Details

analyze485.0ms (7.4%)

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%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample4.0s (60.8%)

Results

1.2s	2062×	body	1024	valid
928.0ms	1961×	body	1024	invalid
655.0ms	4626×	body	128	valid
422.0ms	1043×	body	512	valid
345.0ms	1012×	body	512	invalid
149.0ms	525×	body	256	invalid
128.0ms	520×	body	256	valid
98.0ms	713×	body	128	invalid
6.0ms	5×	body	2048	valid

preprocess46.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

748×	`times-frac_binary64`
390×	`fma-def_binary64`
320×	`unswap-sqr_binary64`
302×	`associate-l_binary64`
234×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	49	36
2	131	36
3	256	34
4	373	34
5	672	34
6	1526	34
7	2651	34
8	3803	34
9	4549	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 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (cos.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (cos.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))
(.f64 1/2 (.f64 (cos.f64 im) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re))))
(*.f64 (cos.f64 im) (fma.f64 1/2 (exp.f64 re) (/.f64 1/2 (exp.f64 re))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-/l*_binary64`
430×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
351×	`fma-def_binary64`
340×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	28	18
2	70	18
3	134	17
4	194	17
5	347	17
6	783	17
7	1356	17
8	3975	17
9	4498	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

prune3.0ms (0%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 50 to 33 computations (34% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(/.f64 1/2 (exp.f64 im))

series9.0ms (0.1%)

Counts

3 → 40

Calls

12 calls:

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

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	182	35
2	2171	35

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

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

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

Outputs

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

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

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

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
468×	`distribute-rgt-out_binary64`
422×	`distribute-lft-out_binary64`
366×	`associate-l_binary64`
319×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	725
1	232	690
2	769	643
3	3192	625

Stop Event

1×	node limit

Counts

103 → 94

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 -1/2 im))
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (.f64 -1/2 im)))
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (+.f64 (.f64 -1/2 im) (*.f64 -1/12 (pow.f64 im 3)))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 1/720 (pow.f64 im 6)))))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im)))))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im))))))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 re 6) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (.f64 1/2 (/.f64 1 (exp.f64 im)))))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6))))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))

Outputs
1/2
(+.f64 1/2 (*.f64 -1/2 im))
(fma.f64 -1/2 im 1/2)
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (.f64 -1/2 im)))
(+.f64 1/2 (fma.f64 1/4 (.f64 im im) (.f64 -1/2 im)))
(+.f64 1/2 (fma.f64 -1/2 im (.f64 1/4 (.f64 im im))))
(fma.f64 1/4 (*.f64 im im) (fma.f64 -1/2 im 1/2))
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (+.f64 (.f64 -1/2 im) (*.f64 -1/12 (pow.f64 im 3)))))
(+.f64 1/2 (fma.f64 1/4 (.f64 im im) (fma.f64 -1/2 im (.f64 -1/12 (pow.f64 im 3)))))
(+.f64 1/2 (fma.f64 -1/2 im (.f64 (.f64 im im) (+.f64 1/4 (*.f64 im -1/12)))))
(+.f64 1/2 (.f64 im (+.f64 -1/2 (.f64 im (+.f64 1/4 (*.f64 im -1/12))))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (.f64 1/2 (.f64 im im)))
(fma.f64 1/2 (*.f64 im im) 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (fma.f64 1/2 (.f64 im im) (.f64 1/24 (pow.f64 im 4))))
(fma.f64 1/24 (pow.f64 im 4) (fma.f64 1/2 (*.f64 im im) 1))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 1/720 (pow.f64 im 6)))))
(+.f64 1 (fma.f64 1/2 (.f64 im im) (fma.f64 1/24 (pow.f64 im 4) (.f64 1/720 (pow.f64 im 6)))))
(+.f64 (.f64 1/720 (pow.f64 im 6)) (fma.f64 1/24 (pow.f64 im 4) (fma.f64 1/2 (.f64 im im) 1)))
(+.f64 (fma.f64 1/2 (.f64 im im) 1) (fma.f64 1/24 (pow.f64 im 4) (.f64 1/720 (pow.f64 im 6))))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im)))))
(fma.f64 -1/2 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 re re)) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (+.f64 (.f64 -1/2 (*.f64 re re)) 1) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (fma.f64 -1/2 (.f64 re re) 1))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im))))))
(fma.f64 -1/2 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 re re)) (fma.f64 1/24 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 4)) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))
(+.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/2 (.f64 re re)) (.f64 1/24 (pow.f64 re 4)))))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 re (*.f64 -1/2 re)) (fma.f64 1/24 (pow.f64 re 4) 1)))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/2 (*.f64 re re)) (fma.f64 1/24 (pow.f64 re 4) 1)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 re 6) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (.f64 1/2 (/.f64 1 (exp.f64 im)))))))
(fma.f64 -1/2 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 re re)) (fma.f64 1/24 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 4)) (fma.f64 1/2 (exp.f64 im) (fma.f64 -1/720 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 6)) (/.f64 1/2 (exp.f64 im))))))
(+.f64 (fma.f64 1/2 (exp.f64 im) (fma.f64 -1/720 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 6)) (/.f64 1/2 (exp.f64 im)))) (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/2 (.f64 re re)) (*.f64 1/24 (pow.f64 re 4)))))
(fma.f64 (.f64 (.f64 re re) -1/4) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (fma.f64 1/24 (pow.f64 re 4) 1) (.f64 -1/720 (pow.f64 re 6)))))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/720 (pow.f64 re 6)) (+.f64 (.f64 1/24 (pow.f64 re 4)) (fma.f64 -1/2 (.f64 re re) 1))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re))
(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (cos.f64 re))
(.f64 (fma.f64 1/2 (.f64 im im) 1) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(+.f64 (fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re)) (.f64 (.f64 1/24 (cos.f64 re)) (pow.f64 im 4)))
(fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (fma.f64 1/24 (*.f64 (pow.f64 im 4) (cos.f64 re)) (cos.f64 re)))
(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4)))))
(.f64 (cos.f64 re) (fma.f64 1/24 (pow.f64 im 4) (fma.f64 1/2 (.f64 im im) 1)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6))))))
(+.f64 (fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re)) (fma.f64 1/24 (.f64 (pow.f64 im 4) (cos.f64 re)) (.f64 1/720 (*.f64 (pow.f64 im 6) (cos.f64 re)))))
(+.f64 (fma.f64 1/24 (.f64 (pow.f64 im 4) (cos.f64 re)) (.f64 1/720 (.f64 (pow.f64 im 6) (cos.f64 re)))) (fma.f64 1/2 (.f64 im (*.f64 im (cos.f64 re))) (cos.f64 re)))
(+.f64 (.f64 (fma.f64 1/24 (pow.f64 im 4) 1) (cos.f64 re)) (.f64 (cos.f64 re) (fma.f64 1/2 (.f64 im im) (.f64 1/720 (pow.f64 im 6)))))
(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (fma.f64 1/2 (.f64 im im) (fma.f64 1/24 (pow.f64 im 4) (*.f64 1/720 (pow.f64 im 6))))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))

prune269.0ms (4.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	2	95

Error

Counts

95 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))
	0.5b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))

Status

Error

Program

▶

0.0b

(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))

0.5b

(+.f64 (*.f64 1/2 (*.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)))))

Compiler

Compiled 1595 to 952 computations (40.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))
	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.1b	(log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))

series4.0ms (0.1%)

Counts

3 → 40

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	im	@	0	(exp.f64 (/.f64 1/2 (exp.f64 im)))
0.0ms	im	@	0	(log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))
0.0ms	re	@	0	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))
0.0ms	im	@	inf	(exp.f64 (/.f64 1/2 (exp.f64 im)))
0.0ms	im	@	-inf	(log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`pow1_binary64`
97×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	205	31
2	2356	31

Stop Event

1×	node limit

Counts

3 → 68

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.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 /.f64 1/2 (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (neg.f64 (neg.f64 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 (exp.f64 im) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (neg.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (sqrt.f64 (exp.f64 im))) (sqrt.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (pow.f64 (cbrt.f64 (exp.f64 im)) 2)) (cbrt.f64 (exp.f64 im)))))) (#(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 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 log1p.f64 (expm1.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 exp.f64 (*.f64 (-.f64 (log.f64 1/2) im) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/2 (exp.f64 im)) (cos.f64 re)) (.f64 (/.f64 1/2 (exp.f64 im)) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 re) (.f64 1/2 (exp.f64 im))) (.f64 (cos.f64 re) (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 re)) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 re) 3) (pow.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) 3) (pow.f64 (cos.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (/.f64 1/2 (exp.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (exp.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) 2) (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (exp.f64 (neg.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (/.f64 1/2 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.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 pow.f64 (exp.f64 (sqrt.f64 (/.f64 1/2 (exp.f64 im)))) (sqrt.f64 (/.f64 1/2 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.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 /.f64 1/2 (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (neg.f64 (neg.f64 (exp.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (exp.f64 im) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (neg.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (*.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (sqrt.f64 (exp.f64 im))) (sqrt.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (pow.f64 (cbrt.f64 (exp.f64 im)) 2)) (cbrt.f64 (exp.f64 im)))))) (#(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 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 log1p.f64 (expm1.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 exp.f64 (*.f64 (-.f64 (log.f64 1/2) im) 1))))))

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

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

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-def_binary64`
513×	`distribute-rgt-out_binary64`
477×	`distribute-lft-out_binary64`
392×	`associate-l_binary64`
353×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	700
1	250	667
2	831	628
3	3399	603

Stop Event

1×	node limit

Counts

108 → 99

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 -1/2 im))
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (.f64 -1/2 im)))
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (+.f64 (.f64 -1/2 im) (*.f64 -1/12 (pow.f64 im 3)))))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im)))))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im))))))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 re 6) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (.f64 1/2 (/.f64 1 (exp.f64 im)))))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6))))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(exp.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (exp.f64 1/2) im)) (exp.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 1/2) im)) (+.f64 (.f64 3/8 (.f64 (exp.f64 1/2) (pow.f64 im 2))) (exp.f64 1/2)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 1/2) im)) (+.f64 (.f64 -11/48 (.f64 (exp.f64 1/2) (pow.f64 im 3))) (+.f64 (.f64 3/8 (.f64 (exp.f64 1/2) (pow.f64 im 2))) (exp.f64 1/2))))

Outputs
1/2
(+.f64 1/2 (*.f64 -1/2 im))
(fma.f64 -1/2 im 1/2)
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (.f64 -1/2 im)))
(+.f64 1/2 (fma.f64 1/4 (.f64 im im) (.f64 -1/2 im)))
(+.f64 1/2 (fma.f64 -1/2 im (.f64 im (.f64 im 1/4))))
(fma.f64 im (*.f64 im 1/4) (fma.f64 -1/2 im 1/2))
(+.f64 1/2 (+.f64 (.f64 1/4 (pow.f64 im 2)) (+.f64 (.f64 -1/2 im) (*.f64 -1/12 (pow.f64 im 3)))))
(+.f64 1/2 (fma.f64 1/4 (.f64 im im) (fma.f64 -1/2 im (.f64 -1/12 (pow.f64 im 3)))))
(+.f64 1/2 (fma.f64 -1/2 im (.f64 (.f64 im im) (+.f64 1/4 (*.f64 im -1/12)))))
(+.f64 1/2 (.f64 im (+.f64 -1/2 (.f64 im (+.f64 1/4 (*.f64 im -1/12))))))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(/.f64 1/2 (exp.f64 im))
(+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im)))
(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im)))))
(fma.f64 -1/2 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 re re)) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (+.f64 (.f64 -1/2 (*.f64 re re)) 1) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (fma.f64 -1/2 (.f64 re re) 1))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (.f64 1/2 (/.f64 1 (exp.f64 im))))))
(fma.f64 -1/2 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 re re)) (fma.f64 1/24 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 4)) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))
(+.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/2 (.f64 re re)) (.f64 1/24 (pow.f64 re 4)))))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/2 (*.f64 re re)) (fma.f64 1/24 (pow.f64 re 4) 1)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (+.f64 (.f64 1/2 (exp.f64 im)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 re 6) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (.f64 1/2 (exp.f64 im))))) (.f64 1/2 (/.f64 1 (exp.f64 im)))))))
(fma.f64 -1/2 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (.f64 re re)) (fma.f64 1/24 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 4)) (fma.f64 1/2 (exp.f64 im) (fma.f64 -1/720 (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (pow.f64 re 6)) (/.f64 1/2 (exp.f64 im))))))
(+.f64 (fma.f64 1/2 (exp.f64 im) (fma.f64 (.f64 -1/720 (pow.f64 re 6)) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (/.f64 1/2 (exp.f64 im)))) (.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/2 (.f64 re re)) (*.f64 1/24 (pow.f64 re 4)))))
(fma.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (fma.f64 -1/2 (.f64 re re) (.f64 1/24 (pow.f64 re 4))) (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (+.f64 1/2 (.f64 (pow.f64 re 6) -1/1440))))
(.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (+.f64 (.f64 -1/720 (pow.f64 re 6)) (+.f64 (.f64 -1/2 (.f64 re re)) (fma.f64 1/24 (pow.f64 re 4) 1))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re))
(fma.f64 (.f64 im im) (.f64 1/2 (cos.f64 re)) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(+.f64 (fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re)) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))))
(fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (fma.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)) (cos.f64 re)))
(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 (.f64 1/2 im) im))))
(.f64 (cos.f64 re) (+.f64 (.f64 (.f64 1/2 im) im) (+.f64 (.f64 1/24 (pow.f64 im 4)) 1)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6))))))
(+.f64 (fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re)) (fma.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)) (.f64 (*.f64 1/720 (cos.f64 re)) (pow.f64 im 6))))
(+.f64 (fma.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6)))) (fma.f64 1/2 (.f64 (*.f64 im im) (cos.f64 re)) (cos.f64 re)))
(+.f64 (cos.f64 re) (fma.f64 1/2 (.f64 im (.f64 im (cos.f64 re))) (.f64 (cos.f64 re) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 1/720 (pow.f64 im 6))))))
(+.f64 (cos.f64 re) (.f64 (cos.f64 re) (+.f64 (.f64 1/24 (pow.f64 im 4)) (+.f64 (.f64 1/720 (pow.f64 im 6)) (.f64 (*.f64 1/2 im) im)))))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 1/2 (/.f64 1 (exp.f64 im))) (*.f64 1/2 (exp.f64 im))))
(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (cos.f64 re))
(exp.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (exp.f64 1/2) im)) (exp.f64 1/2))
(fma.f64 -1/2 (*.f64 im (exp.f64 1/2)) (exp.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 1/2) im)) (+.f64 (.f64 3/8 (.f64 (exp.f64 1/2) (pow.f64 im 2))) (exp.f64 1/2)))
(fma.f64 -1/2 (.f64 im (exp.f64 1/2)) (fma.f64 3/8 (.f64 (*.f64 im im) (exp.f64 1/2)) (exp.f64 1/2)))
(fma.f64 -1/2 (.f64 im (exp.f64 1/2)) (fma.f64 3/8 (.f64 im (*.f64 im (exp.f64 1/2))) (exp.f64 1/2)))
(+.f64 (exp.f64 1/2) (.f64 (exp.f64 1/2) (+.f64 (.f64 -1/2 im) (.f64 (.f64 3/8 im) im))))
(+.f64 (exp.f64 1/2) (.f64 (.f64 im (exp.f64 1/2)) (+.f64 (*.f64 3/8 im) -1/2)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 1/2) im)) (+.f64 (.f64 -11/48 (.f64 (exp.f64 1/2) (pow.f64 im 3))) (+.f64 (.f64 3/8 (.f64 (exp.f64 1/2) (pow.f64 im 2))) (exp.f64 1/2))))
(fma.f64 -1/2 (.f64 im (exp.f64 1/2)) (fma.f64 -11/48 (.f64 (pow.f64 im 3) (exp.f64 1/2)) (fma.f64 3/8 (.f64 (.f64 im im) (exp.f64 1/2)) (exp.f64 1/2))))
(fma.f64 -1/2 (.f64 im (exp.f64 1/2)) (fma.f64 -11/48 (.f64 (pow.f64 im 3) (exp.f64 1/2)) (fma.f64 3/8 (.f64 im (.f64 im (exp.f64 1/2))) (exp.f64 1/2))))
(+.f64 (.f64 (exp.f64 1/2) (+.f64 (.f64 (.f64 3/8 im) im) (.f64 (pow.f64 im 3) -11/48))) (fma.f64 -1/2 (*.f64 im (exp.f64 1/2)) (exp.f64 1/2)))
(+.f64 (exp.f64 1/2) (.f64 (exp.f64 1/2) (+.f64 (.f64 (pow.f64 im 3) -11/48) (.f64 im (+.f64 (.f64 3/8 im) -1/2)))))

prune980.0ms (14.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	128	2	130

Error

Counts

130 → 2

Alt Table

Status

Error

Program

✓

0.0b

(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))

▶

0.5b

(+.f64 (*.f64 1/2 (*.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)))))

Compiler

Compiled 2205 to 1358 computations (38.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
✓	0.0b	(*.f64 (cos.f64 re) (pow.f64 im 4))
✓	0.1b	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
✓	0.1b	(*.f64 (cos.f64 re) (pow.f64 im 2))

series14.0ms (0.2%)

Counts

4 → 22

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	re	@	0	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
1.0ms	re	@	inf	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
1.0ms	im	@	0	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
1.0ms	re	@	-inf	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
1.0ms	re	@	0	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))

rewrite69.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
171×	`add-sqr-sqrt_binary64`
166×	`pow1_binary64`
164×	`*-un-lft-identity_binary64`
163×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	59
1	353	57
2	4477	57

Stop Event

1×	node limit

Counts

4 → 83

Calls

Call 1

Inputs
(*.f64 (cos.f64 re) (pow.f64 im 2))
(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
(*.f64 (cos.f64 re) (pow.f64 im 4))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 re) (.f64 im im)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 re) (.f64 im im))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 im (sqrt.f64 (cos.f64 re))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 im 4) (pow.f64 (cos.f64 re) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 im) im) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 re) (.f64 im im)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 re) 3) (pow.f64 im 6)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 im 6) (pow.f64 (cos.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 re) (.f64 im im))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (cos.f64 re) (.f64 im im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 re) (.f64 im im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 re) (*.f64 im im))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 re) 1/24)) (.f64 im im)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 re)) (pow.f64 im 4)) 1/24))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 re) (pow.f64 im 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 re) (pow.f64 im 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (cos.f64 re) (pow.f64 im 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 re) (pow.f64 im 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 im im) (sqrt.f64 (cos.f64 re))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (cos.f64 re) 2) (pow.f64 im 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 re)) (pow.f64 im 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 re) (pow.f64 im 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (cos.f64 re) (pow.f64 im 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 re) 3) (pow.f64 (pow.f64 im 4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 im 4) 3) (pow.f64 (cos.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 re) (pow.f64 im 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (cos.f64 re) (pow.f64 im 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 re) (pow.f64 im 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 re) (pow.f64 im 4))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (neg.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))) (/.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2) (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (neg.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) (pow.f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) 2) (cbrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) (sqrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 1/8 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3)) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 3)) (/.f64 1 (+.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (-.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2)) (/.f64 1 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (neg.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (-.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2))))) (+.f64 (.f64 1/8 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3)) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (neg.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) (-.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 1/8 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3)) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 3)) (+.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (-.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 1/8 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3)) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 3)) (+.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2) (-.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (.f64 (.f64 (cos.f64 re) (.f64 im im)) (.f64 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2)) (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (neg.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 1/8 (pow.f64 (.f64 (cos.f64 re) (.f64 im im)) 3)) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 3))) (neg.f64 (+.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (-.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2) (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2))) (neg.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (neg.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re)) 3) (pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 3)) (+.f64 (.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re)) (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re))) (-.f64 (pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 2) (.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2) (pow.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) 2)) (-.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re)) (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re))) (pow.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24)) 2)) (-.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (pow.f64 im 4) 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (.f64 (cos.f64 re) (.f64 im im)) (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)) (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)) 2)) (cbrt.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2))) 2) (cbrt.f64 (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2))) (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) (sqrt.f64 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re))) (.f64 (cos.f64 re) (.f64 (.f64 im im) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 re) 1/2)) im) (.f64 (sqrt.f64 (.f64 (cos.f64 re) 1/2)) im) (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cos.f64 re) 1/2) (.f64 im im) (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (.f64 (cos.f64 re) (.f64 im im)) 1/2 (fma.f64 (.f64 (cos.f64 re) 1/24) (pow.f64 im 4) (cos.f64 re)))) 1))))))

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
520×	`distribute-rgt-out_binary64`
416×	`associate-l_binary64`
377×	`unswap-sqr_binary64`
351×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	598
1	233	556
2	757	491
3	3732	484

Stop Event

1×	node limit

Counts

105 → 120

Calls

Call 1

Inputs
(pow.f64 im 2)
(+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2)))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))) (.f64 -1/720 (.f64 (pow.f64 re 6) (pow.f64 im 2))))))
(*.f64 1/24 (pow.f64 im 4))
(+.f64 (.f64 -1/48 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (*.f64 1/24 (pow.f64 im 4)))
(+.f64 (.f64 -1/48 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 1/576 (*.f64 (pow.f64 re 4) (pow.f64 im 4)))))
(+.f64 (.f64 -1/17280 (.f64 (pow.f64 re 6) (pow.f64 im 4))) (+.f64 (.f64 -1/48 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 1/576 (*.f64 (pow.f64 re 4) (pow.f64 im 4))))))
(pow.f64 im 4)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (pow.f64 im 4))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 4))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (pow.f64 im 4)))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 4))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (+.f64 (pow.f64 im 4) (.f64 -1/720 (.f64 (pow.f64 re 6) (pow.f64 im 4))))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 2) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 im 2)) (.f64 -1/48 (pow.f64 im 4))) 1/2)) (+.f64 (.f64 1/2 (pow.f64 im 2)) (*.f64 1/24 (pow.f64 im 4)))))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 2) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 im 2)) (.f64 -1/48 (pow.f64 im 4))) 1/2)) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 (+.f64 1/24 (+.f64 (.f64 1/576 (pow.f64 im 4)) (.f64 1/48 (pow.f64 im 2)))) (pow.f64 re 4))))))
(+.f64 (.f64 (pow.f64 re 6) (-.f64 (+.f64 (.f64 -1/1440 (pow.f64 im 2)) (.f64 -1/17280 (pow.f64 im 4))) 1/720)) (+.f64 1 (+.f64 (.f64 (pow.f64 re 2) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 im 2)) (.f64 -1/48 (pow.f64 im 4))) 1/2)) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 (+.f64 1/24 (+.f64 (.f64 1/576 (pow.f64 im 4)) (*.f64 1/48 (pow.f64 im 2)))) (pow.f64 re 4)))))))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))))
(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))))

Outputs
(pow.f64 im 2)
(*.f64 im im)
(+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))))
(+.f64 (.f64 im im) (.f64 -1/2 (.f64 (.f64 im im) (*.f64 re re))))
(.f64 (+.f64 (.f64 -1/2 (.f64 re re)) 1) (.f64 im im))
(.f64 (.f64 im im) (fma.f64 -1/2 (*.f64 re re) 1))
(.f64 im (.f64 (fma.f64 -1/2 (*.f64 re re) 1) im))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2)))))
(fma.f64 1/24 (.f64 (.f64 im im) (pow.f64 re 4)) (+.f64 (.f64 im im) (.f64 -1/2 (.f64 (.f64 im im) (*.f64 re re)))))
(fma.f64 1/24 (.f64 (.f64 (pow.f64 re 4) im) im) (.f64 (+.f64 (.f64 -1/2 (.f64 re re)) 1) (.f64 im im)))
(.f64 (.f64 im im) (+.f64 (.f64 -1/2 (.f64 re re)) (fma.f64 1/24 (pow.f64 re 4) 1)))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))) (.f64 -1/720 (.f64 (pow.f64 re 6) (pow.f64 im 2))))))
(fma.f64 1/24 (.f64 (.f64 im im) (pow.f64 re 4)) (+.f64 (.f64 im im) (fma.f64 -1/2 (.f64 (.f64 im im) (.f64 re re)) (.f64 -1/720 (.f64 (*.f64 im im) (pow.f64 re 6))))))
(fma.f64 1/24 (.f64 (.f64 (pow.f64 re 4) im) im) (fma.f64 im im (.f64 (.f64 im im) (+.f64 (.f64 -1/2 (.f64 re re)) (*.f64 -1/720 (pow.f64 re 6))))))
(fma.f64 im im (.f64 (.f64 im im) (+.f64 (.f64 1/24 (pow.f64 re 4)) (fma.f64 -1/2 (.f64 re re) (*.f64 -1/720 (pow.f64 re 6))))))
(.f64 (.f64 im im) (+.f64 (fma.f64 1/24 (pow.f64 re 4) 1) (fma.f64 -1/2 (.f64 re re) (.f64 -1/720 (pow.f64 re 6)))))
(*.f64 1/24 (pow.f64 im 4))
(+.f64 (.f64 -1/48 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (*.f64 1/24 (pow.f64 im 4)))
(fma.f64 -1/48 (.f64 (.f64 re re) (pow.f64 im 4)) (*.f64 1/24 (pow.f64 im 4)))
(.f64 (pow.f64 im 4) (+.f64 (.f64 (*.f64 re re) -1/48) 1/24))
(.f64 (pow.f64 im 4) (fma.f64 (.f64 re re) -1/48 1/24))
(+.f64 (.f64 -1/48 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 1/576 (*.f64 (pow.f64 re 4) (pow.f64 im 4)))))
(fma.f64 -1/48 (.f64 (.f64 re re) (pow.f64 im 4)) (fma.f64 1/24 (pow.f64 im 4) (.f64 1/576 (.f64 (pow.f64 re 4) (pow.f64 im 4)))))
(fma.f64 -1/48 (.f64 re (.f64 re (pow.f64 im 4))) (.f64 (pow.f64 im 4) (+.f64 1/24 (.f64 (pow.f64 re 4) 1/576))))
(.f64 (pow.f64 im 4) (+.f64 (.f64 re (*.f64 re -1/48)) (fma.f64 (pow.f64 re 4) 1/576 1/24)))
(+.f64 (.f64 -1/17280 (.f64 (pow.f64 re 6) (pow.f64 im 4))) (+.f64 (.f64 -1/48 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 1/576 (*.f64 (pow.f64 re 4) (pow.f64 im 4))))))
(fma.f64 -1/17280 (.f64 (pow.f64 re 6) (pow.f64 im 4)) (fma.f64 -1/48 (.f64 (.f64 re re) (pow.f64 im 4)) (fma.f64 1/24 (pow.f64 im 4) (.f64 1/576 (*.f64 (pow.f64 re 4) (pow.f64 im 4))))))
(+.f64 (.f64 (pow.f64 im 4) (+.f64 1/24 (.f64 (pow.f64 re 4) 1/576))) (.f64 (pow.f64 im 4) (+.f64 (.f64 (pow.f64 re 6) -1/17280) (.f64 (.f64 re re) -1/48))))
(.f64 (pow.f64 im 4) (+.f64 (fma.f64 (pow.f64 re 4) 1/576 1/24) (fma.f64 (pow.f64 re 6) -1/17280 (.f64 re (*.f64 re -1/48)))))
(pow.f64 im 4)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (pow.f64 im 4))
(fma.f64 -1/2 (.f64 (.f64 re re) (pow.f64 im 4)) (pow.f64 im 4))
(.f64 (+.f64 (.f64 -1/2 (*.f64 re re)) 1) (pow.f64 im 4))
(.f64 (pow.f64 im 4) (fma.f64 -1/2 (.f64 re re) 1))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 4))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (pow.f64 im 4)))
(fma.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 4)) (fma.f64 -1/2 (.f64 (*.f64 re re) (pow.f64 im 4)) (pow.f64 im 4)))
(+.f64 (pow.f64 im 4) (.f64 (pow.f64 im 4) (+.f64 (.f64 1/24 (pow.f64 re 4)) (.f64 -1/2 (.f64 re re)))))
(.f64 (pow.f64 im 4) (+.f64 (fma.f64 -1/2 (.f64 re re) 1) (*.f64 1/24 (pow.f64 re 4))))
(.f64 (pow.f64 im 4) (+.f64 (.f64 -1/2 (*.f64 re re)) (fma.f64 1/24 (pow.f64 re 4) 1)))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 4))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 4))) (+.f64 (pow.f64 im 4) (.f64 -1/720 (.f64 (pow.f64 re 6) (pow.f64 im 4))))))
(fma.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 4)) (+.f64 (fma.f64 -1/2 (.f64 (.f64 re re) (pow.f64 im 4)) (pow.f64 im 4)) (.f64 -1/720 (*.f64 (pow.f64 re 6) (pow.f64 im 4)))))
(+.f64 (.f64 (+.f64 (.f64 -1/720 (pow.f64 re 6)) 1) (pow.f64 im 4)) (.f64 (pow.f64 im 4) (+.f64 (.f64 1/24 (pow.f64 re 4)) (.f64 -1/2 (.f64 re re)))))
(fma.f64 (pow.f64 im 4) (fma.f64 1/24 (pow.f64 re 4) (.f64 -1/2 (.f64 re re))) (*.f64 (pow.f64 im 4) (fma.f64 -1/720 (pow.f64 re 6) 1)))
(.f64 (pow.f64 im 4) (+.f64 (fma.f64 -1/720 (pow.f64 re 6) 1) (fma.f64 1/24 (pow.f64 re 4) (.f64 -1/2 (*.f64 re re)))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (fma.f64 1/2 (.f64 im im) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (fma.f64 (.f64 im im) 1/2 (.f64 1/24 (pow.f64 im 4))))
(fma.f64 im (*.f64 im 1/2) (fma.f64 1/24 (pow.f64 im 4) 1))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 2) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 im 2)) (.f64 -1/48 (pow.f64 im 4))) 1/2)) (+.f64 (.f64 1/2 (pow.f64 im 2)) (*.f64 1/24 (pow.f64 im 4)))))
(+.f64 1 (fma.f64 (.f64 re re) (+.f64 (fma.f64 -1/4 (.f64 im im) (.f64 (pow.f64 im 4) -1/48)) -1/2) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4)))))
(+.f64 1 (fma.f64 (.f64 re re) (fma.f64 (.f64 im im) -1/4 (fma.f64 (pow.f64 im 4) -1/48 -1/2)) (fma.f64 (.f64 im im) 1/2 (.f64 1/24 (pow.f64 im 4)))))
(fma.f64 (.f64 re re) (fma.f64 im (.f64 im -1/4) (fma.f64 (pow.f64 im 4) -1/48 -1/2)) (fma.f64 im (*.f64 im 1/2) (fma.f64 1/24 (pow.f64 im 4) 1)))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 2) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 im 2)) (.f64 -1/48 (pow.f64 im 4))) 1/2)) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 (+.f64 1/24 (+.f64 (.f64 1/576 (pow.f64 im 4)) (.f64 1/48 (pow.f64 im 2)))) (pow.f64 re 4))))))
(+.f64 1 (fma.f64 (.f64 re re) (+.f64 (fma.f64 -1/4 (.f64 im im) (.f64 (pow.f64 im 4) -1/48)) -1/2) (fma.f64 1/2 (.f64 im im) (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 re 4) (+.f64 1/24 (fma.f64 1/576 (pow.f64 im 4) (.f64 (*.f64 im im) 1/48))))))))
(+.f64 1 (fma.f64 (.f64 re re) (fma.f64 (.f64 im im) -1/4 (fma.f64 (pow.f64 im 4) -1/48 -1/2)) (fma.f64 (.f64 im im) 1/2 (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 re 4) (+.f64 1/24 (fma.f64 (pow.f64 im 4) 1/576 (.f64 im (.f64 im 1/48)))))))))
(+.f64 (.f64 (pow.f64 re 4) (fma.f64 im (.f64 im 1/48) (fma.f64 (pow.f64 im 4) 1/576 1/24))) (fma.f64 (.f64 re re) (fma.f64 im (.f64 im -1/4) (fma.f64 (pow.f64 im 4) -1/48 -1/2)) (fma.f64 im (*.f64 im 1/2) (fma.f64 1/24 (pow.f64 im 4) 1))))
(+.f64 (.f64 (pow.f64 re 6) (-.f64 (+.f64 (.f64 -1/1440 (pow.f64 im 2)) (.f64 -1/17280 (pow.f64 im 4))) 1/720)) (+.f64 1 (+.f64 (.f64 (pow.f64 re 2) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 im 2)) (.f64 -1/48 (pow.f64 im 4))) 1/2)) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 (+.f64 1/24 (+.f64 (.f64 1/576 (pow.f64 im 4)) (*.f64 1/48 (pow.f64 im 2)))) (pow.f64 re 4)))))))
(fma.f64 (pow.f64 re 6) (+.f64 (fma.f64 -1/1440 (.f64 im im) (.f64 (pow.f64 im 4) -1/17280)) -1/720) (+.f64 1 (fma.f64 (.f64 re re) (+.f64 (fma.f64 -1/4 (.f64 im im) (.f64 (pow.f64 im 4) -1/48)) -1/2) (fma.f64 1/2 (.f64 im im) (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 re 4) (+.f64 1/24 (fma.f64 1/576 (pow.f64 im 4) (.f64 (*.f64 im im) 1/48)))))))))
(+.f64 (fma.f64 (.f64 re re) (fma.f64 (.f64 im im) -1/4 (fma.f64 (pow.f64 im 4) -1/48 -1/2)) (fma.f64 (.f64 im im) 1/2 (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 re 4) (+.f64 1/24 (fma.f64 (pow.f64 im 4) 1/576 (.f64 im (.f64 im 1/48)))))))) (fma.f64 (pow.f64 re 6) (fma.f64 (*.f64 im im) -1/1440 (fma.f64 (pow.f64 im 4) -1/17280 -1/720)) 1))
(+.f64 (fma.f64 im (.f64 im 1/2) (fma.f64 (.f64 re re) (fma.f64 im (.f64 im -1/4) (fma.f64 (pow.f64 im 4) -1/48 -1/2)) (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 re 4) (fma.f64 im (.f64 im 1/48) (fma.f64 (pow.f64 im 4) 1/576 1/24)))))) (fma.f64 (pow.f64 re 6) (fma.f64 im (.f64 im -1/1440) (fma.f64 (pow.f64 im 4) -1/17280 -1/720)) 1))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (cos.f64 re))
(.f64 (fma.f64 im (.f64 im 1/2) 1) (cos.f64 re))
(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
(.f64 1/24 (.f64 (pow.f64 im 4) (cos.f64 re)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))))
(fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (.f64 1/24 (.f64 (pow.f64 im 4) (cos.f64 re))))
(fma.f64 (.f64 1/24 (cos.f64 re)) (pow.f64 im 4) (.f64 1/2 (.f64 (.f64 im im) (cos.f64 re))))
(.f64 (cos.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 1/24 (pow.f64 im 4))))
(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
(.f64 1/24 (.f64 (pow.f64 im 4) (cos.f64 re)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))))
(fma.f64 1/2 (.f64 (.f64 im im) (cos.f64 re)) (.f64 1/24 (.f64 (pow.f64 im 4) (cos.f64 re))))
(fma.f64 (.f64 1/24 (cos.f64 re)) (pow.f64 im 4) (.f64 1/2 (.f64 (.f64 im im) (cos.f64 re))))
(.f64 (cos.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 1/24 (pow.f64 im 4))))

prune387.0ms (5.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	120	2	122

Error

Counts

122 → 2

Alt Table

Status

Error

Program

✓

0.0b

(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))

✓

0.5b

(+.f64 (*.f64 1/2 (*.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (*.f64 1/24 (*.f64 (cos.f64 re) (pow.f64 im 4)))))

Compiler

Compiled 3445 to 2046 computations (40.6% saved)

regimes26.0ms (0.4%)

Accuracy

Total -0.5b remaining (-6393.6%)

Threshold costs -0.5b (-6393.6%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (exp.f64 (/.f64 1/2 (exp.f64 im))))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

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

Results

4.0ms	0.0b	`re`
5.0ms	0.0b	`im`
4.0ms	0.0b	`(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))`
4.0ms	0.0b	`(*.f64 1/2 (cos.f64 re))`
3.0ms	0.0b	`(cos.f64 re)`
3.0ms	0.0b	`(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))`

Compiler

Compiled 94 to 62 computations (34% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	12	21

Stop Event

1×

saturated

Calls

Call 1

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

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

end25.0ms (0.4%)

Stop Event

1×

done

Compiler

Compiled 30 to 22 computations (26.7% saved)

Details

analyze485.0ms (7.4%)

sample4.0s (60.8%)

preprocess46.0ms (0.7%)

simplify34.0ms (0.5%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series9.0ms (0.1%)

rewrite45.0ms (0.7%)

simplify35.0ms (0.5%)

prune269.0ms (4.1%)

localize10.0ms (0.1%)

series4.0ms (0.1%)

rewrite46.0ms (0.7%)

simplify36.0ms (0.6%)

prune980.0ms (14.9%)

localize11.0ms (0.2%)

series14.0ms (0.2%)

rewrite69.0ms (1%)

simplify35.0ms (0.5%)

prune387.0ms (5.9%)

regimes26.0ms (0.4%)

simplify2.0ms (0%)

end25.0ms (0.4%)

Profiling