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)

sample7.7s (49.9%)

Results

5.9s	4772×	body	1024	valid
1.1s	1472×	body	512	valid
357.0ms	1485×	body	128	valid
250.0ms	513×	body	256	valid
32.0ms	14×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify45.0ms (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

1.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.6b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	3.2b	(*.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 3 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (sin.f64 ky) (sin.f64 th))
✓	2.6b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series179.0ms (1.2%)

Counts

3 → 84

Calls

3 calls:

149.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
22.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
8.0ms	(*.f64 (sin.f64 ky) (sin.f64 th))

rewrite51.0ms (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	34
1	210	34
2	2913	34

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

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

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
213×	`associate-/r/_binary64`
186×	`fma-neg_binary64`
168×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	2472
1	637	2312
2	2395	2085

Stop Event

1×	node limit

Counts

166 → 139

prune130.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	8	141

Error

Counts

141 → 8

Alt Table

Status	Error	Program
	0.5b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	7.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) 3)))
	27.9b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (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))
	3.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	3.6b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 3) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	2.7b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 3530 to 1548 computations (56.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series247.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

152.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
95.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite44.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
178×	`log-pow_binary64`
169×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	203	31
2	2623	31

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

43.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
43.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
675×	`fma-def_binary64`
333×	`cancel-sign-sub-inv_binary64`
154×	`sub-neg_binary64`
131×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2390
1	592	2374
2	2243	2361

Stop Event

1×	node limit

Counts

126 → 107

prune134.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	142	8	150

Error

Counts

150 → 8

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	7.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) 3)))
	27.9b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (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))
	3.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	3.6b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 3) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	2.7b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 3975 to 1877 computations (52.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
✓	0.3b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
✓	0.4b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

series366.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

159.0ms

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

142.0ms

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

65.0ms

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

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

608×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
202×	`log-pow_binary64`
153×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	245	44
2	3124	44

Stop Event

1×	node limit

Counts

3 → 108

Calls

3 calls:

53.0ms

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

53.0ms

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

53.0ms

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

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

563×	`cancel-sign-sub-inv_binary64`
229×	`times-frac_binary64`
220×	`fma-def_binary64`
217×	`fma-neg_binary64`
205×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	4149
1	841	3769
2	3392	3767

Stop Event

1×	node limit

Counts

216 → 181

prune193.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	216	8	224

Error

Counts

224 → 8

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	7.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) 3)))
	27.9b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
▶	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (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))
	3.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	3.6b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 3) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	2.7b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 6257 to 2862 computations (54.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.3b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)
✓	0.6b	(cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series2.5s (16.1%)

Counts

4 → 108

Calls

4 calls:

856.0ms	(/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
739.0ms	(pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)
707.0ms	(cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
168.0ms	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite66.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
205×	`prod-diff_binary64`
147×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	294	56
2	3898	56

Stop Event

1×	node limit

Counts

4 → 131

Calls

4 calls:

63.0ms	(/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
63.0ms	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
63.0ms	(pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)
63.0ms	(cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64`
338×	`fma-def_binary64`
324×	`associate-r_binary64`
306×	`fma-neg_binary64`
225×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	339	4030
1	1097	3937
2	4244	3935

Stop Event

1×	node limit

Counts

239 → 208

prune201.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	250	8	258

Error

Counts

258 → 8

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	7.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) 3)))
	27.9b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
✓	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (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))
	3.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
	3.6b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 3) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	2.7b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 8756 to 4047 computations (53.8% saved)

regimes1.4s (8.8%)

Accuracy

Total 0.2b remaining (85.3%)

Threshold costs 0.2b (85.3%)

Counts

144 → 1

Compiler

Compiled 22994 to 15584 computations (32.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	11	18

Stop Event

1×

saturated

end123.0ms (0.8%)

Compiler: Compiled 170 to 114 computations (32.9% saved)

Details

analyze1.7s (11.3%)

sample7.7s (49.9%)

simplify45.0ms (0.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series179.0ms (1.2%)

rewrite51.0ms (0.3%)

simplify48.0ms (0.3%)

prune130.0ms (0.8%)

localize9.0ms (0.1%)

series247.0ms (1.6%)

rewrite44.0ms (0.3%)

simplify48.0ms (0.3%)

prune134.0ms (0.9%)

localize11.0ms (0.1%)

series366.0ms (2.4%)

rewrite55.0ms (0.4%)

simplify72.0ms (0.5%)

prune193.0ms (1.3%)

localize13.0ms (0.1%)

series2.5s (16.1%)

rewrite66.0ms (0.4%)

simplify83.0ms (0.5%)

prune201.0ms (1.3%)

regimes1.4s (8.8%)

simplify3.0ms (0%)

end123.0ms (0.8%)

Profiling