Details

analyze2.5s (16%)

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)

sample228.0ms (1.4%)

Algorithm

1×

intervals

Results

175.0ms	167×	body	1024	valid
24.0ms	38×	body	512	valid
11.0ms	42×	body	128	valid
4.0ms	9×	body	256	valid

Compiler

Compiled 42 to 32 computations (23.8% 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
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	3.0b	(*.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 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))

series381.0ms (2.4%)

Counts

4 → 88

Calls

4 calls:

216.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
134.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
30.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms	(sin.f64 kx)

rewrite16.0ms (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:

8.0ms	(*.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)))
1.0ms	(sin.f64 kx)
0.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify140.0ms (0.9%)

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

prune186.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	190	8	198
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	192	8	200

Error

0.0b

Counts

200 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	6.4b	(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))
	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (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))
	5.1b	(.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)))
	25.7b	(cbrt.f64 (.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)))) (.f64 (*.f64 (sin.f64 th) (sin.f64 th)) (sin.f64 th))))
▶	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	2.3b	(.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)))

Compiler

Compiled 5456 to 2097 computations (61.6% saved)

localize13.0ms (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 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
✓	0.6b	(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series1.7s (10.6%)

Counts

2 → 60

Calls

2 calls:

1.5s	(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
204.0ms	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (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 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.0ms	(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify102.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

875×	`times-frac_binary64`
610×	`fma-def_binary64`
357×	`fma-neg_binary64`
323×	`cancel-sign-sub-inv_binary64`
144×	`sub-neg_binary64`

Counts

91 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	3063
1	607	2924
2	2122	2906
3	4939	2904
4	5125	2904

prune165.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	187	8	195

Error

0.0b

Counts

195 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	6.4b	(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (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))
	5.1b	(.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)))
	25.7b	(cbrt.f64 (.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)))) (.f64 (*.f64 (sin.f64 th) (sin.f64 th)) (sin.f64 th))))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	2.3b	(.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)))

Compiler

Compiled 5635 to 2488 computations (55.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series378.0ms (2.4%)

Counts

4 → 84

Calls

4 calls:

206.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (sin.f64 kx))))) (sin.f64 th))
168.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (sin.f64 kx)))))
3.0ms	(expm1.f64 (sin.f64 kx))
2.0ms	(log1p.f64 (expm1.f64 (sin.f64 kx)))

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 → 85

Calls

4 calls:

6.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (sin.f64 kx))))) (sin.f64 th))
3.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (sin.f64 kx)))))
0.0ms	(expm1.f64 (sin.f64 kx))
0.0ms	(log1p.f64 (expm1.f64 (sin.f64 kx)))

simplify131.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
439×	`cancel-sign-sub-inv_binary64`
317×	`fma-neg_binary64`
280×	`neg-mul-1_binary64`
186×	`sub-neg_binary64`

Counts

169 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	311	4201
1	839	4006
2	2819	3985
3	4602	3983
4	4961	3983

prune155.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	192	8	200

Error

Counts

200 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (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))
	5.1b	(.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)))
	3.3b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (cbrt.f64 (.f64 (*.f64 (expm1.f64 (sin.f64 kx)) (expm1.f64 (sin.f64 kx))) (expm1.f64 (sin.f64 kx))))))) (sin.f64 th))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	2.3b	(.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)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	30.9b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (.f64 (sin.f64 th) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 5330 to 1906 computations (64.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series388.0ms (2.4%)

Counts

3 → 84

Calls

3 calls:

206.0ms

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

130.0ms

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

53.0ms

(/.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:

12.0ms

(*.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)))

2.0ms

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

simplify170.0ms (1.1%)

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 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	7761
1	1001	7004
2	3670	6977
3	4959	6977

prune301.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	377	8	385

Error

Counts

385 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (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))
	5.1b	(.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)))
	3.3b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (log1p.f64 (cbrt.f64 (.f64 (*.f64 (expm1.f64 (sin.f64 kx)) (expm1.f64 (sin.f64 kx))) (expm1.f64 (sin.f64 kx))))))) (sin.f64 th))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	2.3b	(.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)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	30.9b	(.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) 1) (.f64 (sin.f64 th) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 10567 to 3824 computations (63.8% saved)

regimes1.8s (11.2%)

Accuracy

Total 0.2b remaining (85.5%)

Threshold costs 0.2b (85.5%)

Counts

178 → 1

Compiler

Compiled 31378 to 20170 computations (35.7% 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

end1.0ms (0%)

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

sample6.9s (43.7%)

Algorithm

1×

intervals

Results

5.0s	4637×	body	1024	valid
981.0ms	1433×	body	512	valid
283.0ms	1412×	body	128	valid
201.0ms	506×	body	256	valid
25.0ms	12×	body	2048	valid

Compiler

Compiled 192 to 127 computations (33.9% saved)

Details

analyze2.5s (16%)

sample228.0ms (1.4%)

simplify84.0ms (0.5%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series381.0ms (2.4%)

rewrite16.0ms (0.1%)

simplify140.0ms (0.9%)

prune186.0ms (1.2%)

localize13.0ms (0.1%)

series1.7s (10.6%)

rewrite5.0ms (0%)

simplify102.0ms (0.6%)

prune165.0ms (1%)

localize12.0ms (0.1%)

series378.0ms (2.4%)

rewrite14.0ms (0.1%)

simplify131.0ms (0.8%)

prune155.0ms (1%)

localize10.0ms (0.1%)

series388.0ms (2.4%)

rewrite37.0ms (0.2%)

simplify170.0ms (1.1%)

prune301.0ms (1.9%)

regimes1.8s (11.2%)

simplify2.0ms (0%)

end1.0ms (0%)

sample6.9s (43.7%)

Profiling