Details

analyze516.0ms (7.6%)

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
6.2%	93.7%	0.1%	6
37.5%	53.1%	9.5%	7
37.5%	51.5%	11%	8
43.7%	39.8%	16.5%	9
43.7%	38.6%	17.7%	10
46.8%	32.6%	20.6%	11
46.8%	31.9%	21.3%	12
48.4%	28.8%	22.8%	13
48.4%	28.5%	23.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample4.0s (59.5%)

Results

1.2s	2094×	body	1024	valid
1.1s	2116×	body	1024	invalid
637.0ms	4683×	body	128	valid
337.0ms	988×	body	512	valid
326.0ms	993×	body	512	invalid
139.0ms	485×	body	256	valid
130.0ms	566×	body	256	invalid
103.0ms	723×	body	128	invalid
7.0ms	6×	body	2048	valid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess42.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

620×	`fma-def_binary64`
330×	`associate-/r/_binary64`
292×	`associate-/l/_binary64`
207×	`div-sub_binary64`
184×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	28	22
2	63	22
3	144	22
4	326	22
5	831	22
6	2550	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

491×	`times-frac_binary64`
402×	`associate-/l*_binary64`
310×	`fma-def_binary64`
305×	`associate-l_binary64`
293×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	16	11
2	35	11
3	77	11
4	171	11
5	431	11
6	1301	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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
	0.4b	(*.f64 (sinh.f64 y) (/.f64 (sin.f64 x) y))
▶	0.3b	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

Compiler

Compiled 52 to 32 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sinh.f64 y) y)
✓	0.0b	(sinh.f64 y)
✓	0.3b	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

series52.0ms (0.8%)

Counts

3 → 48

Calls

12 calls:

8.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))	y	-inf
7.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))	y	inf
6.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))	x	inf
5.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))	x	-inf
5.0ms	(/.f64 (sinh.f64 y) y)	y	-inf

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
142×	`log1p-udef_binary64`
80×	`egg-rr`
78×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	20
2	2014	20

Stop Event

1×	node limit

Counts

3 → 80

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
492×	`fma-def_binary64`
218×	`associate-l_binary64`
216×	`associate-/l*_binary64`
199×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1037
1	386	985
2	1185	957
3	4522	955

Stop Event

1×	node limit

Counts

128 → 119

prune109.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	3	121

Error

0.2b

Counts

121 → 3

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))
	1.5b	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))
	0.5b	(*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (/.f64 (sinh.f64 y) y) 3)))

Compiler

Compiled 1799 to 875 computations (51.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (sinh.f64 y))
	0.0b	(sinh.f64 y)
✓	0.2b	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))

series57.0ms (0.8%)

Counts

2 → 36

Calls

9 calls:

14.0ms	(/.f64 y (sinh.f64 y))	y	inf
12.0ms	(/.f64 y (sinh.f64 y))	y	-inf
7.0ms	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))	y	-inf
6.0ms	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))	y	inf
5.0ms	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))	x	-inf

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

855×	`log1p-expm1-u_binary64`
855×	`expm1-log1p-u_binary64`
82×	`add-sqr-sqrt_binary64`
80×	`prod-diff_binary64`
77×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	154	17
2	2259	17

Stop Event

1×	node limit

Counts

2 → 77

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

921×	`times-frac_binary64`
357×	`fma-def_binary64`
204×	`associate-/l*_binary64`
165×	`associate-r_binary64`
161×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	887
1	340	851
2	1070	832
3	4179	832

Stop Event

1×	node limit

Counts

113 → 106

prune118.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	138	3	141

Error

0.2b

Counts

141 → 3

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))
	1.5b	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))
▶	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 y (sinh.f64 y)))) (/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y)))))

Compiler

Compiled 2088 to 936 computations (55.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y))))
✓	0.0b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 y (sinh.f64 y)))) (/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y)))))
	0.0b	(sinh.f64 y)
✓	0.2b	(sqrt.f64 (/.f64 y (sinh.f64 y)))

series114.0ms (1.7%)

Counts

3 → 40

Calls

15 calls:

34.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y))))	y	-inf
14.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y))))	y	inf
12.0ms	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 y (sinh.f64 y)))) (/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y)))))	y	-inf
8.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y))))	x	inf
6.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y))))	x	-inf

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

604×	`log-prod_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
188×	`log-div_binary64`
186×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	235	32
2	3212	32

Stop Event

1×	node limit

Counts

3 → 136

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
346×	`associate-r_binary64`
308×	`associate-l_binary64`
220×	`cancel-sign-sub-inv_binary64`
198×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1249
1	427	1158
2	1385	1074

Stop Event

1×	node limit

Counts

176 → 179

prune223.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	288	3	291

Error

0.2b

Counts

291 → 3

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))
▶	1.5b	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 y (sinh.f64 y)))) (/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y)))))

Compiler

Compiled 6153 to 2314 computations (62.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/5040 (pow.f64 y 7) y)
✓	0.0b	(fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y)))
✓	0.0b	(/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y)
✓	0.0b	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))

series65.0ms (1%)

Counts

4 → 60

Calls

15 calls:

18.0ms	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))	x	inf
17.0ms	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))	x	-inf
13.0ms	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))	x	0
2.0ms	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))	y	-inf
2.0ms	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))	y	inf

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

321×	`log1p-udef_binary64`
195×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	85
1	388	85
2	4466	85

Stop Event

1×	node limit

Counts

4 → 104

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

700×	`associate-l_binary64`
628×	`associate-r_binary64`
352×	`associate--l+_binary64`
237×	`cancel-sign-sub-inv_binary64`
180×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1448
1	380	1352
2	1450	1301

Stop Event

1×	node limit

Counts

164 → 154

prune153.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	153	4	157

Error

0.2b

Counts

157 → 4

Alt Table

Status	Error	Program
	36.4b	(exp.f64 (log.f64 (*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y))) y))))
✓	0.3b	(/.f64 (sin.f64 x) (/.f64 y (sinh.f64 y)))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 y (sinh.f64 y)))) (/.f64 (sin.f64 x) (sqrt.f64 (/.f64 y (sinh.f64 y)))))
	36.7b	(*.f64 (sin.f64 x) (/.f64 (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (exp.f64 (log.f64 (fma.f64 1/5040 (pow.f64 y 7) y))))) y))

Compiler

Compiled 4170 to 2945 computations (29.4% saved)

regimes743.0ms (10.9%)

Accuracy

Total 0.0b remaining (12.8%)

Threshold costs 0.0b (12.8%)

Counts

153 → 1

Compiler

Compiled 11473 to 8278 computations (27.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15

Stop Event

1×

saturated

end79.0ms (1.2%)

Stop Event

1×

fuel

Compiler

Compiled 99 to 70 computations (29.3% saved)

Details

analyze516.0ms (7.6%)

sample4.0s (59.5%)

preprocess42.0ms (0.6%)

simplify19.0ms (0.3%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series52.0ms (0.8%)

rewrite48.0ms (0.7%)

simplify51.0ms (0.7%)

prune109.0ms (1.6%)

localize7.0ms (0.1%)

series57.0ms (0.8%)

rewrite56.0ms (0.8%)

simplify48.0ms (0.7%)

prune118.0ms (1.7%)

localize9.0ms (0.1%)

series114.0ms (1.7%)

rewrite62.0ms (0.9%)

simplify45.0ms (0.7%)

prune223.0ms (3.3%)

localize14.0ms (0.2%)

series65.0ms (1%)

rewrite73.0ms (1.1%)

simplify39.0ms (0.6%)

prune153.0ms (2.3%)

regimes743.0ms (10.9%)

simplify2.0ms (0%)

end79.0ms (1.2%)

Profiling