Details

analyze1.8s (13.2%)

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)

sample203.0ms (1.5%)

Algorithm

1×

intervals

Results

145.0ms	141×	body	1024	valid
31.0ms	51×	body	512	valid
7.0ms	44×	body	128	valid
7.0ms	19×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify92.0ms (0.7%)

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 → 1

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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.1b	(*.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 80 to 55 computations (31.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(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))

rewrite119.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`

Counts

3 → 119

Calls

3 calls:

15.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
13.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
12.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 1772 to 316 computations (82.2% saved)

series205.0ms (1.5%)

Error

0.1b

Counts

3 → 37

Calls

3 calls:

95.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
54.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
34.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

Compiler

Compiled 2576 to 1729 computations (32.9% saved)

simplify116.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
402×	`cancel-sign-sub-inv_binary64`
195×	`fma-neg_binary64`
186×	`unswap-sqr_binary64`
177×	`associate-r_binary64`

Counts

156 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	3226
1	718	2952
2	2824	2873
3	4997	2873
4	5017	2873

prune75.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

Counts

105 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (cbrt.f64 (sin.f64 ky)))) (sin.f64 th))
	2.7b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	4.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	0.5b	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
▶	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
	2.7b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	28.6b	(.f64 (sqrt.f64 (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sqrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 2065 to 812 computations (60.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
0.3b	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))

rewrite109.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
12×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

3 → 123

Calls

3 calls:

14.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
13.0ms	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
9.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

Compiler

Compiled 1955 to 321 computations (83.6% saved)

series230.0ms (1.7%)

Error

Counts

3 → 44

Calls

3 calls:

94.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
74.0ms	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
36.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

Compiler

Compiled 3082 to 2011 computations (34.8% saved)

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
441×	`cancel-sign-sub-inv_binary64`
209×	`times-frac_binary64`
198×	`associate-r_binary64`
188×	`associate-/r*_binary64`

Counts

167 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	3694
1	762	3239
2	3165	3160
3	5223	3160

prune43.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	73	8	81

Error

Counts

81 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (cbrt.f64 (sin.f64 ky)))) (sin.f64 th))
	2.7b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	4.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	0.5b	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
	2.7b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
▶	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	28.6b	(.f64 (sqrt.f64 (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sqrt.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 1614 to 687 computations (57.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
0.2b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
0.2b	(/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

rewrite167.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-cube-cbrt_binary64`
24×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 165

Calls

4 calls:

15.0ms	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
14.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
14.0ms	(/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
13.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

Compiler

Compiled 2603 to 960 computations (63.1% saved)

series257.0ms (1.9%)

Error

Counts

4 → 47

Calls

4 calls:

92.0ms	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
52.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
46.0ms	(/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
35.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

Compiler

Compiled 3216 to 2198 computations (31.7% saved)

simplify142.0ms (1%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
236×	`associate-r_binary64`
230×	`fma-neg_binary64`
190×	`associate-l_binary64`
185×	`times-frac_binary64`

Counts

212 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	4041
1	843	3647
2	3407	3474
3	4848	3474
4	4960	3474

prune57.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	114	7	121

Error

Counts

121 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (cbrt.f64 (sin.f64 ky)))) (sin.f64 th))
	4.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	0.5b	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
	2.7b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	0.6b	(.f64 (.f64 (sin.f64 ky) (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) -1/2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) -1/2))) (sin.f64 th))

Compiler

Compiled 2006 to 854 computations (57.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.1b	(/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
0.2b	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
0.5b	(*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

rewrite150.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
21×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 176

Calls

4 calls:

17.0ms	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
15.0ms	(/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
14.0ms	(*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
10.0ms	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

Compiler

Compiled 3746 to 518 computations (86.2% saved)

series260.0ms (1.9%)

Error

Counts

4 → 47

Calls

4 calls:

96.0ms	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
51.0ms	(/.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
46.0ms	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
38.0ms	(*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

Compiler

Compiled 3395 to 2264 computations (33.3% saved)

simplify176.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-def_binary64`
283×	`fma-neg_binary64`
228×	`associate-r_binary64`
212×	`times-frac_binary64`
165×	`associate-l_binary64`

Counts

223 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	348	4188
1	881	3815
2	3483	3691
3	4899	3691
4	4991	3691
5	4925	3691

prune87.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (cbrt.f64 (sin.f64 ky)))) (sin.f64 th))
	4.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	0.5b	(.f64 (/.f64 (sin.f64 ky) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
	2.7b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	0.6b	(.f64 (.f64 (sin.f64 ky) (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) -1/2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) -1/2))) (sin.f64 th))

Compiler

Compiled 2633 to 940 computations (64.3% saved)

regimes1.9s (14.1%)

Accuracy

Total 0.2b remaining (81.3%)

Threshold costs 0.2b (81.3%)

Compiler

Compiled 32389 to 20821 computations (35.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	23	22
2	34	22
3	43	22
4	47	22
5	48	22
6	48	22

end1.0ms (0%)

Compiler: Compiled 16 to 11 computations (31.3% saved)

sample7.2s (53.3%)

Algorithm

1×

intervals

Results

5.5s	4673×	body	1024	valid
835.0ms	1396×	body	512	valid
244.0ms	1387×	body	128	valid
192.0ms	528×	body	256	valid
30.0ms	16×	body	2048	valid

Compiler

Compiled 173 to 111 computations (35.8% saved)

Details

analyze1.8s (13.2%)

sample203.0ms (1.5%)

simplify92.0ms (0.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite119.0ms (0.9%)

series205.0ms (1.5%)

simplify116.0ms (0.9%)

prune75.0ms (0.5%)

localize9.0ms (0.1%)

rewrite109.0ms (0.8%)

series230.0ms (1.7%)

simplify101.0ms (0.7%)

prune43.0ms (0.3%)

localize12.0ms (0.1%)

rewrite167.0ms (1.2%)

series257.0ms (1.9%)

simplify142.0ms (1%)

prune57.0ms (0.4%)

localize14.0ms (0.1%)

rewrite150.0ms (1.1%)

series260.0ms (1.9%)

simplify176.0ms (1.3%)

prune87.0ms (0.6%)

regimes1.9s (14.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample7.2s (53.3%)

Profiling