Details

analyze506.0ms (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.0s (48.5%)

Results

846.0ms	6208×	body	128	valid
463.0ms	668×	body	2048	valid
357.0ms	548×	body	4096	valid
199.0ms	470×	body	1024	valid
72.0ms	223×	body	512	valid
34.0ms	139×	body	256	valid

Compiler

Compiled 40 to 28 computations (30% saved)

preprocess33.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

316×	`fma-def_binary64`
164×	`fma-neg_binary64`
86×	`distribute-rgt-in_binary64`
48×	`distribute-lft-in_binary64`
48×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	30
1	33	30
2	51	30
3	88	30
4	135	30
5	185	30
6	305	30
7	478	30
8	682	30
9	833	30
10	1083	30
11	1243	30
12	1261	30
13	1265	30
0	2	2

Stop Event

1×	saturated
1×	saturated

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)

simplify23.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

201×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
43×	`cancel-sign-sub-inv_binary64`
27×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15

Stop Event

1×

saturated

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 (hypot.f64 re im) re))))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

14.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	38.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.5b	(-.f64 (hypot.f64 re im) re)

series46.0ms (1.1%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
11.0ms	im	@	0	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
6.0ms	re	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
6.0ms	im	@	-inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
5.0ms	im	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
4.0ms	re	@	-inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
85×	`pow1_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	173	19
2	2206	19

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

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

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

Outputs

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

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

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-def_binary64`
371×	`associate-l_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
236×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1017
1	421	994
2	1460	945

Stop Event

1×	node limit

Counts

94 → 107

Calls

Call 1

Inputs
im
(-.f64 im re)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) re)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) 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 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(*.f64 -2 re)
(neg.f64 (+.f64 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 2 re) (*.f64 1/2 (/.f64 (pow.f64 im 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 2 re) (.f64 1/2 (/.f64 (pow.f64 im 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 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
im
(-.f64 im re)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) re)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re))
(*.f64 -1 im)
(neg.f64 (+.f64 re im))
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re 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 re im)))
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (.f64 (sqrt.f64 2) (sqrt.f64 im))) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 3)) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.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 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.f64 1/32 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (.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 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.f64 1/32 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (+.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 1/8192 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (.f64 5/256 (.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 7)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))))))))

Outputs
im
(-.f64 im re)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) re)
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) im) re)
(-.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) im) re)
(fma.f64 1/2 (/.f64 re (/.f64 im re)) (-.f64 im re))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re))
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(-.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
(.f64 1/2 (/.f64 (.f64 im im) re))
(*.f64 1/2 (/.f64 im (/.f64 re im)))
(.f64 (/.f64 1/2 re) (.f64 im im))
(-.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 (.f64 im im) re)) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (/.f64 (*.f64 -1/8 (pow.f64 im 4)) (pow.f64 re 3)))
(fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 (.f64 im im) re))) (*.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 im (/.f64 re im)) (/.f64 (*.f64 -1/8 (pow.f64 im 4)) (pow.f64 re 3))))
(fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 (.f64 im im) re))) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 im (/.f64 re im)))) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (/.f64 (.f64 1/8 (pow.f64 im 4)) (pow.f64 re 3))))
(fma.f64 1/2 (.f64 (/.f64 im re) im) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (.f64 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) -5/128))))
(*.f64 -2 re)
(*.f64 re -2)
(neg.f64 (+.f64 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))
(neg.f64 (fma.f64 2 re (.f64 1/2 (/.f64 (.f64 im im) re))))
(+.f64 (.f64 re -2) (.f64 (/.f64 im (/.f64 re im)) -1/2))
(fma.f64 re -2 (.f64 (.f64 (/.f64 im re) im) -1/2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 2 re) (*.f64 1/2 (/.f64 (pow.f64 im 2) re))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (fma.f64 2 re (.f64 1/2 (/.f64 (*.f64 im im) re))))
(-.f64 (/.f64 (.f64 1/8 (pow.f64 im 4)) (pow.f64 re 3)) (fma.f64 1/2 (/.f64 im (/.f64 re im)) (.f64 re 2)))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 re -2 (.f64 (.f64 (/.f64 im re) im) -1/2)))
(-.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 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
(-.f64 (.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 2 re (.f64 1/2 (/.f64 (*.f64 im im) re)))))
(-.f64 (/.f64 (.f64 1/8 (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 im (/.f64 re im)) (.f64 re 2))))
(+.f64 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 re -2 (.f64 (.f64 (/.f64 im re) im) -1/2))) (/.f64 (*.f64 -1/16 (pow.f64 im 6)) (pow.f64 re 5)))
(*.f64 1/2 (/.f64 (pow.f64 im 2) re))
(.f64 1/2 (/.f64 (.f64 im im) re))
(*.f64 1/2 (/.f64 im (/.f64 re im)))
(.f64 (/.f64 1/2 re) (.f64 im im))
(-.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 (.f64 im im) re)) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (/.f64 (*.f64 -1/8 (pow.f64 im 4)) (pow.f64 re 3)))
(fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 (.f64 im im) re))) (*.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 im (/.f64 re im)) (/.f64 (*.f64 -1/8 (pow.f64 im 4)) (pow.f64 re 3))))
(fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 (.f64 im im) re))) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 im (/.f64 re im)))) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (/.f64 (.f64 1/8 (pow.f64 im 4)) (pow.f64 re 3))))
(fma.f64 1/2 (.f64 (/.f64 im re) im) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (.f64 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) -5/128))))
im
(-.f64 im re)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) re)
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) im) re)
(-.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) im) re)
(fma.f64 1/2 (/.f64 re (/.f64 im re)) (-.f64 im re))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re))
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(-.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(*.f64 -1 im)
(neg.f64 im)
(neg.f64 (+.f64 re im))
(neg.f64 (+.f64 im re))
(-.f64 (neg.f64 im) re)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im)))
(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) (+.f64 im re)))
(-.f64 (*.f64 (/.f64 re (/.f64 im re)) -1/2) (+.f64 im 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 re im)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (fma.f64 1/2 (/.f64 (.f64 re re) im) (+.f64 im re)))
(-.f64 (*.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 im (fma.f64 1/2 (/.f64 re (/.f64 im re)) re)))
(-.f64 (*.f64 (/.f64 1/8 (pow.f64 im 3)) (pow.f64 re 4)) (+.f64 im (fma.f64 1/2 (/.f64 re (/.f64 im re)) re)))
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.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 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) (*.f64 re (sqrt.f64 2))))
(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (.f64 (sqrt.f64 2) (sqrt.f64 im))) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(+.f64 (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 re re) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (.f64 (sqrt.f64 2) (sqrt.f64 im))) (.f64 -1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))
(fma.f64 1/8 (.f64 (.f64 re re) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) (.f64 re (sqrt.f64 2)))))
(fma.f64 1/8 (.f64 (.f64 re (sqrt.f64 2)) (.f64 re (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 3)) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(+.f64 (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 re re) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 1/16 (.f64 (.f64 (pow.f64 re 3) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))) (.f64 -1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))
(+.f64 (fma.f64 1/8 (.f64 (.f64 re re) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (fma.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (pow.f64 re 3) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))) (.f64 (sqrt.f64 2) (sqrt.f64 im)))) (.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) (*.f64 re (sqrt.f64 2))))
(+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 im 5))) (.f64 (pow.f64 re 3) 1/16)))) (.f64 (sqrt.f64 2) (-.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 im 3))) (.f64 (.f64 re re) 1/8)) (.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2)))))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) im) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
(-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.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 (.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) im) (sqrt.f64 (/.f64 1 re))) (.f64 -1/16 (*.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3))) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))))
(fma.f64 (sqrt.f64 1/2) (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))) (.f64 (.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) -1/16))
(fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (*.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16)))
(-.f64 (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.f64 1/32 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (.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 (fma.f64 (.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) im) (sqrt.f64 (/.f64 1 re)) (.f64 1/32 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 5))) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))))) (fma.f64 1/512 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 1/16 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))))))
(-.f64 (fma.f64 (sqrt.f64 1/2) (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (.f64 1/32 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 5))))) (fma.f64 1/16 (.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (*.f64 1/512 (sqrt.f64 2)) (/.f64 1/2 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2)))))))
(+.f64 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (.f64 (/.f64 (.f64 1/32 (sqrt.f64 2)) (sqrt.f64 1/2)) (pow.f64 im 5)) (.f64 1/256 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 5)))))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16)))
(-.f64 (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.f64 1/32 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (+.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 1/8192 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (.f64 5/256 (.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 7)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))))))))
(-.f64 (fma.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))) (fma.f64 (.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) im) (sqrt.f64 (/.f64 1 re)) (.f64 1/32 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 5))) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))))) (fma.f64 1/512 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3))) (fma.f64 1/16 (.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (fma.f64 1/8192 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 im 7)))) (.f64 5/256 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 7)))))))))
(-.f64 (fma.f64 1/512 (.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 1/2 (sqrt.f64 1/2))) (pow.f64 im 7)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))) (fma.f64 (sqrt.f64 1/2) (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (.f64 1/32 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 5)))))) (fma.f64 1/512 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (/.f64 (pow.f64 im 5) 1/2))) (fma.f64 1/16 (.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (.f64 1/8192 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 1/2) 5)) (pow.f64 im 7))) (.f64 5/256 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 7))))))))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (.f64 1/256 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 7))) (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (.f64 (/.f64 (.f64 1/32 (sqrt.f64 2)) (sqrt.f64 1/2)) (pow.f64 im 5)) (.f64 1/256 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 5))))))) (fma.f64 1/16 (.f64 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (fma.f64 5/256 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (pow.f64 im 7)) (.f64 (/.f64 (*.f64 1/8192 (sqrt.f64 2)) (pow.f64 (sqrt.f64 1/2) 5)) (pow.f64 im 7))))))

prune78.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Error

0.1b

Counts

109 → 7

Alt Table

Status	Error	Program
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2))))
	46.8b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))))
	56.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 1/2 re) (.f64 im im)))))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	52.8b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16))))

Compiler

Compiled 2524 to 1777 computations (29.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (hypot.f64 re im) re))
✓	0.0b	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)))
✓	0.4b	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
	0.5b	(-.f64 (hypot.f64 re im) re)

series91.0ms (2.2%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
10.0ms	im	@	0	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)))
7.0ms	im	@	inf	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
7.0ms	re	@	inf	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
7.0ms	im	@	-inf	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)
7.0ms	im	@	0	(pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2)

rewrite69.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`log1p-expm1-u_binary64`
877×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`
95×	`pow1_binary64`
93×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	217	28
2	2445	28

Stop Event

1×	node limit

Counts

3 → 94

Calls

Call 1

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

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

Outputs

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

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

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

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
452×	`times-frac_binary64`
443×	`associate-/l*_binary64`
329×	`cancel-sign-sub-inv_binary64`
173×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1138
1	507	1097
2	1798	1018

Stop Event

1×	node limit

Counts

118 → 138

Calls

Call 1

Inputs
im
(-.f64 im re)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) re)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 im 2)) re)
(-.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 im 2)) re) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (/.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 im 2)) re)) (*.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (/.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 im 2)) re)) (+.f64 (.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (.f64 (sqrt.f64 2) (sqrt.f64 im))) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 3)) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
(-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.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 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.f64 1/32 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (.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 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (.f64 1/32 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (+.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 1/8192 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 7)) (pow.f64 (sqrt.f64 1/2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (.f64 5/256 (.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 im 7)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))))))))
(sqrt.f64 im)
(-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))
(-.f64 (+.f64 (sqrt.f64 im) (.f64 1/8 (.f64 (pow.f64 re 2) (sqrt.f64 (/.f64 1 (pow.f64 im 3)))))) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 re 3) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))) (+.f64 (sqrt.f64 im) (.f64 1/8 (.f64 (pow.f64 re 2) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))
(.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))
(-.f64 (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))) (.f64 1/16 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))))
(-.f64 (+.f64 (.f64 1/32 (.f64 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (.f64 1/512 (.f64 (/.f64 (pow.f64 im 5) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9)))))))
(-.f64 (+.f64 (.f64 1/32 (.f64 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))) (.f64 1/512 (.f64 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 5/256 (.f64 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (pow.f64 im 5) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (.f64 1/8192 (.f64 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))))))))

Outputs
im
(-.f64 im re)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) re)
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) im) re)
(-.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) im) re)
(-.f64 (fma.f64 1/2 (*.f64 (/.f64 re im) re) im) re)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re))
(-.f64 (fma.f64 1/2 (/.f64 (*.f64 re re) im) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(-.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(-.f64 (fma.f64 1/2 (*.f64 (/.f64 re im) re) im) (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re))
(/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 im 2)) re)
(/.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 im im)) re)
(.f64 (/.f64 1/2 re) (.f64 im im))
(*.f64 (/.f64 im (/.f64 re im)) 1/2)
(-.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 im 2)) re) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
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(-.f64 (fma.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 (/.f64 1 re))) (fma.f64 (.f64 1/32 (sqrt.f64 (/.f64 1 (pow.f64 re 9)))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) -1/16)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2)))))
(-.f64 (+.f64 (.f64 1/32 (.f64 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))) (.f64 1/512 (.f64 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 5/256 (.f64 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 13))))) (+.f64 (.f64 1/512 (.f64 (/.f64 (pow.f64 im 5) (pow.f64 (sqrt.f64 1/2) 3)) (sqrt.f64 (/.f64 1 (pow.f64 re 9))))) (.f64 1/8192 (.f64 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5)) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))))))))
(-.f64 (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 (.f64 im (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 re)) (.f64 (.f64 1/512 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 3))) (sqrt.f64 (/.f64 1 (pow.f64 re 13)))))) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 5/256 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) (fma.f64 1/512 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 1/8192 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))))))))
(-.f64 (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (.f64 1/512 (/.f64 (pow.f64 im 7) (.f64 1/2 (sqrt.f64 1/2))))))) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 5/256 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) (fma.f64 1/512 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (.f64 1/2 (sqrt.f64 1/2)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (*.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))))))))
(-.f64 (fma.f64 im (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (.f64 1/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2)))))) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (/.f64 (*.f64 5/256 (pow.f64 im 7)) (sqrt.f64 1/2)))))))

prune136.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	206	6	212

Error

0.1b

Counts

212 → 6

Alt Table

Status	Error	Program
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (/.f64 im (/.f64 re im)) 1/2))))
	46.8b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))))
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	46.8b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re))))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2))))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 4874 to 3304 computations (32.2% 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 im (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re))))
✓	0.2b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))
✓	0.2b	(.f64 (sqrt.f64 1/2) (.f64 im (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))))

series51.0ms (1.2%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	im	@	inf	(.f64 (sqrt.f64 1/2) (.f64 im (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))))
5.0ms	im	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 im (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))))
4.0ms	im	@	0	(.f64 (sqrt.f64 1/2) (.f64 im (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))))
3.0ms	re	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 im (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re)))))
3.0ms	im	@	-inf	(.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 re))))

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`log-prod_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
189×	`pow3_binary64`
181×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	263	33
2	2921	33

Stop Event

1×	node limit

Counts

4 → 91

Calls

Call 1

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

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

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

27×	`associate-l_binary64`
20×	`associate-r_binary64`
13×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	396
1	25	396
2	48	396
3	88	396
4	88	396

Stop Event

1×

saturated

Counts

115 → 95

Calls

Call 1

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

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

prune61.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	93	8	101

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
	46.8b	(.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 2 re)) (*.f64 (sqrt.f64 1/2) im))) 2))
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (/.f64 im (/.f64 re im)) 1/2))))
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2))))
▶	46.8b	(.f64 1/2 (+.f64 0 (.f64 (sqrt.f64 (/.f64 2 re)) (*.f64 (sqrt.f64 1/2) im))))
	46.8b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (*.f64 im (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) 2))))
	46.8b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 (*.f64 im (sqrt.f64 (/.f64 2 re)))) 2)))
	47.0b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 im (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (pow.f64 re -1/2)) 3)))))

Compiler

Compiled 1730 to 1471 computations (15% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series32.0ms (0.8%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	im	@	inf	(.f64 (sqrt.f64 (/.f64 2 re)) (.f64 (sqrt.f64 1/2) im))
5.0ms	im	@	-inf	(.f64 (sqrt.f64 (/.f64 2 re)) (.f64 (sqrt.f64 1/2) im))
4.0ms	im	@	0	(.f64 (sqrt.f64 (/.f64 2 re)) (.f64 (sqrt.f64 1/2) im))
4.0ms	re	@	0	(.f64 (sqrt.f64 (/.f64 2 re)) (.f64 (sqrt.f64 1/2) im))
3.0ms	re	@	inf	(.f64 (sqrt.f64 (/.f64 2 re)) (.f64 (sqrt.f64 1/2) im))

rewrite48.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

861×	`log1p-expm1-u_binary64`
861×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
94×	`*-un-lft-identity_binary64`
94×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	208	24
2	2390	24

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

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

Outputs

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

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

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

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

24×	`associate-l_binary64`
16×	`associate-r_binary64`
14×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	228
1	22	228
2	43	228
3	83	228
4	85	228

Stop Event

1×

saturated

Counts

75 → 65

Calls

Call 1

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

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

prune38.0ms (0.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	65	8	73

Error

Counts

73 → 8

Alt Table

Status	Error	Program
	46.7b	(.f64 1/2 (+.f64 0 (pow.f64 (.f64 im (sqrt.f64 (*.f64 (/.f64 2 re) 1/2))) 1)))
	46.8b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (*.f64 im (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 re))) 2))))
✓	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (-.f64 (hypot.f64 re im) re)) 2))))
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (/.f64 im (/.f64 re im)) 1/2))))
✓	46.8b	(.f64 1/2 (+.f64 0 (.f64 (sqrt.f64 (/.f64 2 re)) (*.f64 (sqrt.f64 1/2) im))))
	46.8b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 (*.f64 im (sqrt.f64 (/.f64 2 re)))) 2)))
	52.4b	(.f64 1/2 (+.f64 0 (.f64 (sqrt.f64 (/.f64 2 re)) (sqrt.f64 (.f64 1/2 (.f64 im im))))))

Compiler

Compiled 1161 to 995 computations (14.3% saved)

regimes422.0ms (10.3%)

Accuracy

Total 8.1b remaining (98.4%)

Threshold costs 0b (0%)

Counts

44 → 4

Compiler

Compiled 4956 to 4139 computations (16.5% saved)

bsearch119.0ms (2.9%)

Algorithm

3×	binary-search

Calls

3 calls:

44.0ms	re
43.0ms	re
31.0ms	re

Steps

Iters	Point		Range
1e+14	∈ [	5379714864.915441	,	105027568806842.6	]
6e-67	∈ [	1.1289654278034395e-67	,	9.22765674403877e-56	]
8.7e-104	∈ [	2.3297512197378806e-106	,	8.799237800027863e-104	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`+-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	78
1	40	78
2	44	78
3	46	78
4	47	78

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 re 7020491856048783/80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (if (<=.f64 re 4553130216154053/7588550360256754183279148073529370729071901715047420004889892225542594864082845696) (*.f64 1/2 (+.f64 0 (pow.f64 (*.f64 im (sqrt.f64 (*.f64 (/.f64 2 re) 1/2))) 1))) (if (<=.f64 re 100000000000000) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (*.f64 1/2 (+.f64 0 (pow.f64 (*.f64 im (sqrt.f64 (*.f64 (/.f64 2 re) 1/2))) 1))))))

Outputs

(if (<=.f64 re 7020491856048783/80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (if (<=.f64 re 4553130216154053/7588550360256754183279148073529370729071901715047420004889892225542594864082845696) (*.f64 1/2 (+.f64 0 (pow.f64 (*.f64 im (sqrt.f64 (*.f64 (/.f64 2 re) 1/2))) 1))) (if (<=.f64 re 100000000000000) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (*.f64 1/2 (+.f64 0 (pow.f64 (*.f64 im (sqrt.f64 (*.f64 (/.f64 2 re) 1/2))) 1))))))

(if (<=.f64 re 7020491856048783/80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (if (<=.f64 re 4553130216154053/7588550360256754183279148073529370729071901715047420004889892225542594864082845696) (*.f64 1/2 (*.f64 im (sqrt.f64 (*.f64 1/2 (/.f64 2 re))))) (if (<=.f64 re 100000000000000) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (*.f64 1/2 (*.f64 im (sqrt.f64 (*.f64 1/2 (/.f64 2 re))))))))

end121.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 229 to 179 computations (21.8% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15

Details

analyze506.0ms (12.3%)

sample2.0s (48.5%)

preprocess33.0ms (0.8%)

simplify23.0ms (0.6%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series46.0ms (1.1%)

rewrite52.0ms (1.3%)

simplify35.0ms (0.8%)

prune78.0ms (1.9%)

localize8.0ms (0.2%)

series91.0ms (2.2%)

rewrite69.0ms (1.7%)

simplify35.0ms (0.9%)

prune136.0ms (3.3%)

localize10.0ms (0.2%)

series51.0ms (1.2%)

rewrite51.0ms (1.2%)

simplify16.0ms (0.4%)

prune61.0ms (1.5%)

localize8.0ms (0.2%)

series32.0ms (0.8%)

rewrite48.0ms (1.2%)

simplify12.0ms (0.3%)

prune38.0ms (0.9%)

regimes422.0ms (10.3%)

bsearch119.0ms (2.9%)

simplify3.0ms (0.1%)

end121.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15