Details

analyze1.6s (11.6%)

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)

sample284.0ms (2%)

Algorithm

1×

intervals

Results

149.0ms	151×	body	1024	valid
23.0ms	42×	body	512	valid
7.0ms	21×	body	256	valid
7.0ms	42×	body	128	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify84.0ms (0.6%)

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))
	4.5b	(*.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)

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)))

series342.0ms (2.5%)

Counts

3 → 84

Calls

3 calls:

196.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
119.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
28.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite15.0ms (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:

5.0ms	(*.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))

simplify101.0ms (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

prune176.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	175	9	184
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	9	186

Error

0.0b

Counts

186 → 9

Alt Table

Status	Error	Program
	7.8b	(.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (.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))
	30.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	1.4b	(.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	4.5b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (*.f64 (sin.f64 kx) (sin.f64 kx))))) (sin.f64 th))
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
	6.4b	(.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)))
	1.4b	(.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)))

Compiler

Compiled 5282 to 2002 computations (62.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series349.0ms (2.5%)

Counts

3 → 84

Calls

3 calls:

202.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
119.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
28.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite13.0ms (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:

5.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
3.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
0.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify97.0ms (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 → 154

Iterations

Useful iterations: 2 (0.0ms)

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

prune200.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Error

0.0b

Counts

163 → 8

Alt Table

Status	Error	Program
	30.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
▶	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
	2.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th)))
	4.5b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (*.f64 (sin.f64 kx) (sin.f64 kx))))) (sin.f64 th))
	6.4b	(.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)))
	1.4b	(.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)))

Compiler

Compiled 4623 to 1872 computations (59.5% saved)

localize13.0ms (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 kx) (sin.f64 ky)))))
✓	0.1b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
	0.2b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	0.2b	(expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

series468.0ms (3.4%)

Counts

3 → 84

Calls

3 calls:

200.0ms

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

140.0ms

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

127.0ms

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

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

0.0ms

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

0.0ms

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

simplify101.0ms (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

prune152.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	168	8	176

Error

0.0b

Counts

176 → 8

Alt Table

Status	Error	Program
	0.3b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))) (sin.f64 th))
	6.4b	(.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)))
▶	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
	30.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	2.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th)))
	4.5b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (*.f64 (sin.f64 kx) (sin.f64 kx))))) (sin.f64 th))
	1.4b	(.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)))

Compiler

Compiled 5341 to 2408 computations (54.9% saved)

localize9.0ms (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))))

series392.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

211.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
181.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

6.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
3.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

simplify130.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def_binary64`
411×	`cancel-sign-sub-inv_binary64`
267×	`fma-neg_binary64`
190×	`times-frac_binary64`
183×	`associate-r_binary64`

Counts

135 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	276	4408
1	778	4225
2	3013	4209
3	4923	4207
4	4967	4207

prune157.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	147	8	155

Error

Counts

155 → 8

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	0.5b	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
	0.3b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))) (sin.f64 th))
	6.4b	(.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)))
✓	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
	30.4b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	31.3b	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
	2.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th)))

Compiler

Compiled 4547 to 1917 computations (57.8% saved)

regimes2.5s (17.8%)

Accuracy

Total 0.2b remaining (86.7%)

Threshold costs 0.2b (86.7%)

Counts

194 → 1

Compiler

Compiled 35307 to 21591 computations (38.8% 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	16	18
2	15	18

end1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample6.7s (48.2%)

Algorithm

1×

intervals

Results

4.8s	4573×	body	1024	valid
903.0ms	1435×	body	512	valid
276.0ms	1436×	body	128	valid
195.0ms	543×	body	256	valid
29.0ms	13×	body	2048	valid

Compiler

Compiled 218 to 126 computations (42.2% saved)

Details

analyze1.6s (11.6%)

sample284.0ms (2%)

simplify84.0ms (0.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series342.0ms (2.5%)

rewrite15.0ms (0.1%)

simplify101.0ms (0.7%)

prune176.0ms (1.3%)

localize9.0ms (0.1%)

series349.0ms (2.5%)

rewrite13.0ms (0.1%)

simplify97.0ms (0.7%)

prune200.0ms (1.4%)

localize13.0ms (0.1%)

series468.0ms (3.4%)

rewrite6.0ms (0%)

simplify101.0ms (0.7%)

prune152.0ms (1.1%)

localize9.0ms (0.1%)

series392.0ms (2.8%)

rewrite12.0ms (0.1%)

simplify130.0ms (0.9%)

prune157.0ms (1.1%)

regimes2.5s (17.8%)

simplify2.0ms (0%)

end1.0ms (0%)

sample6.7s (48.2%)

Profiling