Details

analyze630.0ms (11%)

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
37.5%	50%	12.6%	7
37.5%	50%	12.6%	8
43.7%	37.5%	18.8%	9
43.7%	37.5%	18.8%	10
46.8%	31.2%	22%	11
46.8%	31.2%	22%	12
48.4%	28.1%	23.5%	13
48.4%	28.1%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample133.0ms (2.3%)

Algorithm

1×

intervals

Results

38.0ms	65×	body	1024	invalid
37.0ms	67×	body	1024	valid
14.0ms	153×	body	128	valid
8.0ms	30×	body	512	invalid
8.0ms	28×	body	512	valid
3.0ms	29×	body	128	invalid
3.0ms	16×	body	256	invalid
2.0ms	8×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
610×	`div-sub_binary64`
491×	`times-frac_binary64`
410×	`associate-/l*_binary64`
352×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	16	11
2	34	11
3	73	11
4	160	11
5	361	11
6	984	11
7	3177	11
8	4701	11
9	5010	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sinh.f64 y) y)
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
✓	0.0b	(sinh.f64 y)

series114.0ms (2%)

Counts

3 → 48

Calls

3 calls:

71.0ms	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
25.0ms	(/.f64 (sinh.f64 y) y)
17.0ms	(sinh.f64 y)

rewrite28.0ms (0.5%)

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 → 74

Calls

3 calls:

11.0ms	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
5.0ms	(/.f64 (sinh.f64 y) y)
4.0ms	(sinh.f64 y)

simplify169.0ms (3%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-def_binary64`
404×	`associate-/l*_binary64`
345×	`times-frac_binary64`
309×	`associate-*r/_binary64`
295×	`associate-*l/_binary64`

Counts

122 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2067
1	528	1896
2	1670	1755
3	4556	1755
4	5388	1755

prune151.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
	0.2b	(+.f64 (cos.f64 x) (.f64 1/6 (.f64 (pow.f64 y 2) (cos.f64 x))))
▶	0.2b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y))

Compiler

Compiled 2035 to 770 computations (62.2% saved)

localize26.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/120 (pow.f64 y 5) y)
✓	0.0b	(/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y)
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y))

series84.0ms (1.5%)

Counts

3 → 48

Calls

3 calls:

71.0ms	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y))
8.0ms	(/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y)
4.0ms	(fma.f64 1/120 (pow.f64 y 5) y)

rewrite16.0ms (0.3%)

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:

7.0ms	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y))
3.0ms	(/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y)
0.0ms	(fma.f64 1/120 (pow.f64 y 5) y)

simplify128.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-def_binary64`
327×	`distribute-rgt-in_binary64`
312×	`distribute-lft-in_binary64`
297×	`cancel-sign-sub-inv_binary64`
243×	`associate-*l/_binary64`

Counts

121 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3025
1	403	2727
2	1524	2663
3	4755	2663
4	4985	2663
5	4962	2663

prune117.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	3	124

Error

Counts

124 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
▶	0.2b	(+.f64 (cos.f64 x) (.f64 1/6 (.f64 (pow.f64 y 2) (cos.f64 x))))
✓	0.2b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y))

Compiler

Compiled 3198 to 2118 computations (33.8% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 y 2) (cos.f64 x))
✓	0.2b	(.f64 1/6 (.f64 (pow.f64 y 2) (cos.f64 x)))

series38.0ms (0.7%)

Counts

2 → 8

Calls

2 calls:

24.0ms	(.f64 1/6 (.f64 (pow.f64 y 2) (cos.f64 x)))
14.0ms	(*.f64 (pow.f64 y 2) (cos.f64 x))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`associate-l_binary64`
10×	`prod-exp_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

6.0ms	(.f64 1/6 (.f64 (pow.f64 y 2) (cos.f64 x)))
5.0ms	(*.f64 (pow.f64 y 2) (cos.f64 x))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
743×	`unswap-sqr_binary64`
656×	`fma-def_binary64`
330×	`*-commutative_binary64`
277×	`cancel-sign-sub-inv_binary64`

Counts

58 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	957
1	247	811
2	817	784
3	1650	752
4	3300	752
5	4963	752

prune74.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	91	3	94

Error

Counts

94 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
✓	0.2b	(+.f64 (cos.f64 x) (.f64 1/6 (.f64 (pow.f64 y 2) (cos.f64 x))))
✓	0.2b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) y))

Compiler

Compiled 1630 to 902 computations (44.7% saved)

regimes82.0ms (1.4%)

Accuracy

Total 0.0b remaining (36.5%)

Threshold costs 0.0b (36.5%)

Counts

16 → 1

Compiler

Compiled 1100 to 739 computations (32.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample3.7s (64.8%)

Algorithm

1×

intervals

Results

978.0ms	1990×	body	1024	valid
929.0ms	1959×	body	1024	invalid
407.0ms	4494×	body	128	valid
243.0ms	1008×	body	512	valid
241.0ms	984×	body	512	invalid
84.0ms	502×	body	256	valid
81.0ms	499×	body	256	invalid
68.0ms	713×	body	128	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 61 to 43 computations (29.5% saved)

Details

analyze630.0ms (11%)

sample133.0ms (2.3%)

simplify102.0ms (1.8%)

prune3.0ms (0.1%)

localize18.0ms (0.3%)

series114.0ms (2%)

rewrite28.0ms (0.5%)

simplify169.0ms (3%)

prune151.0ms (2.6%)

localize26.0ms (0.5%)

series84.0ms (1.5%)

rewrite16.0ms (0.3%)

simplify128.0ms (2.2%)

prune117.0ms (2%)

localize9.0ms (0.1%)

series38.0ms (0.7%)

rewrite14.0ms (0.3%)

simplify73.0ms (1.3%)

prune74.0ms (1.3%)

regimes82.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.7s (64.8%)

Profiling