Details

analyze577.0ms (14.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
6.2%	43.7%	50%	4
12.5%	37.5%	50%	5
18.7%	31.2%	50%	6
23.4%	26.5%	50%	7
27.3%	22.6%	50%	8
30%	19.9%	50%	9
32.2%	17.8%	50%	10
33.7%	16.3%	50%	11
34.8%	15.2%	50%	12
35.5%	14.4%	50%	13
36.1%	13.8%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.8s (46.1%)

Results

830.0ms	6246×	body	128	valid
364.0ms	573×	body	4096	valid
331.0ms	628×	body	2048	valid
199.0ms	443×	body	1024	valid
78.0ms	242×	body	512	valid
28.0ms	124×	body	256	valid

preprocess35.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

421×	`rule-b-ac--ab*bc_binary64`
340×	`rule--ab--+aa+ab_binary64`
308×	`rule-a-*a1_binary64`
308×	`rule-a--a0_binary64`
308×	`rule-a-+a0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	30
1	130	30
2	390	30
3	1804	30
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) im))))

Outputs
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) im))))
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) im))))

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify19.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

351×	`rule-+a-bc-+b-ac_binary64`
247×	`rule-b-ac--ab*bc_binary64`
221×	`rule-a-bc-nega-cb_binary64`
215×	`rule--ab--+aa+ab_binary64`
201×	`rule-a-*a1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	84	15
2	270	15
3	1228	15

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Outputs

(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re))))

(*.f64 1/2 (sqrt.f64 (*.f64 -2 (-.f64 re (hypot.f64 re im)))))

(*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.9b	(-.f64 (hypot.f64 re im) re)

series14.0ms (0.4%)

Counts

3 → 56

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	im	@	0	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
1.0ms	re	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
1.0ms	im	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
1.0ms	re	@	inf	(-.f64 (hypot.f64 re im) re)
1.0ms	re	@	0	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))

rewrite46.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

411×	`rule-ab-ba_binary64`
207×	`rule-aa-fabsaa_binary64`
180×	`rule-/ab-*+aa/1/2b_binary64`
166×	`rule-+ab-+ba_binary64`
166×	`rule-nega--0a_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	218	23
2	3092	8

Stop Event

1×	node limit

Counts

3 → 114

Calls

Call 1

Inputs
(-.f64 (hypot.f64 re im) re)
(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
(hypot.f64 re im)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 re (.f64 re 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 re 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 re (fma.f64 -1 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 re (fma.f64 -1 re re))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 re (fma.f64 (neg.f64 (cbrt.f64 re)) (pow.f64 (cbrt.f64 re) 2) re))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 re (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) re))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 re 2) re)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 re)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 re)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 0 0) re)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1 re re) re)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 (cbrt.f64 re)) (pow.f64 (cbrt.f64 re) 2) re) re)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re) re) re)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 re 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 re -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 re 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 re)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 re) (pow.f64 (cbrt.f64 re) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 re) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 re) (neg.f64 (sqrt.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 re re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 re)) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 re)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 re re) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 re re) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (.f64 re re)) (+.f64 (pow.f64 re 3) (pow.f64 re 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 re 3) (pow.f64 re 3)) (/.f64 1/2 (.f64 re re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (+.f64 (pow.f64 re 3) (pow.f64 re 3))) (fabs.f64 (/.f64 1/2 (.f64 re re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 re 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 re -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 re 3) (.f64 re re))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 re 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 re) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 re) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 re 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 re)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 re re))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 re)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 re))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 re (+.f64 re re)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 re (/.f64 0 (*.f64 re re))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 re 3))))) (#(struct:change #<rule egg-rr> (2) ((x . re)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 re 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 0 0 re)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 0 1 re)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 re) (sqrt.f64 re) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 re))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 re 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 re 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2))) (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 re 2)))) (exp.f64 (log1p.f64 (sqrt.f64 (.f64 re 2))))) (+.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 re 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2))) (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2)))) (+.f64 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2))) (sqrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 re 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 re 2)) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 re 2)) (fabs.f64 (pow.f64 1 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 re 2))) (cbrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 re 2)) (cbrt.f64 (sqrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 re 2) 1/4) (pow.f64 (.f64 re 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 re) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 re) (sqrt.f64 -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 re) (pow.f64 -2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 -2) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (.f64 re 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 2)) (sqrt.f64 (cbrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 -2 1/2) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 re 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 1/2) (pow.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (.f64 re 2) 3/2) (pow.f64 (.f64 re 2) 3/2)) (/.f64 1/2 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 2))) (fabs.f64 (sqrt.f64 (cbrt.f64 (.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (sqrt.f64 -2)) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (pow.f64 -2 1/2)) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 2) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 (.f64 re 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 re 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 re 2) 3/2) (.f64 re 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 re 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 re 2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 re 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 re 2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 re 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (sqrt.f64 (.f64 re 2)) (+.f64 (sqrt.f64 (.f64 re 2)) (sqrt.f64 (.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 re 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 re 2)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 re 2)) (cbrt.f64 (sqrt.f64 (.f64 re 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (.f64 re 2) 1/4) (pow.f64 (.f64 re 2) 1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 2) (sqrt.f64 re) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 re 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x . 0)))))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2))) (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2)))) (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2))))) (+.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2))) (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2)))) (+.f64 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2))) (sqrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 re 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 re 2)) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 re 2)) (fabs.f64 (pow.f64 1 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 re 2))) (cbrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 re 2)) (cbrt.f64 (sqrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 re 2) 1/4) (pow.f64 (*.f64 re 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 re) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 re) (sqrt.f64 -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 re) (pow.f64 -2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 -2) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 re 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 -2 1/2) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 re 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 1/2) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 re 2) 3/2) (pow.f64 (*.f64 re 2) 3/2)) (/.f64 1/2 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 2))) (fabs.f64 (sqrt.f64 (cbrt.f64 (*.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (sqrt.f64 -2)) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (pow.f64 -2 1/2)) (sqrt.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fabs.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 2) 1/2)) (fabs.f64 (pow.f64 (cbrt.f64 (*.f64 re 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 re 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 re 2) 3/2) (*.f64 re 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 re 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 re 2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 re 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 re 2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 1 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (sqrt.f64 (*.f64 re 2)) (+.f64 (sqrt.f64 (*.f64 re 2)) (sqrt.f64 (*.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 re 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 re 2)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 re 2)) (cbrt.f64 (sqrt.f64 (*.f64 re 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 re 2) 1/4) (pow.f64 (*.f64 re 2) 1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 2) (sqrt.f64 re) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 re 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x . 0)))))

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

421×	`fma-def_binary64`
341×	`fma-neg_binary64`
269×	`rule-ab-ba_binary64`
256×	`rule-a-*a1_binary64`
256×	`rule-a--a0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	174	1561
1	1281	1531

Stop Event

1×	node limit

Counts

170 → 187

Calls

Call 1

Inputs
im
(+.f64 (*.f64 -1 re) im)
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)))
(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 im 4)) 2) (.f64 1/16 (pow.f64 im 8))) (pow.f64 re 7))) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(*.f64 -2 re)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -2 re))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (*.f64 -2 re)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -2 re))))
(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 re 6)))) (pow.f64 im 8)) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
im
(+.f64 (*.f64 -1 re) im)
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)))
(*.f64 -1 im)
(+.f64 (.f64 -1 re) (.f64 -1 im))
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (*.f64 -1 im)))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))))
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (.f64 (sqrt.f64 2) (sqrt.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 2))) (sqrt.f64 (/.f64 1 im))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 2))) (sqrt.f64 (/.f64 1 im)))) (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 3))) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re))) (.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 re 6)))) re)) (.f64 -1/16 (/.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 re 2))))) (pow.f64 im 7))) (sqrt.f64 1/2)) (sqrt.f64 re))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re))) (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))))
im
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5))) im)))
re
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)) re)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 re (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 re (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(*.f64 -1 re)
(+.f64 (.f64 -1 re) (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (*.f64 -1/2 (/.f64 (pow.f64 im 2) re))))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
re
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)) re)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 re (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 re (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
im
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5))) im)))
(*.f64 -1 im)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (*.f64 -1 im)))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))))

Outputs
im
(+.f64 (*.f64 -1 re) im)
(fma.f64 -1 re im)
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(fma.f64 -1 re (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)))
(fma.f64 -1 re (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im)))
(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
(.f64 1/2 (/.f64 (.f64 im im) re))
(.f64 1/2 (.f64 im (/.f64 im re)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (.f64 im (/.f64 im re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (.f64 im (/.f64 im re)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 im 4)) 2) (.f64 1/16 (pow.f64 im 8))) (pow.f64 re 7))) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 im 4)) 2) (.f64 1/16 (pow.f64 im 8))) (pow.f64 re 7)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (.f64 im (/.f64 im re)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 (fma.f64 1/16 (pow.f64 im 8) (pow.f64 (.f64 -1/8 (pow.f64 im 4)) 2)) (/.f64 (pow.f64 re 7) -1/2)))))
(*.f64 -2 re)
(*.f64 re -2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -2 re))
(fma.f64 -1/2 (/.f64 (.f64 im im) re) (.f64 re -2))
(fma.f64 re -2 (.f64 (.f64 im (/.f64 im re)) -1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (*.f64 -2 re)))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 -1/2 (/.f64 (.f64 im im) re) (.f64 re -2)))
(fma.f64 (.f64 im (/.f64 im re)) -1/2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (.f64 re -2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -2 re))))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/2 (/.f64 (.f64 im im) re) (.f64 re -2))))
(fma.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16 (fma.f64 (.f64 im (/.f64 im re)) -1/2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (.f64 re -2))))
(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
(.f64 1/2 (/.f64 (.f64 im im) re))
(.f64 1/2 (.f64 im (/.f64 im re)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (.f64 im (/.f64 im re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (.f64 im (/.f64 im re)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 re 6)))) (pow.f64 im 8)) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 -1/2 (/.f64 (.f64 (pow.f64 im 8) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6)))) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (.f64 im (/.f64 im re)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/2 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))) (/.f64 (pow.f64 im 8) re)) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
im
(+.f64 (*.f64 -1 re) im)
(fma.f64 -1 re im)
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(fma.f64 -1 re (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)))
(fma.f64 -1 re (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im)))
(*.f64 -1 im)
(*.f64 im -1)
(neg.f64 im)
(+.f64 (.f64 -1 re) (.f64 -1 im))
(fma.f64 -1 re (*.f64 im -1))
(*.f64 -1 (+.f64 re im))
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (*.f64 -1 im)))
(fma.f64 -1 re (fma.f64 -1/2 (/.f64 (.f64 re re) im) (.f64 im -1)))
(fma.f64 -1 re (fma.f64 (/.f64 (*.f64 re re) im) -1/2 (neg.f64 im)))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))))
(fma.f64 -1 re (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 -1/2 (/.f64 (.f64 re re) im) (.f64 im -1))))
(fma.f64 -1 re (fma.f64 (/.f64 (*.f64 re re) im) -1/2 (fma.f64 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) 1/8 (neg.f64 im))))
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (.f64 (sqrt.f64 2) (sqrt.f64 im)))
(fma.f64 -1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))) (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
(fma.f64 -1/2 (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 2))) (sqrt.f64 (/.f64 1 im))))))
(fma.f64 -1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 (sqrt.f64 2) (.f64 (.f64 re re) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))))))))
(fma.f64 -1/2 (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) (sqrt.f64 2))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 (.f64 re re) (.f64 (sqrt.f64 2) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))))) (.f64 (sqrt.f64 2) (sqrt.f64 im))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 2))) (sqrt.f64 (/.f64 1 im)))) (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 3))) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))))
(fma.f64 -1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 (sqrt.f64 2) (.f64 (.f64 re re) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))))) (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 re 3) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)))) (.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))))
(fma.f64 -1/2 (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) (sqrt.f64 2))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 (.f64 re re) (.f64 (sqrt.f64 2) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 1/4 (.f64 (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 im 3))) (.f64 (pow.f64 re 3) (sqrt.f64 2))))))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))
(fma.f64 -1/16 (.f64 (.f64 (pow.f64 im 3) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (.f64 (.f64 (sqrt.f64 2) (*.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re))))
(fma.f64 (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 -1/16 (/.f64 (*.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)))))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re))) (.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))))
(fma.f64 -1/16 (.f64 (.f64 (pow.f64 im 3) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (fma.f64 1/2 (.f64 (.f64 (.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 -1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 1 (sqrt.f64 1/2)))) 2)) (pow.f64 im 5)) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 re)) (.f64 (.f64 (sqrt.f64 2) (.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)))))
(fma.f64 -1/16 (.f64 (pow.f64 im 3) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)))) (fma.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 -1/16 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (sqrt.f64 1/2))) 2)) (sqrt.f64 1/2))) (.f64 1/2 (sqrt.f64 re)) (.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 re 6)))) re)) (.f64 -1/16 (/.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 re 2))))) (pow.f64 im 7))) (sqrt.f64 1/2)) (sqrt.f64 re))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re))) (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))))
(fma.f64 -1/16 (.f64 (.f64 (pow.f64 im 3) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (fma.f64 1/2 (.f64 (sqrt.f64 re) (.f64 (.f64 (-.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))) re)) (.f64 -1/16 (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 -1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 1 (sqrt.f64 1/2)))) 2)) (.f64 (.f64 re re) (pow.f64 (sqrt.f64 1/2) 2))))) (pow.f64 im 7)) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)))) (fma.f64 1/2 (.f64 (.f64 (.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 -1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 1 (sqrt.f64 1/2)))) 2)) (pow.f64 im 5)) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 re)) (.f64 (.f64 (sqrt.f64 2) (*.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re))))))
(fma.f64 (.f64 (sqrt.f64 2) (/.f64 (.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))) (/.f64 re -1/2)) (.f64 -1/16 (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 -1/16 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (sqrt.f64 1/2))) 2)) (.f64 re (.f64 (pow.f64 (sqrt.f64 1/2) 2) re))))) (pow.f64 im 7)) (sqrt.f64 1/2))) (.f64 1/2 (sqrt.f64 re)) (fma.f64 -1/16 (.f64 (pow.f64 im 3) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)))) (fma.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 -1/16 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (sqrt.f64 1/2))) 2)) (sqrt.f64 1/2))) (.f64 1/2 (sqrt.f64 re)) (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2))))))
im
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)
(fma.f64 1/2 (/.f64 (*.f64 re re) im) im)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5))) im)))
(fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) (fma.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) im)))
(fma.f64 1/2 (/.f64 (*.f64 re re) im) (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) im)))
re
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)) re)
(fma.f64 1/2 (/.f64 (*.f64 im im) re) re)
(fma.f64 1/2 (*.f64 im (/.f64 im re)) re)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 re (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(+.f64 re (fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (*.f64 im (/.f64 im re)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) re))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 re (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (+.f64 re (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (*.f64 im (/.f64 im re)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) re)))
(*.f64 -1 re)
(neg.f64 re)
(+.f64 (.f64 -1 re) (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))
(fma.f64 -1 re (/.f64 (.f64 (.f64 im im) -1/2) re))
(fma.f64 (*.f64 im (/.f64 im re)) -1/2 (neg.f64 re))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (*.f64 -1/2 (/.f64 (pow.f64 im 2) re))))
(fma.f64 -1 re (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 (.f64 (.f64 im im) -1/2) re)))
(fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (fma.f64 (*.f64 im (/.f64 im re)) -1/2 (neg.f64 re)))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
(fma.f64 -1 re (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (/.f64 (.f64 (.f64 im im) -1/2) re))))
(fma.f64 -1 re (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (fma.f64 (.f64 im (/.f64 im re)) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))
re
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)) re)
(fma.f64 1/2 (/.f64 (*.f64 im im) re) re)
(fma.f64 1/2 (*.f64 im (/.f64 im re)) re)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 re (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(+.f64 re (fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (*.f64 im (/.f64 im re)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) re))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 re (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (+.f64 re (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (*.f64 im (/.f64 im re)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) re)))
im
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)
(fma.f64 1/2 (/.f64 (*.f64 re re) im) im)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5))) im)))
(fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) (fma.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) im)))
(fma.f64 1/2 (/.f64 (*.f64 re re) im) (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) im)))
(*.f64 -1 im)
(*.f64 im -1)
(neg.f64 im)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))
(fma.f64 -1/2 (/.f64 (.f64 re re) im) (.f64 im -1))
(fma.f64 (/.f64 (*.f64 re re) im) -1/2 (neg.f64 im))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (*.f64 -1 im)))
(fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 -1/2 (/.f64 (.f64 re re) im) (.f64 im -1)))
(fma.f64 (/.f64 (*.f64 re re) im) -1/2 (fma.f64 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) 1/8 (neg.f64 im)))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))))
(fma.f64 -1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 -1/2 (/.f64 (.f64 re re) im) (.f64 im -1))))
(fma.f64 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) 1/8 (fma.f64 -1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) (fma.f64 (/.f64 (*.f64 re re) im) -1/2 (neg.f64 im))))

prune102.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	5	188

Error

0.2b

Counts

188 → 5

Alt Table

Status	Error	Program
	50.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (.f64 im (/.f64 im re))))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	45.9b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2))))
	45.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))

Compiler

Compiled 3550 to 2800 computations (21.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2))
✓	0.4b	(*.f64 im (sqrt.f64 1/2))

series10.0ms (0.3%)

Counts

4 → 24

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	re	@	0	(*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2))
1.0ms	im	@	0	(.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))
1.0ms	re	@	0	(.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))
1.0ms	im	@	inf	(.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))
1.0ms	im	@	0	(*.f64 im (sqrt.f64 1/2))

rewrite57.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`rule-aa-fabsaa_binary64`
236×	`rule-/ab-*+aa/1/2b_binary64`
217×	`rule-nega-/a-1_binary64`
216×	`rule-nega-*a-1_binary64`
215×	`rule-nega--0a_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	326	34
2	3879	34

Stop Event

1×	node limit

Counts

4 → 143

Calls

Call 1

Inputs
(*.f64 im (sqrt.f64 1/2))
(*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2))
(.f64 (.f64 im (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2)))
(sqrt.f64 (/.f64 1 re))

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

simplify27.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

307×	`rule-b-ac--ab*bc_binary64`
226×	`rule-*a/cb-/a/bc_binary64`
226×	`rule-a-bc-nega-cb_binary64`
217×	`rule-/a*bc-//abc_binary64`
196×	`rule-ab-ba_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	300
1	75	300
2	233	300
3	1122	300

Stop Event

1×	node limit

Counts

167 → 146

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))

Outputs
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(*.f64 (sqrt.f64 1/2) im)
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 im (sqrt.f64 2))))

prune103.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	142	9	151

Error

0.1b

Counts

151 → 9

Alt Table

Status	Error	Program
	45.9b	(.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 re)) im))) 2))
✓	45.9b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 2))))
	50.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (.f64 im (/.f64 im re))))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	57.3b	(.f64 1/2 (/.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 re)) im)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 re)) im)) 2)))
▶	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re)))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))
	45.9b	(.f64 1/2 (.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 re))) 2)))
	49.1b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (cbrt.f64 (pow.f64 (/.f64 1 re) 3/2)) (sqrt.f64 2))))

Compiler

Compiled 2712 to 2268 computations (16.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re)))
✓	0.1b	(/.f64 (*.f64 im (sqrt.f64 1/2)) (/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re))))
✓	0.1b	(/.f64 (sqrt.f64 2) (sqrt.f64 re))
	0.4b	(*.f64 im (sqrt.f64 1/2))

series6.0ms (0.2%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	re	@	-inf	(/.f64 (*.f64 im (sqrt.f64 1/2)) (/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re))))
1.0ms	re	@	-inf	(/.f64 (sqrt.f64 2) (sqrt.f64 re))
1.0ms	re	@	0	(/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re)))
1.0ms	re	@	-inf	(/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re)))
0.0ms	re	@	inf	(/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re)))

rewrite59.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

290×	`rule-aa-fabsaa_binary64`
226×	`rule-nega-/a-1_binary64`
225×	`rule-nega--0a_binary64`
225×	`rule-nega-*a-1_binary64`
137×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	335	26
2	4170	26

Stop Event

1×	node limit

Counts

3 → 136

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 2) (sqrt.f64 re))
(/.f64 (*.f64 im (sqrt.f64 1/2)) (/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re))))
(/.f64 1 (/.f64 (sqrt.f64 2) (sqrt.f64 re)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (/.f64 2 re)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 2 re)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 2 re)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (/.f64 2 re)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 2 re)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (/.f64 2 re)) (sqrt.f64 (/.f64 2 re))) (sqrt.f64 (/.f64 2 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 2 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (/.f64 2 re))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 re))) (cbrt.f64 (/.f64 2 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 re)) (cbrt.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (sqrt.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) (sqrt.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (sqrt.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 2)) (/.f64 1/2 (sqrt.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 re)) (*.f64 2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (/.f64 2 re)) (sqrt.f64 (/.f64 2 re))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 re) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 2 re)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 re))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 re))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 2 re)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 2 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 2 re)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 re 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 2 re))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 2 re)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 2 re)) (cbrt.f64 (sqrt.f64 (/.f64 2 re))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) (sqrt.f64 (sqrt.f64 (/.f64 2 re))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (sqrt.f64 2)) (/.f64 1/2 (sqrt.f64 re)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 2 re))))))))

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (/.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 re 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (/.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 re 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (/.f64 re 2)) (sqrt.f64 (/.f64 re 2))) (sqrt.f64 (/.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 re) (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (/.f64 re 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 re)) (/.f64 (cbrt.f64 re) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 re 2))) (cbrt.f64 (pow.f64 (/.f64 2 re) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 2 re) -1)) (cbrt.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 re 1/4) (/.f64 (pow.f64 re 1/4) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 re 2))) (sqrt.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 (/.f64 re 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 re) (sqrt.f64 re)) (/.f64 1/2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (/.f64 re 2)) (sqrt.f64 (/.f64 re 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 2 re)) -1) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 re))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) -1) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (sqrt.f64 2)) -1) (pow.f64 (/.f64 1/2 (sqrt.f64 re)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 re)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 re 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 re 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 re) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 re 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 re 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 2 re) -1))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 re 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 re 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 re 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 re 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 re 3/2) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 re 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (*.f64 1/2 (sqrt.f64 (/.f64 re 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (/.f64 re 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 re 2)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (/.f64 2 re) -1)) (cbrt.f64 (sqrt.f64 (/.f64 re 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sqrt.f64 (/.f64 re 2))) (sqrt.f64 (sqrt.f64 (/.f64 re 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 re 2))))))))

simplify25.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

313×	`rule-b-ac--ab*bc_binary64`
229×	`rule-*a/cb-/a/bc_binary64`
226×	`rule-a-bc-nega-cb_binary64`
215×	`rule-/a*bc-//abc_binary64`
198×	`rule-ab-ba_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	228
1	75	228
2	233	228
3	1124	228

Stop Event

1×	node limit

Counts

148 → 138

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))

Outputs
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (.f64 (sqrt.f64 2) im) (*.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (*.f64 im (sqrt.f64 (/.f64 1 re)))))

prune127.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	3	3	6
Picked	1	0	1
Done	1	1	2
Total	172	8	180

Error

0.1b

Counts

180 → 8

Alt Table

Status	Error	Program
	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) 2))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))
	50.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (.f64 im (/.f64 im re))))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (/.f64 1 (*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (sqrt.f64 re))))))
▶	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))
	45.8b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 im (sqrt.f64 1/2))) (/.f64 (sqrt.f64 (.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 re 2)))))
	49.1b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 1/2)) (.f64 (cbrt.f64 (pow.f64 (/.f64 1 re) 3/2)) (sqrt.f64 2))))

Compiler

Compiled 3036 to 2556 computations (15.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (/.f64 2 re) -1/2)
✓	0.1b	(/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))
	0.4b	(*.f64 im (sqrt.f64 1/2))

series58.0ms (1.5%)

Counts

2 → 24

Calls

9 calls:

Time	Variable		Point	Expression
22.0ms	re	@	0	(pow.f64 (/.f64 2 re) -1/2)
20.0ms	re	@	-inf	(pow.f64 (/.f64 2 re) -1/2)
11.0ms	re	@	inf	(pow.f64 (/.f64 2 re) -1/2)
1.0ms	re	@	inf	(/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))
1.0ms	im	@	0	(/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))

rewrite54.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`rule-aa-fabsaa_binary64`
246×	`rule-/ab-*+aa/1/2b_binary64`
200×	`rule-nega--0a_binary64`
200×	`rule-nega-/a-1_binary64`
200×	`rule-nega-*a-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	285	22
2	3541	22

Stop Event

1×	node limit

Counts

2 → 91

Calls

Call 1

Inputs
(/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))
(pow.f64 (/.f64 2 re) -1/2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 0 (neg.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)) (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))) (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))) (exp.f64 (log1p.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))))) (+.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)) (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))) (+.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)) (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))) (+.f64 (+.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)) (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))) (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))))))) (#(struct:change #<rule egg-rr> 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2 re) -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (*.f64 im (sqrt.f64 1/2))) (pow.f64 (/.f64 2 re) -1/4)) (/.f64 (sqrt.f64 (*.f64 im (sqrt.f64 1/2))) (pow.f64 (/.f64 2 re) -1/4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (+.f64 im im)) (/.f64 1/2 (pow.f64 (/.f64 2 re) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (/.f64 2 re) -1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 2 re) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 2 re) -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (/.f64 2 re) -1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 0 (neg.f64 (pow.f64 (/.f64 2 re) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 2 re) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (/.f64 2 re) -1/2) (pow.f64 (/.f64 2 re) -1/2)) (pow.f64 (/.f64 2 re) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 2 re) -1/2))) (exp.f64 (log1p.f64 (pow.f64 (/.f64 2 re) -1/2)))) (+.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 2 re) -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (pow.f64 (/.f64 2 re) -1/2) (pow.f64 (/.f64 2 re) -1/2)) (+.f64 (pow.f64 (/.f64 2 re) -1/2) (pow.f64 (/.f64 2 re) -1/2))) (+.f64 (+.f64 (pow.f64 (/.f64 2 re) -1/2) (pow.f64 (/.f64 2 re) -1/2)) (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 2 re) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 2 re) -1/2) (pow.f64 1 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 2 re) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (/.f64 2 re) -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 2 re) -1/2)) (cbrt.f64 (pow.f64 (/.f64 2 re) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 2 re) -1)) (cbrt.f64 (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 2 re) -1/4) (pow.f64 (/.f64 2 re) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (/.f64 2 re) -1/2) (pow.f64 (/.f64 2 re) -1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 4 -1/2) (pow.f64 (/.f64 1/2 re) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 re)) 2) -1/2) (pow.f64 (cbrt.f64 (/.f64 2 re)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 2 re)) -1/2) (pow.f64 (sqrt.f64 (/.f64 2 re)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 2 re) -1/2)) (neg.f64 (pow.f64 (/.f64 2 re) -1/2))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 2 re) -1/2) 3) (pow.f64 (pow.f64 (/.f64 2 re) -1/2) 3)) (/.f64 1/2 (pow.f64 (/.f64 2 re) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (/.f64 2 re) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (/.f64 2 re) -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (pow.f64 (/.f64 2 re) -1/2) 3) (pow.f64 (/.f64 2 re) -1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 2 re) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (/.f64 2 re) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 2 re) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (/.f64 2 re) -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 2 re) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 2 re) -1/2) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (/.f64 2 re) -1)) (cbrt.f64 (pow.f64 (/.f64 2 re) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 2 re) -1/4) (pow.f64 (/.f64 2 re) -1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 (/.f64 2 re))))))))

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

455×	`rule-a-*a1_binary64`
455×	`rule-a--a0_binary64`
455×	`rule-a-+a0_binary64`
454×	`rule-a-/a1_binary64`
373×	`rule--ab--+aa+ab_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	420
1	196	396
2	561	360
3	2573	360

Stop Event

1×	node limit

Counts

115 → 98

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))

Outputs
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 re)) (*.f64 (sqrt.f64 1/2) im)))
(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 2) (.f64 -1 (log.f64 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 2) (log.f64 (/.f64 1 re)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 2) (*.f64 -1 (log.f64 re))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 2) (log.f64 re)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2)))
(*.f64 (pow.f64 (/.f64 -1 re) -1/2) (pow.f64 -2 -1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2)))
(*.f64 (pow.f64 (/.f64 -1 re) -1/2) (pow.f64 -2 -1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2)))
(*.f64 (pow.f64 (/.f64 -1 re) -1/2) (pow.f64 -2 -1/2))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 (/.f64 -1 re)) (log.f64 -2)))
(*.f64 (pow.f64 (/.f64 -1 re) -1/2) (pow.f64 -2 -1/2))

prune96.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Error

0.1b

Counts

139 → 8

Alt Table

Status	Error	Program
	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) 2))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))))
	50.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (.f64 im (/.f64 im re))))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (/.f64 1 (*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (sqrt.f64 re))))))
✓	45.8b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 1/2)) (pow.f64 (/.f64 2 re) -1/2)))
	45.8b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 im (sqrt.f64 1/2))) (/.f64 (sqrt.f64 (.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 re 2)))))
	45.8b	(.f64 1/2 (pow.f64 (/.f64 (sqrt.f64 (.f64 im (sqrt.f64 1/2))) (pow.f64 (/.f64 2 re) -1/4)) 2))

Compiler

Compiled 2521 to 2149 computations (14.8% saved)

regimes442.0ms (11.1%)

Accuracy

Total -53.4b remaining (-663.9%)

Threshold costs -53.4b (-663.9%)

Counts

60 → 2

Compiler

Compiled 943 to 771 computations (18.2% saved)

bsearch67.0ms (1.7%)

Algorithm

1×	binary-search

Calls

1 calls:

66.0ms

re

Steps

Iters	Point		Range
7.962544944086704e-55	∈ [	7.962544944086704e-55	,	1.4188263376585514e-54	]

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	42

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 re 85867914810947/107839786668602559178668060348078522694548577690162289924414440996864) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (*.f64 1/2 (/.f64 (*.f64 im (sqrt.f64 1/2)) (*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2)))))

Outputs

(if (<=.f64 re 85867914810947/107839786668602559178668060348078522694548577690162289924414440996864) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (*.f64 1/2 (/.f64 (*.f64 im (sqrt.f64 1/2)) (*.f64 (pow.f64 2 -1/2) (pow.f64 re 1/2)))))

end116.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 184 to 149 computations (19% saved)

Details

analyze577.0ms (14.4%)

sample1.8s (46.1%)

preprocess35.0ms (0.9%)

simplify19.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series14.0ms (0.4%)

rewrite46.0ms (1.1%)

simplify37.0ms (0.9%)

prune102.0ms (2.6%)

localize10.0ms (0.2%)

series10.0ms (0.3%)

rewrite57.0ms (1.4%)

simplify27.0ms (0.7%)

prune103.0ms (2.6%)

localize10.0ms (0.3%)

series6.0ms (0.2%)

rewrite59.0ms (1.5%)

simplify25.0ms (0.6%)

prune127.0ms (3.2%)

localize9.0ms (0.2%)

series58.0ms (1.5%)

rewrite54.0ms (1.3%)

simplify36.0ms (0.9%)

prune96.0ms (2.4%)

regimes442.0ms (11.1%)

bsearch67.0ms (1.7%)

simplify1.0ms (0%)

end116.0ms (2.9%)

Profiling