Details

analyze1.9s (10.9%)

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)

sample9.0s (51.6%)

Results

7.0s	4833×	body	1024	valid
1.2s	1451×	body	512	valid
353.0ms	1400×	body	128	valid
314.0ms	556×	body	256	valid
44.0ms	16×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify84.0ms (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
	2.4b	(*.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)

localize9.0ms (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))
✓	0.1b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	0.1b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series341.0ms (2%)

Counts

4 → 88

Calls

4 calls:

192.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
120.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
27.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms	(sin.f64 kx)

rewrite13.0ms (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	(sin.f64 kx)
0.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify137.0ms (0.8%)

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 → 200

Iterations

Useful iterations: 3 (0.0ms)

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

prune192.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Error

0.0b

Counts

202 → 8

Alt Table

Status	Error	Program
	16.2b	(.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))
	0.6b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (.f64 (*.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) (cbrt.f64 (sin.f64 kx))))) (sin.f64 th))
▶	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	0.3b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	2.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	34.1b	(fma.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 (.f64 (sin.f64 ky) (pow.f64 th 3)) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) -1/6)))
	31.4b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	3.8b	(.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)))

Compiler

Compiled 5541 to 2151 computations (61.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 kx)
✓	0.1b	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
✓	0.3b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

series423.0ms (2.4%)

Counts

3 → 96

Calls

3 calls:

209.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
185.0ms	(/.f64 (sin.f64 th) (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×	`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))))
2.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
1.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify192.0ms (1.1%)

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

prune164.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Status	Error	Program
	16.2b	(.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))
	0.6b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (.f64 (*.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) (cbrt.f64 (sin.f64 kx))))) (sin.f64 th))
▶	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
	33.6b	(.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th))
	2.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
	3.8b	(.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)))

Compiler

Compiled 4941 to 2135 computations (56.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series568.0ms (3.2%)

Counts

4 → 96

Calls

4 calls:

196.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
190.0ms	(log1p.f64 (sin.f64 kx))
180.0ms	(/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
2.0ms	(expm1.f64 (log1p.f64 (sin.f64 kx)))

rewrite15.0ms (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-r_binary64`

Counts

4 → 85

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
2.0ms	(/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
0.0ms	(log1p.f64 (sin.f64 kx))
0.0ms	(expm1.f64 (log1p.f64 (sin.f64 kx)))

simplify135.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

857×	`fma-def_binary64`
507×	`cancel-sign-sub-inv_binary64`
252×	`fma-neg_binary64`
196×	`associate-r_binary64`
190×	`times-frac_binary64`

Counts

181 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	4720
1	861	4526
2	3234	4506
3	4996	4506
4	4981	4506

prune167.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	200	7	207

Error

Counts

207 → 7

Alt Table

Status	Error	Program
	16.2b	(.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))
	2.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
	0.6b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (.f64 (*.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) (cbrt.f64 (sin.f64 kx))))) (sin.f64 th))
	2.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
	3.8b	(.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 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))

Compiler

Compiled 5731 to 2089 computations (63.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series448.0ms (2.6%)

Counts

3 → 108

Calls

3 calls:

194.0ms

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

179.0ms

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

74.0ms

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

rewrite38.0ms (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-r_binary64`

Counts

3 → 182

Calls

3 calls:

14.0ms

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

4.0ms

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

2.0ms

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

simplify261.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

280×	`fma-neg_binary64`
261×	`times-frac_binary64`
260×	`associate-r_binary64`
245×	`associate-/l*_binary64`
228×	`associate-/r*_binary64`

Counts

290 → 359

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	8816
1	1085	7862
2	4295	7835
3	4870	7835
4	4977	7835
5	4948	7835

prune333.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	386	0	386
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	386	7	393

Error

Counts

393 → 7

Alt Table

Status	Error	Program
	16.2b	(.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))
	2.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
	0.6b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (.f64 (*.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) (cbrt.f64 (sin.f64 kx))))) (sin.f64 th))
	2.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
✓	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
	3.8b	(.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 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))

Compiler

Compiled 11089 to 3986 computations (64.1% saved)

regimes2.9s (16.4%)

Accuracy

Total 0.2b remaining (81.5%)

Threshold costs 0.2b (81.5%)

Counts

259 → 1

Compiler

Compiled 48476 to 29583 computations (39% saved)

simplify2.0ms (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

end124.0ms (0.7%)

Compiler: Compiled 172 to 107 computations (37.8% saved)

Details

analyze1.9s (10.9%)

sample9.0s (51.6%)

simplify84.0ms (0.5%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series341.0ms (2%)

rewrite13.0ms (0.1%)

simplify137.0ms (0.8%)

prune192.0ms (1.1%)

localize10.0ms (0.1%)

series423.0ms (2.4%)

rewrite13.0ms (0.1%)

simplify192.0ms (1.1%)

prune164.0ms (0.9%)

localize13.0ms (0.1%)

series568.0ms (3.2%)

rewrite15.0ms (0.1%)

simplify135.0ms (0.8%)

prune167.0ms (1%)

localize11.0ms (0.1%)

series448.0ms (2.6%)

rewrite38.0ms (0.2%)

simplify261.0ms (1.5%)

prune333.0ms (1.9%)

regimes2.9s (16.4%)

simplify2.0ms (0%)

end124.0ms (0.7%)

Profiling