Details

analyze1.8s (9.8%)

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)

sample8.1s (44.2%)

Results

6.2s	4834×	body	1024	valid
1.1s	1418×	body	512	valid
354.0ms	1428×	body	128	valid
310.0ms	556×	body	256	valid
42.0ms	20×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify83.0ms (0.5%)

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
	5.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 th)
✓	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))

series346.0ms (1.9%)

Counts

4 → 88

Calls

4 calls:

190.0ms	(*.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)))
28.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms	(sin.f64 th)

rewrite14.0ms (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:

5.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
2.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
1.0ms	(sin.f64 th)

simplify166.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

541×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
225×	`sub-neg_binary64`
206×	`fma-def_binary64`
167×	`*-commutative_binary64`

Counts

170 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	335	4692
1	934	4356
2	3244	4356
3	4863	4352
4	4998	4352
5	4955	4352

prune196.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	189	9	198
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	191	9	200

Error

Counts

200 → 9

Alt Table

Status	Error	Program
	6.3b	(.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))
	9.0b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	2.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (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))
	3.4b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	27.1b	(.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)))
	1.2b	(.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))))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))

Compiler

Compiled 5560 to 2084 computations (62.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(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))

series361.0ms (2%)

Counts

3 → 84

Calls

3 calls:

191.0ms

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

121.0ms

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

49.0ms

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

rewrite37.0ms (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:

10.0ms

(*.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)))

3.0ms

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

simplify172.0ms (0.9%)

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

prune387.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	377	7	384

Error

Counts

384 → 7

Alt Table

Status	Error	Program
	0.3b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
	26.9b	(.f64 (sqrt.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
▶	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	3.4b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	27.1b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (sin.f64 ky)))) (.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky)))) (sin.f64 th)))
	6.3b	(.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 10653 to 3888 computations (63.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

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

series187.0ms (1%)

Counts

1 → 36

Calls

1 calls:

187.0ms

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

rewrite14.0ms (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 (0.7%)

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

prune203.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	242	7	249

Error

Counts

249 → 7

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
	26.9b	(.f64 (sqrt.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	3.4b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	27.1b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (sin.f64 ky)))) (.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky)))) (sin.f64 th)))
	6.3b	(.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 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))

Compiler

Compiled 6521 to 2110 computations (67.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
✓	0.7b	(log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

series2.1s (11.7%)

Counts

2 → 60

Calls

2 calls:

2.0s	(log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
184.0ms	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 31

Calls

2 calls:

3.0ms	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
1.0ms	(log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

simplify112.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

875×	`times-frac_binary64`
614×	`fma-def_binary64`
357×	`fma-neg_binary64`
323×	`cancel-sign-sub-inv_binary64`
143×	`sub-neg_binary64`

Counts

91 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	3177
1	610	3018
2	2151	2906
3	4989	2904
4	5175	2904

prune264.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	285	7	292

Error

Counts

292 → 7

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
	26.9b	(.f64 (sqrt.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	3.4b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	27.1b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (sin.f64 ky)))) (.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky)))) (sin.f64 th)))
	6.3b	(.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 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))

Compiler

Compiled 8463 to 3637 computations (57% saved)

regimes3.5s (18.9%)

Accuracy

Total 0.2b remaining (82.8%)

Threshold costs 0.2b (82.8%)

Counts

281 → 1

Compiler

Compiled 50954 to 31530 computations (38.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	10	18

end116.0ms (0.6%)

Compiler: Compiled 161 to 107 computations (33.5% saved)

Details

analyze1.8s (9.8%)

sample8.1s (44.2%)

simplify83.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series346.0ms (1.9%)

rewrite14.0ms (0.1%)

simplify166.0ms (0.9%)

prune196.0ms (1.1%)

localize10.0ms (0.1%)

series361.0ms (2%)

rewrite37.0ms (0.2%)

simplify172.0ms (0.9%)

prune387.0ms (2.1%)

localize9.0ms (0%)

series187.0ms (1%)

rewrite14.0ms (0.1%)

simplify125.0ms (0.7%)

prune203.0ms (1.1%)

localize12.0ms (0.1%)

series2.1s (11.7%)

rewrite5.0ms (0%)

simplify112.0ms (0.6%)

prune264.0ms (1.4%)

regimes3.5s (18.9%)

simplify2.0ms (0%)

end116.0ms (0.6%)

Profiling