Details

analyze526.0ms (10.4%)

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
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample4.3s (85.1%)

Results

1.4s	2047×	body	1024	valid
1.1s	2019×	body	1024	invalid
674.0ms	4667×	body	128	valid
397.0ms	1055×	body	512	valid
353.0ms	984×	body	512	invalid
131.0ms	484×	body	256	valid
119.0ms	773×	body	128	invalid
112.0ms	460×	body	256	invalid
4.0ms	3×	body	2048	valid
2.0ms	1×	body	2048	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess39.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

692×	`times-frac_binary64`
480×	`fma-def_binary64`
341×	`associate-/r/_binary64`
306×	`associate-/l/_binary64`
305×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	36
1	50	36
2	135	36
3	273	34
4	361	34
5	489	34
6	837	34
7	2180	34
8	4821	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (-.f64 0 re)) (exp.f64 re)))

Outputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (sin.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (-.f64 0 re)) (exp.f64 re)))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))
(.f64 1/2 (.f64 (sin.f64 im) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re))))
(*.f64 (sin.f64 im) (fma.f64 1/2 (exp.f64 re) (/.f64 1/2 (exp.f64 re))))

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify32.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
455×	`associate-/r*_binary64`
357×	`associate-/l*_binary64`
346×	`times-frac_binary64`
315×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	28	18
2	71	18
3	140	17
4	185	17
5	252	17
6	430	17
7	1107	17
8	3311	17
9	3702	17
10	4192	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Outputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (sin.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (exp.f64 im))

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	im	@	-inf	(/.f64 1/2 (exp.f64 im))
1.0ms	im	@	0	(/.f64 1/2 (exp.f64 im))
1.0ms	im	@	inf	(/.f64 1/2 (exp.f64 im))

rewrite31.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

468×	`pow1_binary64`
436×	`add-log-exp_binary64`
436×	`log1p-expm1-u_binary64`
436×	`expm1-log1p-u_binary64`
427×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	103	6
2	1201	6

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(/.f64 1/2 (exp.f64 im))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/2 (exp.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (exp.f64 (neg.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (exp.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) (pow.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) 2) (cbrt.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 (exp.f64 im))) (sqrt.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (/.f64 1 (neg.f64 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (neg.f64 im)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (exp.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (exp.f64 im)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (exp.f64 im))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (exp.f64 im) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (exp.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 1/2) im))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (exp.f64 im))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/2 (exp.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (exp.f64 (neg.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (exp.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) (pow.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) 2) (cbrt.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (exp.f64 im))) (sqrt.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 1 (neg.f64 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (neg.f64 im)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (exp.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (exp.f64 im)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (exp.f64 im))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (exp.f64 im))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (exp.f64 im) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (exp.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 1/2) im))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (exp.f64 im))))))))

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
563×	`cancel-sign-sub-inv_binary64`
488×	`distribute-rgt-neg-in_binary64`
284×	`unswap-sqr_binary64`
178×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	47
1	51	43
2	134	39
3	447	31
4	1508	31
5	3885	31

Stop Event

1×	node limit

Counts

24 → 27

Calls

Call 1

Inputs
1/2
(-.f64 1/2 (*.f64 1/2 im))
(-.f64 (+.f64 1/2 (.f64 1/4 (pow.f64 im 2))) (.f64 1/2 im))
(-.f64 (+.f64 1/2 (.f64 1/4 (pow.f64 im 2))) (+.f64 (.f64 1/12 (pow.f64 im 3)) (*.f64 1/2 im)))

Outputs
1/2
(-.f64 1/2 (*.f64 1/2 im))
(+.f64 1/2 (*.f64 -1/2 im))
(fma.f64 im -1/2 1/2)
(-.f64 (+.f64 1/2 (.f64 1/4 (pow.f64 im 2))) (.f64 1/2 im))
(+.f64 1/2 (-.f64 (.f64 1/4 (.f64 im im)) (*.f64 1/2 im)))
(-.f64 (fma.f64 1/4 (.f64 im im) 1/2) (.f64 1/2 im))
(fma.f64 1/4 (*.f64 im im) (fma.f64 im -1/2 1/2))
(fma.f64 im (fma.f64 im 1/4 -1/2) 1/2)
(-.f64 (+.f64 1/2 (.f64 1/4 (pow.f64 im 2))) (+.f64 (.f64 1/12 (pow.f64 im 3)) (*.f64 1/2 im)))
(-.f64 (+.f64 1/2 (.f64 1/4 (.f64 im im))) (fma.f64 1/12 (pow.f64 im 3) (*.f64 1/2 im)))
(-.f64 (fma.f64 1/4 (.f64 im im) 1/2) (fma.f64 1/2 im (.f64 1/12 (pow.f64 im 3))))
(+.f64 (fma.f64 im (.f64 im 1/4) 1/2) (fma.f64 im -1/2 (.f64 (pow.f64 im 3) -1/12)))
(fma.f64 (pow.f64 im 3) -1/12 (fma.f64 im (fma.f64 im 1/4 -1/2) 1/2))

prune15.0ms (0.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	1	28

Error

Counts

28 → 1

Alt Table

Status	Error	Program
✓	0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 406 to 239 computations (41.1% saved)

regimes25.0ms (0.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

3 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Outputs
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

end40.0ms (0.8%)

Stop Event

1×

done

Compiler

Compiled 39 to 27 computations (30.8% saved)

Details

analyze526.0ms (10.4%)

sample4.3s (85.1%)

preprocess39.0ms (0.8%)

simplify32.0ms (0.6%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite31.0ms (0.6%)

simplify31.0ms (0.6%)

prune15.0ms (0.3%)

regimes25.0ms (0.5%)

simplify2.0ms (0%)

end40.0ms (0.8%)

Profiling