Details

analyze527.0ms (15.5%)

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)

sample1.8s (53.5%)

Results

798.0ms	6262×	body	128	valid
375.0ms	709×	body	2048	valid
355.0ms	509×	body	4096	valid
180.0ms	429×	body	1024	valid
74.0ms	232×	body	512	valid
25.0ms	115×	body	256	valid

Compiler

Compiled 40 to 28 computations (30% saved)

preprocess33.0ms (1%)

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)

simplify22.0ms (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))))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.2b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.6b	(-.f64 (hypot.f64 re im) re)

series20.0ms (0.6%)

Counts

3 → 56

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	im	@	0	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
2.0ms	re	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
2.0ms	im	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
1.0ms	re	@	inf	(-.f64 (hypot.f64 re im) re)
1.0ms	re	@	-inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))

rewrite46.0ms (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	23
1	173	23
2	2206	23

Stop Event

1×	node limit

Counts

3 → 81

Calls

Call 1

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

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

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 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 expm1.f64 (log1p.f64 (-.f64 (hypot.f64 re im) re)))))))

((#(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 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 expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2))))))))

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

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary64`
365×	`associate-/l*_binary64`
347×	`times-frac_binary64`
280×	`cancel-sign-sub-inv_binary64`
254×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	1505
1	491	1464
2	1680	1399

Stop Event

1×	node limit

Counts

137 → 153

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

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

prune94.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	148	6	154

Error

0.1b

Counts

154 → 6

Alt Table

Status	Error	Program
	51.9b	(.f64 1/2 (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 5))) (*.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3))) -1/16))))
	46.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)) (.f64 im (sqrt.f64 2))))
	46.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
▶	32.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
✓	14.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	50.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 im (/.f64 re im))))))

Compiler

Compiled 3363 to 2349 computations (30.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

series2.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite30.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`pow1_binary64`
450×	`add-log-exp_binary64`
450×	`log1p-expm1-u_binary64`
450×	`expm1-log1p-u_binary64`
439×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	121	6
2	1297	6

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 im))

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

Outputs

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

14 → 14

Calls

Call 1

Inputs

Outputs

prune18.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	14	6	20

Error

0.1b

Counts

20 → 6

Alt Table

Status	Error	Program
	51.9b	(.f64 1/2 (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 5))) (*.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3))) -1/16))))
	46.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 (/.f64 1 re)) (sqrt.f64 1/2)) (.f64 im (sqrt.f64 2))))
▶	46.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	32.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
✓	14.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	50.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 im (/.f64 re im))))))

Compiler

Compiled 305 to 265 computations (13.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.4%)

Counts

4 → 0

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	im	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
2.0ms	im	@	0	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
1.0ms	im	@	0	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
1.0ms	re	@	0	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
1.0ms	re	@	0	(sqrt.f64 (/.f64 1 re))

rewrite47.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

915×	`log1p-expm1-u_binary64`
915×	`expm1-log1p-u_binary64`
121×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
115×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	261	17
2	2902	17

Stop Event

1×	node limit

Counts

4 → 74

Calls

Call 1

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

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

74 → 74

Calls

Call 1

Inputs

Outputs

prune48.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	74	6	80

Error

0.1b

Counts

80 → 6

Alt Table

Status	Error	Program
	52.3b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (pow.f64 (/.f64 (pow.f64 re -1/2) re) 1/3)))
✓	32.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	46.4b	(.f64 1/2 (.f64 (pow.f64 (sqrt.f64 im) 2) (sqrt.f64 (/.f64 1 re))))
	46.3b	(.f64 1/2 (.f64 (pow.f64 im 1) (sqrt.f64 (/.f64 1 re))))
✓	14.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	46.3b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))

Compiler

Compiled 1165 to 943 computations (19.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
✓	0.1b	(/.f64 im (sqrt.f64 re))

series11.0ms (0.3%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	re	@	-inf	(/.f64 im (sqrt.f64 re))
2.0ms	im	@	-inf	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
1.0ms	im	@	inf	(/.f64 im (sqrt.f64 re))
1.0ms	re	@	0	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
1.0ms	re	@	0	(/.f64 im (sqrt.f64 re))

rewrite47.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

719×	`pow1_binary64`
667×	`add-log-exp_binary64`
667×	`log1p-expm1-u_binary64`
667×	`expm1-log1p-u_binary64`
72×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	146	15
2	1806	15

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

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

Outputs

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

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

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	252
1	15	252
2	22	252
3	24	252

Stop Event

1×

saturated

Counts

77 → 56

Calls

Call 1

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

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

prune27.0ms (0.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	55	7	62

Error

0.1b

Counts

62 → 7

Alt Table

Status	Error	Program
	52.3b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (pow.f64 (/.f64 (pow.f64 re -1/2) re) 1/3)))
✓	32.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	46.4b	(/.f64 (/.f64 (*.f64 im 1/2) (pow.f64 re 1/4)) (pow.f64 re 1/4))
✓	14.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	46.4b	(.f64 1/2 (.f64 (pow.f64 (sqrt.f64 im) 2) (sqrt.f64 (/.f64 1 re))))
	46.3b	(.f64 (sqrt.f64 (/.f64 1 re)) (.f64 im 1/2))
✓	46.3b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))

Compiler

Compiled 621 to 361 computations (41.9% saved)

regimes342.0ms (10%)

Accuracy

Total 7.6b remaining (98.8%)

Threshold costs 0b (0%)

Counts

46 → 2

Compiler

Compiled 543 to 410 computations (24.5% saved)

bsearch57.0ms (1.7%)

Algorithm

1×	binary-search

Calls

1 calls:

57.0ms

re

Steps

Iters	Point		Range
1.1e+37	∈ [	3.7595623274743217e+24	,	2.9303186338222314e+37	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	30
1	22	30
2	27	30
3	29	30
4	30	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 re 11000000000000000319053058524521168896) (.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (/.f64 (*.f64 im 1/2) (sqrt.f64 re)))

Outputs

(if (<=.f64 re 11000000000000000319053058524521168896) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (/.f64 (*.f64 im 1/2) (sqrt.f64 re)))

(if (<=.f64 re 11000000000000000319053058524521168896) (*.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))) (/.f64 (*.f64 1/2 im) (sqrt.f64 re)))

end106.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 128 to 100 computations (21.9% 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

analyze527.0ms (15.5%)

sample1.8s (53.5%)

preprocess33.0ms (1%)

simplify22.0ms (0.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite46.0ms (1.3%)

simplify42.0ms (1.2%)

prune94.0ms (2.7%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite30.0ms (0.9%)

simplify6.0ms (0.2%)

prune18.0ms (0.5%)

localize9.0ms (0.3%)

series13.0ms (0.4%)

rewrite47.0ms (1.4%)

simplify6.0ms (0.2%)

prune48.0ms (1.4%)

localize4.0ms (0.1%)

series11.0ms (0.3%)

rewrite47.0ms (1.4%)

simplify12.0ms (0.3%)

prune27.0ms (0.8%)

regimes342.0ms (10%)

bsearch57.0ms (1.7%)

simplify2.0ms (0.1%)

end106.0ms (3.1%)

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