
230×	`cancel-sign-sub-inv_binary64`
162×	`neg-sub0_binary64`

Counts

108 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	271	4113
1	693	3975
2	2360	3911
3	4564	3898
4	5064	3898

prune195.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	260	7	267

Error

Counts

267 → 7

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky))))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	33.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	32.1b	(.f64 (/.f64 (sqrt.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 th))))
	33.3b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	7.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))

Compiler

Compiled 6830 to 2244 computations (67.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.1b	(/.f64 1 (sin.f64 ky))
✓	0.1b	(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky))))
✓	0.3b	(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky)))

series291.0ms (2%)

Counts

3 → 64

Calls

3 calls:

202.0ms	(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky))))
83.0ms	(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky)))
6.0ms	(/.f64 1 (sin.f64 ky))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 100

Calls

3 calls:

6.0ms	(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky)))
6.0ms	(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky))))
3.0ms	(/.f64 1 (sin.f64 ky))

simplify125.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
355×	`cancel-sign-sub-inv_binary64`
316×	`fma-neg_binary64`
224×	`associate-/l/_binary64`
166×	`times-frac_binary64`

Counts

164 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	4211
1	808	3717
2	2772	3518
3	4868	3518
4	5003	3518

prune193.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	221	7	228

Error

Counts

228 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 ky))))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	33.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	32.1b	(.f64 (/.f64 (sqrt.f64 (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 th))))
	33.3b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	7.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))

Compiler

Compiled 5520 to 2446 computations (55.7% saved)

regimes3.4s (23.1%)

Accuracy

Total 0.2b remaining (79.9%)

Threshold costs 0.2b (79.9%)

Counts

277 → 1

Compiler

Compiled 47642 to 30867 computations (35.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	15	18
2	14	18

end1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample6.5s (43.5%)

Algorithm

1×

intervals

Results

4.7s	4606×	body	1024	valid
865.0ms	1420×	body	512	valid
231.0ms	1433×	body	128	valid
204.0ms	530×	body	256	valid
21.0ms	11×	body	2048	valid

Compiler

Compiled 174 to 114 computations (34.5% saved)

Details

analyze1.7s (11.3%)

sample305.0ms (2%)

simplify82.0ms (0.6%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series355.0ms (2.4%)

rewrite15.0ms (0.1%)

simplify215.0ms (1.4%)

prune183.0ms (1.2%)

localize10.0ms (0.1%)

series410.0ms (2.8%)

rewrite36.0ms (0.2%)

simplify166.0ms (1.1%)

prune298.0ms (2%)

localize9.0ms (0.1%)

series203.0ms (1.4%)

rewrite13.0ms (0.1%)

simplify125.0ms (0.8%)

prune195.0ms (1.3%)

localize10.0ms (0.1%)

series291.0ms (2%)

rewrite22.0ms (0.1%)

simplify125.0ms (0.8%)

prune193.0ms (1.3%)

regimes3.4s (23.1%)

simplify2.0ms (0%)

end1.0ms (0%)

sample6.5s (43.5%)

Profiling