Details

analyze1.8s (10.5%)

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)

sample8.0s (47.4%)

Results

6.2s	4805×	body	1024	valid
1.1s	1429×	body	512	valid
389.0ms	1483×	body	128	valid
279.0ms	518×	body	256	valid
47.0ms	21×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-l_binary64`
330×	`sqr-pow_binary64`
320×	`*-commutative_binary64`
275×	`associate-/r/_binary64`
269×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	26	18
2	51	18
3	79	18
4	160	18
5	450	18
6	1702	18
7	3048	18
8	3896	18
9	4149	18
10	4488	18
11	4978	18

Stop Event

1×	node limit

Counts

1 → 2

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

2.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.8b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	4.8b	(*.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)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 kx)
✓	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (sin.f64 ky) (sin.f64 th))
✓	2.9b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series239.0ms (1.4%)

Counts

4 → 88

Calls

4 calls:

206.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
23.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
8.0ms	(*.f64 (sin.f64 ky) (sin.f64 th))
1.0ms	(sin.f64 kx)

rewrite54.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

373×	`prod-diff_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
183×	`log-pow_binary64`
149×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	210	37
2	2913	37

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

52.0ms	(sin.f64 kx)
52.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
52.0ms	(*.f64 (sin.f64 ky) (sin.f64 th))
52.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
564×	`cancel-sign-sub-inv_binary64`
205×	`fma-neg_binary64`
184×	`distribute-rgt-neg-in_binary64`
174×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2524
1	675	2364
2	2521	2133

Stop Event

1×	node limit

Counts

189 → 165

prune148.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	157	8	165
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	8	167

Error

Counts

167 → 8

Alt Table

Status	Error	Program
	3.2b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	5.1b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	2.8b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.9b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
	3.7b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 3954 to 1715 computations (56.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series231.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

162.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
68.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

rewrite51.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log-prod_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
183×	`log-pow_binary64`
171×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	209	31
2	2860	31

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

49.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
49.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
382×	`cancel-sign-sub-inv_binary64`
232×	`associate-/r/_binary64`
138×	`fma-neg_binary64`
136×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2827
1	642	2459
2	2481	2219

Stop Event

1×	node limit

Counts

154 → 131

prune177.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	192	8	200

Error

Counts

200 → 8

Alt Table

Status	Error	Program
	3.0b	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th)))) 1)
	3.2b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	5.1b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	2.8b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
▶	0.3b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.9b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)

Compiler

Compiled 5227 to 2492 computations (52.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 kx)
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.3b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series310.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

156.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
154.0ms	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite93.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`log-prod_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
184×	`log-pow_binary64`
176×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	249	31
2	2890	31

Stop Event

1×	node limit

Counts

2 → 84

Calls

2 calls:

91.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
91.0ms	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
411×	`cancel-sign-sub-inv_binary64`
368×	`associate-/r/_binary64`
177×	`fma-neg_binary64`
174×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2908
1	627	2884
2	2492	2627

Stop Event

1×	node limit

Counts

156 → 133

prune186.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

Counts

202 → 8

Alt Table

Status	Error	Program
	3.0b	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th)))) 1)
	3.2b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	5.1b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	2.8b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.3b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.9b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
▶	1.2b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)

Compiler

Compiled 5154 to 2495 computations (51.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
	0.2b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
✓	7.0b	(cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))

series3.2s (19.2%)

Counts

2 → 72

Calls

2 calls:

1.7s	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
1.6s	(cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
210×	`log-pow_binary64`
171×	`prod-diff_binary64`
129×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	271	38
2	3380	38

Stop Event

1×	node limit

Counts

2 → 91

Calls

2 calls:

57.0ms	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
57.0ms	(cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

463×	`cancel-sign-sub-inv_binary64`
211×	`fma-def_binary64`
200×	`fma-neg_binary64`
174×	`distribute-rgt-neg-in_binary64`
174×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4510
1	696	4118
2	2704	3598

Stop Event

1×	node limit

Counts

163 → 142

prune244.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	273	8	281

Error

Counts

281 → 8

Alt Table

Status	Error	Program
	3.2b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	5.1b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	3.0b	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th))))
✓	1.2b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
	2.8b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.3b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.9b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 9046 to 4081 computations (54.9% saved)

regimes1.6s (9.5%)

Accuracy

Total 0.2b remaining (86.3%)

Threshold costs 0.2b (86.3%)

Counts

164 → 1

Compiler

Compiled 25749 to 17989 computations (30.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	17	18

Stop Event

1×

saturated

end124.0ms (0.7%)

Compiler: Compiled 164 to 114 computations (30.5% saved)

Details

analyze1.8s (10.5%)

sample8.0s (47.4%)

simplify44.0ms (0.3%)

prune4.0ms (0%)

localize8.0ms (0%)

series239.0ms (1.4%)

rewrite54.0ms (0.3%)

simplify52.0ms (0.3%)

prune148.0ms (0.9%)

localize10.0ms (0.1%)

series231.0ms (1.4%)

rewrite51.0ms (0.3%)

simplify54.0ms (0.3%)

prune177.0ms (1%)

localize9.0ms (0.1%)

series310.0ms (1.8%)

rewrite93.0ms (0.6%)

simplify60.0ms (0.4%)

prune186.0ms (1.1%)

localize13.0ms (0.1%)

series3.2s (19.2%)

rewrite61.0ms (0.4%)

simplify73.0ms (0.4%)

prune244.0ms (1.4%)

regimes1.6s (9.5%)

simplify2.0ms (0%)

end124.0ms (0.7%)

Profiling