Details

analyze1.8s (13%)

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)

sample7.8s (57.2%)

Results

6.1s	4801×	body	1024	valid
1.1s	1421×	body	512	valid
353.0ms	1486×	body	128	valid
268.0ms	536×	body	256	valid
30.0ms	12×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify46.0ms (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

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.0b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	2.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize8.0ms (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))
✓	2.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series188.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

156.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
24.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
8.0ms	(*.f64 (sin.f64 ky) (sin.f64 th))

rewrite53.0ms (0.4%)

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:

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)))

simplify54.0ms (0.4%)

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

prune122.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	9	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

Counts

141 → 9

Alt Table

Status	Error	Program
	2.2b	(/.f64 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (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))
	24.9b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 3))
	4.2b	(.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))))))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	29.3b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 2) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 3574 to 1570 computations (56.1% saved)

localize10.0ms (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)))

series308.0ms (2.2%)

Counts

2 → 60

Calls

2 calls:

178.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
130.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite45.0ms (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)))

simplify54.0ms (0.4%)

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

prune138.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	143	8	151

Error

Counts

151 → 8

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	2.2b	(/.f64 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	29.3b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 2) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
▶	0.3b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	4.2b	(.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))))))

Compiler

Compiled 3999 to 1884 computations (52.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.1b	(*.f64 (log1p.f64 (expm1.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)))
✓	0.2b	(expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series359.0ms (2.6%)

Counts

3 → 84

Calls

3 calls:

162.0ms

(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

104.0ms

(expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

92.0ms

(log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`log-prod_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
192×	`log-pow_binary64`
179×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	223	46
2	2762	46

Stop Event

1×	node limit

Counts

3 → 96

Calls

3 calls:

50.0ms

(log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

50.0ms

(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

50.0ms

(expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-def_binary64`
427×	`cancel-sign-sub-inv_binary64`
230×	`sub-neg_binary64`
177×	`fma-neg_binary64`
166×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	3189
1	749	3157
2	2876	3126

Stop Event

1×	node limit

Counts

180 → 153

prune178.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	206	8	214

Error

Counts

214 → 8

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
	10.9b	(*.f64 (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 3))) (sin.f64 th))
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	2.2b	(/.f64 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
▶	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
✓	0.3b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	4.2b	(.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))))))

Compiler

Compiled 5834 to 2696 computations (53.8% 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) (/.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))

series211.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

149.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
61.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

rewrite48.0ms (0.4%)

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:

46.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
46.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

simplify54.0ms (0.4%)

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	643	2459
2	2479	2219

Stop Event

1×	node limit

Counts

154 → 131

prune136.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	166	8	174

Error

Counts

174 → 8

Alt Table

Status	Error	Program
	10.9b	(*.f64 (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 3))) (sin.f64 th))
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 th) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	2.2b	(/.f64 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) 3)
✓	0.3b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	4.2b	(.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))))))

Compiler

Compiled 4312 to 1826 computations (57.7% saved)

regimes1.8s (13.1%)

Accuracy

Total 0.2b remaining (89.5%)

Threshold costs 0.2b (89.5%)

Counts

192 → 1

Compiler

Compiled 30318 to 20841 computations (31.3% saved)

simplify2.0ms (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	21	22
2	31	22
3	40	22
4	45	22
5	48	22
6	49	22

Stop Event

1×

saturated

end135.0ms (1%)

Compiler: Compiled 181 to 119 computations (34.3% saved)

Details

analyze1.8s (13%)

sample7.8s (57.2%)

simplify46.0ms (0.3%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series188.0ms (1.4%)

rewrite53.0ms (0.4%)

simplify54.0ms (0.4%)

prune122.0ms (0.9%)

localize10.0ms (0.1%)

series308.0ms (2.2%)

rewrite45.0ms (0.3%)

simplify54.0ms (0.4%)

prune138.0ms (1%)

localize11.0ms (0.1%)

series359.0ms (2.6%)

rewrite52.0ms (0.4%)

simplify61.0ms (0.4%)

prune178.0ms (1.3%)

localize9.0ms (0.1%)

series211.0ms (1.5%)

rewrite48.0ms (0.4%)

simplify54.0ms (0.4%)

prune136.0ms (1%)

regimes1.8s (13.1%)

simplify2.0ms (0%)

end135.0ms (1%)

Profiling