Details

analyze1.7s (6.9%)

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)

sample8.0s (33.4%)

Results

6.0s	4694×	body	1024	valid
1.2s	1508×	body	512	valid
365.0ms	1465×	body	128	valid
285.0ms	572×	body	256	valid
42.0ms	17×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify110.0ms (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

prune7.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.3b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	0.3b	(*.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)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series539.0ms (2.2%)

Counts

4 → 88

Calls

4 calls:

308.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
184.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
43.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
3.0ms	(sin.f64 kx)

rewrite28.0ms (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:

10.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
6.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms	(sin.f64 kx)
1.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify265.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
224×	`sub-neg_binary64`
206×	`fma-def_binary64`
167×	`*-commutative_binary64`

Counts

170 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	343	4685
1	947	4356
2	3270	4356
3	4915	4352
4	4990	4352

prune470.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	186	12	198
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	188	12	200

Error

Counts

200 → 12

Alt Table

Status	Error	Program
▶	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	30.3b	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	3.1b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	28.0b	(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))))
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	36.2b	(.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)))
	34.3b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (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))) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	1.4b	(.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))))
	3.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))

Compiler

Compiled 5740 to 2189 computations (61.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series4.0s (16.8%)

Counts

2 → 72

Calls

2 calls:

3.7s	(log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
307.0ms	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

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

simplify171.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

482×	`cancel-sign-sub-inv_binary64`
246×	`fma-neg_binary64`
220×	`unswap-sqr_binary64`
212×	`times-frac_binary64`
208×	`sub-neg_binary64`

Counts

94 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	4081
1	829	3981
2	3462	3955
3	5121	3955

prune471.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	231	12	243

Error

Counts

243 → 12

Alt Table

Status	Error	Program
✓	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	30.3b	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	3.1b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	28.0b	(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))))
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	36.2b	(.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)))
	34.3b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
▶	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (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))) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	1.4b	(.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))))
	3.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))

Compiler

Compiled 8437 to 3727 computations (55.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
✓	0.4b	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

series703.0ms (2.9%)

Counts

3 → 96

Calls

3 calls:

291.0ms

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

258.0ms

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

153.0ms

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

rewrite36.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 95

Calls

3 calls:

13.0ms

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

8.0ms

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

4.0ms

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

simplify256.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

505×	`cancel-sign-sub-inv_binary64`
260×	`fma-neg_binary64`
258×	`associate-r_binary64`
224×	`times-frac_binary64`
221×	`associate-/l*_binary64`

Counts

191 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	324	5455
1	919	5141
2	3589	5141
3	4979	5141
4	4969	5141

prune422.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	228	11	239

Error

Counts

239 → 11

Alt Table

Status	Error	Program
	3.1b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	28.0b	(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))))
▶	0.7b	(.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (sqrt.f64 (/.f64 1 (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))) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	15.3b	(*.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3)))
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
✓	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	36.2b	(.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)))
✓	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	1.4b	(.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))))
	3.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))

Compiler

Compiled 6872 to 3188 computations (53.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))

series877.0ms (3.6%)

Counts

3 → 108

Calls

3 calls:

314.0ms

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

291.0ms

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

271.0ms

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

rewrite76.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`associate-l_binary64`
30×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 99

Calls

3 calls:

22.0ms

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

20.0ms

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

15.0ms

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

simplify316.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

487×	`associate-r_binary64`
388×	`fma-neg_binary64`
359×	`associate-l_binary64`
250×	`*-commutative_binary64`
245×	`fma-def_binary64`

Counts

207 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	6877
1	1073	6385
2	4220	6383
3	4919	6383
4	4946	6383

prune585.0ms (2.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	323	11	334

Error

Counts

334 → 11

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (sqrt.f64 (/.f64 1 (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))) (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	15.3b	(*.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3)))
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
✓	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	36.2b	(.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)))
	3.1b	(/.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)))
	1.4b	(.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))))
	3.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))
	0.7b	(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))

Compiler

Compiled 12202 to 5937 computations (51.3% saved)

regimes4.6s (19.1%)

Accuracy

Total 0.2b remaining (90%)

Threshold costs 0.2b (90%)

Counts

253 → 1

Compiler

Compiled 50423 to 30283 computations (39.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	16	18
2	15	18

end314.0ms (1.3%)

Compiler: Compiled 280 to 154 computations (45% saved)

Details

analyze1.7s (6.9%)

sample8.0s (33.4%)

simplify110.0ms (0.5%)

prune7.0ms (0%)

localize18.0ms (0.1%)

series539.0ms (2.2%)

rewrite28.0ms (0.1%)

simplify265.0ms (1.1%)

prune470.0ms (2%)

localize24.0ms (0.1%)

series4.0s (16.8%)

rewrite3.0ms (0%)

simplify171.0ms (0.7%)

prune471.0ms (2%)

localize19.0ms (0.1%)

series703.0ms (2.9%)

rewrite36.0ms (0.1%)

simplify256.0ms (1.1%)

prune422.0ms (1.8%)

localize24.0ms (0.1%)

series877.0ms (3.6%)

rewrite76.0ms (0.3%)

simplify316.0ms (1.3%)

prune585.0ms (2.4%)

regimes4.6s (19.1%)

simplify4.0ms (0%)

end314.0ms (1.3%)

Profiling