Details

analyze1.9s (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)

sample8.2s (55.2%)

Results

6.3s	4781×	body	1024	valid
1.2s	1455×	body	512	valid
371.0ms	1484×	body	128	valid
265.0ms	518×	body	256	valid
41.0ms	18×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify80.0ms (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
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	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))

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 (/.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)))

series411.0ms (2.8%)

Counts

3 → 84

Calls

3 calls:

216.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
163.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
32.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-l_binary64`

Counts

3 → 73

Calls

3 calls:

9.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
3.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
479×	`cancel-sign-sub-inv_binary64`
212×	`sub-neg_binary64`
168×	`fma-neg_binary64`
164×	`*-commutative_binary64`

Counts

157 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	4580
1	903	4251
2	3145	4236
3	5043	4236

prune186.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	174	10	184
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	175	11	186

Error

0.0b

Counts

186 → 11

Alt Table

Status	Error	Program
	31.7b	(cbrt.f64 (.f64 (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (*.f64 (sin.f64 th) (sin.f64 th)) (sin.f64 th))))
	8.1b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	18.0b	(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
▶	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	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))
	5.1b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	1.2b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	20.0b	(.f64 (cbrt.f64 (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	9.4b	(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))

Compiler

Compiled 5338 to 2058 computations (61.4% saved)

localize12.0ms (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)))))
✓	0.2b	(*.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)))
✓	0.3b	(expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series478.0ms (3.2%)

Counts

3 → 84

Calls

3 calls:

212.0ms

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

135.0ms

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

130.0ms

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

3.0ms

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

0.0ms

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

0.0ms

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

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

126 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	4100
1	799	3936
2	2918	3907
3	4994	3907

prune218.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Error

0.0b

Counts

199 → 9

Alt Table

Status	Error	Program
	18.0b	(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	27.5b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 3))
▶	0.2b	(*.f64 (log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))) (sin.f64 th))
	8.1b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	1.2b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	20.0b	(.f64 (cbrt.f64 (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	9.4b	(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))

Compiler

Compiled 5825 to 2559 computations (56.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))))
✓	0.2b	(*.f64 (log1p.f64 (log1p.f64 (expm1.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)))
	0.3b	(expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series346.0ms (2.3%)

Counts

2 → 60

Calls

2 calls:

207.0ms

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

139.0ms

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

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

0.0ms

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

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
687×	`fma-def_binary64`
333×	`cancel-sign-sub-inv_binary64`
154×	`sub-neg_binary64`
140×	`associate-r_binary64`

Counts

91 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	3230
1	638	2969
2	2263	2956
3	5050	2956

prune176.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	187	9	196

Error

0.0b

Counts

196 → 9

Alt Table

Status	Error	Program
	18.0b	(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	27.5b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 3))
✓	0.2b	(*.f64 (log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))) (sin.f64 th))
	8.1b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	1.2b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
▶	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	20.0b	(.f64 (cbrt.f64 (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	9.4b	(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))

Compiler

Compiled 6085 to 2730 computations (55.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series437.0ms (2.9%)

Counts

3 → 96

Calls

3 calls:

206.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
202.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
29.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 73

Calls

3 calls:

6.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
4.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify192.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

555×	`cancel-sign-sub-inv_binary64`
257×	`fma-neg_binary64`
228×	`times-frac_binary64`
214×	`sub-neg_binary64`
201×	`associate-r_binary64`

Counts

169 → 147

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	326	5096
1	920	4768
2	3574	4768
3	4914	4768
4	4986	4768
5	5000	4768
6	4959	4768

prune127.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	148	8	156

Error

0.0b

Counts

156 → 8

Alt Table

Status	Error	Program
	5.2b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 1 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	18.0b	(*.f64 (log.f64 (exp.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	27.5b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 3))
	34.1b	(*.f64 (sin.f64 ky) (log.f64 (exp.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
✓	0.2b	(*.f64 (log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))) (sin.f64 th))
	9.4b	(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))

Compiler

Compiled 4506 to 1917 computations (57.5% saved)

regimes1.6s (10.6%)

Accuracy

Total 0.2b remaining (76.8%)

Threshold costs 0.2b (76.8%)

Counts

104 → 1

Compiler

Compiled 17813 to 11016 computations (38.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	11	18
2	11	18

end121.0ms (0.8%)

Compiler: Compiled 158 to 108 computations (31.6% saved)

Details

analyze1.9s (13%)

sample8.2s (55.2%)

simplify80.0ms (0.5%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series411.0ms (2.8%)

rewrite16.0ms (0.1%)

simplify108.0ms (0.7%)

prune186.0ms (1.3%)

localize12.0ms (0.1%)

series478.0ms (3.2%)

rewrite6.0ms (0%)

simplify98.0ms (0.7%)

prune218.0ms (1.5%)

localize14.0ms (0.1%)

series346.0ms (2.3%)

rewrite5.0ms (0%)

simplify81.0ms (0.5%)

prune176.0ms (1.2%)

localize8.0ms (0.1%)

series437.0ms (2.9%)

rewrite14.0ms (0.1%)

simplify192.0ms (1.3%)

prune127.0ms (0.9%)

regimes1.6s (10.6%)

simplify2.0ms (0%)

end121.0ms (0.8%)

Profiling