Details

analyze630.0ms (17.2%)

Algorithm

1×

Search

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

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.0s (55.9%)

Results

916.0ms	6255×	body	128	valid
401.0ms	679×	body	2048	valid
386.0ms	532×	body	4096	valid
222.0ms	426×	body	1024	valid
77.0ms	229×	body	512	valid
30.0ms	135×	body	256	valid

preprocess39.0ms (1.1%)

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)

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

12.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	37.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series22.0ms (0.6%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
10.0ms	re	@	0	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
2.0ms	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)))
1.0ms	im	@	inf	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
1.0ms	re	@	inf	(-.f64 (hypot.f64 re im) re)

rewrite49.0ms (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 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 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 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 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 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 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))))))

simplify38.0ms (1%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-def_binary64`
507×	`times-frac_binary64`
391×	`associate-/l*_binary64`
296×	`associate-/r*_binary64`
187×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1087
1	469	1055
2	1531	1011

Stop Event

1×	node limit

Counts

94 → 110

Calls

Call 1

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

Outputs
im
(+.f64 (*.f64 -1 re) im)
(fma.f64 -1 re im)
(-.f64 im re)
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(fma.f64 -1 re (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(-.f64 (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 -1 re) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)))
(fma.f64 -1 re (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im)))
(-.f64 (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 re (/.f64 im re)) im)) re)
(fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (-.f64 (fma.f64 1/2 (*.f64 (/.f64 re im) re) im) 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))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (/.f64 (*.f64 -1/8 (pow.f64 im 4)) (pow.f64 re 3)))
(fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (*.f64 1/2 (/.f64 im (/.f64 re im))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 (*.f64 1/16 (pow.f64 im 6)) (pow.f64 re 5))))
(fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 1/2 (/.f64 im (/.f64 re im)) (/.f64 (pow.f64 im 6) (/.f64 (pow.f64 re 5) 1/16))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 im 4)) 2) (.f64 1/16 (pow.f64 im 8))) (pow.f64 re 7))) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 im 4)) 2) (.f64 1/16 (pow.f64 im 8))) (pow.f64 re 7)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 (.f64 -1/2 (fma.f64 1/16 (pow.f64 im 8) (.f64 (pow.f64 im 8) 1/64))) (pow.f64 re 7)))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 (/.f64 -1/2 (pow.f64 re 7)) (.f64 (pow.f64 im 8) 5/64)))))
(*.f64 -2 re)
(*.f64 re -2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -2 re))
(fma.f64 -1/2 (/.f64 (.f64 im im) re) (.f64 re -2))
(fma.f64 (/.f64 im (/.f64 re im)) -1/2 (*.f64 re -2))
(fma.f64 re -2 (*.f64 (/.f64 im (/.f64 re im)) -1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (*.f64 -2 re)))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 -1/2 (/.f64 (.f64 im im) re) (.f64 re -2)))
(fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (fma.f64 (/.f64 im (/.f64 re im)) -1/2 (*.f64 re -2)))
(fma.f64 re -2 (fma.f64 (/.f64 im (/.f64 re im)) -1/2 (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)) (.f64 -2 re))))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 -1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (fma.f64 -1/2 (/.f64 (.f64 im im) re) (.f64 re -2))))
(fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (fma.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16 (fma.f64 (/.f64 im (/.f64 re im)) -1/2 (*.f64 re -2))))
(fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) 1/8 (fma.f64 (/.f64 im (/.f64 re im)) -1/2 (fma.f64 re -2 (*.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))
(*.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))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (/.f64 (*.f64 -1/8 (pow.f64 im 4)) (pow.f64 re 3)))
(fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (*.f64 1/2 (/.f64 im (/.f64 re im))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 (*.f64 1/16 (pow.f64 im 6)) (pow.f64 re 5))))
(fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 1/2 (/.f64 im (/.f64 re im)) (/.f64 (pow.f64 im 6) (/.f64 (pow.f64 re 5) 1/16))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 re 6)))) (pow.f64 im 8)) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 (.f64 im im) re) (fma.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))) (/.f64 re (pow.f64 im 8))) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (fma.f64 -1/2 (/.f64 (pow.f64 im 8) (/.f64 re (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))))) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 (*.f64 1/16 (pow.f64 im 6)) (pow.f64 re 5)))))
(fma.f64 1/2 (/.f64 im (/.f64 re im)) (fma.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (/.f64 (fma.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) -1/2 (/.f64 -1/32 (pow.f64 re 6))) (/.f64 re (pow.f64 im 8))))))
im
(+.f64 (*.f64 -1 re) im)
(fma.f64 -1 re im)
(-.f64 im re)
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(fma.f64 -1 re (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(-.f64 (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 -1 re) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im)))
(fma.f64 -1 re (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im)))
(-.f64 (fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 1/2 (/.f64 re (/.f64 im re)) im)) re)
(fma.f64 -1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (-.f64 (fma.f64 1/2 (*.f64 (/.f64 re im) re) im) re))
(*.f64 -1 im)
(neg.f64 im)
(+.f64 (.f64 -1 re) (.f64 -1 im))
(*.f64 -1 (+.f64 re im))
(-.f64 (neg.f64 re) im)
(+.f64 (.f64 -1 re) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (*.f64 -1 im)))
(fma.f64 -1 re (fma.f64 -1/2 (/.f64 (*.f64 re re) im) (neg.f64 im)))
(-.f64 (-.f64 (/.f64 -1/2 (/.f64 im (*.f64 re re))) im) re)
(-.f64 (.f64 (/.f64 -1/2 im) (.f64 re re)) (+.f64 im re))
(+.f64 (.f64 -1 re) (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 re 2) im)) (.f64 -1 im))))
(fma.f64 -1 re (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (fma.f64 -1/2 (/.f64 (*.f64 re re) im) (neg.f64 im))))
(-.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) 1/8 (/.f64 -1/2 (/.f64 im (*.f64 re re)))) im) re)
(-.f64 (fma.f64 (.f64 (/.f64 re im) re) -1/2 (.f64 (/.f64 1/8 (pow.f64 im 3)) (pow.f64 re 4))) (+.f64 im re))
(*.f64 (sqrt.f64 2) (sqrt.f64 im))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (.f64 (sqrt.f64 2) (sqrt.f64 im)))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 re (sqrt.f64 (/.f64 1 im)))) (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
(fma.f64 -1/2 (.f64 re (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 im)))) (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
(.f64 (sqrt.f64 2) (+.f64 (.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) -1/2) (sqrt.f64 im)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 2))) (sqrt.f64 (/.f64 1 im))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 re (sqrt.f64 (/.f64 1 im)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 re re) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))) (sqrt.f64 (/.f64 1 im)))))))
(fma.f64 -1/2 (.f64 re (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 im)))) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re (.f64 re (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 im))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (+.f64 (.f64 1/2 (.f64 (+.f64 (/.f64 1/2 im) (.f64 (/.f64 1 im) -1/4)) (.f64 (.f64 re re) (sqrt.f64 2)))) (.f64 (.f64 -1/2 re) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 2))) (sqrt.f64 (/.f64 1 im)))) (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/2 (/.f64 1 im)) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (pow.f64 re 3))) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 re (sqrt.f64 (/.f64 1 im)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 re re) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))) (sqrt.f64 (/.f64 1 im)))) (.f64 1/4 (.f64 (sqrt.f64 2) (.f64 (.f64 (pow.f64 re 3) (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2))) (sqrt.f64 (/.f64 1 (pow.f64 im 3)))))))))
(fma.f64 -1/2 (.f64 re (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 im)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 im) (fma.f64 1/4 (.f64 (sqrt.f64 2) (.f64 (pow.f64 re 3) (.f64 (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (sqrt.f64 (/.f64 1 (pow.f64 im 3)))))) (.f64 (.f64 (-.f64 (/.f64 1/2 im) (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 im))) 2)) (.f64 (.f64 re re) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 1 im)) 1/2)))))
(+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 (.f64 (.f64 re re) (.f64 (+.f64 (/.f64 1/2 im) (.f64 (/.f64 1 im) -1/4)) (sqrt.f64 (/.f64 1 im)))) 1/2))) (.f64 (sqrt.f64 2) (+.f64 (.f64 (.f64 (+.f64 (/.f64 1/2 im) (.f64 (/.f64 1 im) -1/4)) (.f64 (pow.f64 re 3) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) 1/4) (.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) -1/2))))
(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (sqrt.f64 2) (*.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 im (*.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)))
(.f64 (.f64 (*.f64 (sqrt.f64 2) im) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 re)))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))
(fma.f64 -1/16 (/.f64 (.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (sqrt.f64 1/2)) (.f64 (.f64 (sqrt.f64 2) (*.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re))))
(fma.f64 (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 -1/16 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3))))))
(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 (.f64 (*.f64 (sqrt.f64 2) im) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 re))))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re))) (.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))))
(fma.f64 -1/16 (/.f64 (.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (sqrt.f64 1/2)) (fma.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (.f64 -1/16 (/.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re)) (.f64 (.f64 (sqrt.f64 2) (.f64 im (sqrt.f64 1/2))) (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)))) (fma.f64 1/2 (.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2)) (pow.f64 im 5))) (sqrt.f64 re)) (.f64 (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)))))
(fma.f64 (sqrt.f64 2) (.f64 im (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))) (fma.f64 (sqrt.f64 re) (.f64 (/.f64 (.f64 1/2 (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 im 5))) (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (/.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 im 3) (sqrt.f64 2)))))))
(+.f64 (.f64 -1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 3)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 re 6)))) re)) (.f64 -1/16 (/.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 re 2))))) (pow.f64 im 7))) (sqrt.f64 1/2)) (sqrt.f64 re))) (+.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (.f64 1/16 (/.f64 1 (pow.f64 re 5))) (pow.f64 (.f64 -1/16 (.f64 (/.f64 1 (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5))))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re))) (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))))
(fma.f64 -1/16 (/.f64 (.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) (sqrt.f64 1/2)) (fma.f64 1/2 (.f64 (sqrt.f64 re) (/.f64 (.f64 (sqrt.f64 2) (.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))) re)) (.f64 1/16 (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (.f64 -1/16 (/.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) 2)) (.f64 (.f64 re re) (pow.f64 (sqrt.f64 1/2) 2))))) (pow.f64 im 7))) (sqrt.f64 1/2))) (fma.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (.f64 -1/16 (/.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 (pow.f64 re 5)))) 2)) (pow.f64 im 5))) (sqrt.f64 1/2)) (sqrt.f64 re)) (.f64 (.f64 (sqrt.f64 2) (*.f64 im (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re))))))
(+.f64 (.f64 (sqrt.f64 re) (+.f64 (/.f64 (.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 im 7)) (-.f64 (/.f64 -1/2 (/.f64 re (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) (/.f64 1/16 (pow.f64 re 6))))) (.f64 -1/8 (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2)) (.f64 re re)))))) (/.f64 (.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 im 5)) (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2)))))) (fma.f64 (.f64 im (.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (sqrt.f64 (/.f64 1 re)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (*.f64 -1/16 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 1/2) (pow.f64 im 3)))))))
(fma.f64 1/2 (.f64 (sqrt.f64 re) (+.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (.f64 (+.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 -1/8 (pow.f64 re 3)) 2) -1/2 (/.f64 -1/32 (pow.f64 re 6))) re) (.f64 1/8 (/.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2)) (.f64 re re)))) (pow.f64 im 7))) (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (.f64 (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 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 (.f64 (.f64 (sqrt.f64 2) im) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 re)))))

prune83.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	6	112

Error

0.2b

Counts

112 → 6

Alt Table

Status	Error	Program
	54.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 im (/.f64 re im))))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	55.1b	(.f64 1/2 (fma.f64 (sqrt.f64 2) (.f64 im (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))) (fma.f64 (sqrt.f64 re) (.f64 (/.f64 (.f64 1/2 (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 im 5))) (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 im 3) (sqrt.f64 2))))))))
▶	48.3b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))))

Compiler

Compiled 2806 to 2005 computations (28.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im))
✓	0.5b	(*.f64 (sqrt.f64 1/2) im)

series15.0ms (0.4%)

Counts

4 → 0

Calls

15 calls:

Time	Variable		Point	Expression
4.0ms	re	@	0	(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
2.0ms	im	@	inf	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im))
1.0ms	im	@	0	(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
1.0ms	re	@	-inf	(.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) im)) (sqrt.f64 (/.f64 1 re)))
1.0ms	im	@	0	(*.f64 (sqrt.f64 1/2) im)

rewrite52.0ms (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	2901	17

Stop Event

1×	node limit

Counts

4 → 74

Calls

Call 1

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

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

simplify8.0ms (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

prune56.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	72	8	80

Error

0.1b

Counts

80 → 8

Alt Table

Status	Error	Program
	54.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 im (/.f64 re im))))))
▶	48.1b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
	48.4b	(.f64 1/2 (.f64 (expm1.f64 (log1p.f64 im)) (sqrt.f64 (/.f64 1 re))))
	55.1b	(.f64 1/2 (fma.f64 (sqrt.f64 2) (.f64 im (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))) (fma.f64 (sqrt.f64 re) (.f64 (/.f64 (.f64 1/2 (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 im 5))) (-.f64 (/.f64 1/16 (pow.f64 re 5)) (pow.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (sqrt.f64 1/2))) 2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 -1/16 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 im 3) (sqrt.f64 2))))))))
	48.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (pow.f64 re -1/2)))
	49.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) im)))) (sqrt.f64 (/.f64 1 re))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))))

Compiler

Compiled 1390 to 1137 computations (18.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 im (sqrt.f64 re))

series4.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

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

rewrite35.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`pow1_binary64`
496×	`add-log-exp_binary64`
496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`
483×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	104	6
2	1347	6

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 im (sqrt.f64 re))

Outputs

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	108
1	10	108

Stop Event

1×

saturated

Counts

43 → 32

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)

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)

prune24.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	32	8	40

Error

0.1b

Counts

40 → 8

Alt Table

Status	Error	Program
	48.2b	(.f64 1/2 (.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (pow.f64 re -1/2))))
	48.4b	(.f64 1/2 (.f64 (expm1.f64 (log1p.f64 im)) (sqrt.f64 (/.f64 1 re))))
✓	48.1b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
▶	48.1b	(.f64 1/2 (.f64 im (pow.f64 re -1/2)))
	48.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (pow.f64 re -1/2)))
	49.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) im)))) (sqrt.f64 (/.f64 1 re))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))))

Compiler

Compiled 555 to 358 computations (35.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	re	@	0	(*.f64 im (pow.f64 re -1/2))
1.0ms	re	@	-inf	(*.f64 im (pow.f64 re -1/2))
0.0ms	im	@	0	(*.f64 im (pow.f64 re -1/2))
0.0ms	re	@	inf	(*.f64 im (pow.f64 re -1/2))
0.0ms	im	@	inf	(*.f64 im (pow.f64 re -1/2))

rewrite33.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`pow1_binary64`
511×	`add-log-exp_binary64`
511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
499×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1414	7

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	108
1	10	108

Stop Event

1×

saturated

Counts

25 → 14

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)

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)

prune13.0ms (0.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	14	8	22

Error

0.1b

Counts

22 → 8

Alt Table

Status	Error	Program
	48.2b	(.f64 1/2 (.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (pow.f64 re -1/2))))
	48.4b	(.f64 1/2 (.f64 (expm1.f64 (log1p.f64 im)) (sqrt.f64 (/.f64 1 re))))
✓	48.1b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
✓	48.1b	(.f64 1/2 (.f64 im (pow.f64 re -1/2)))
	48.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) im)) (pow.f64 re -1/2)))
	49.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) im)))) (sqrt.f64 (/.f64 1 re))))
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 1/2 (/.f64 (pow.f64 im 2) re)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))))))

Compiler

Compiled 262 to 210 computations (19.8% saved)

regimes299.0ms (8.2%)

Accuracy

Total 6.5b remaining (98.2%)

Threshold costs 0b (0%)

Counts

44 → 2

Compiler

Compiled 692 to 532 computations (23.1% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(-.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)

Steps

Iters	Point		Range
0.0	∈ [	0.0	,	1.0152228977210767e-268	]

Compiler

Compiled 20 to 14 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	29	44
2	34	44
3	36	44
4	37	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) 0) (.f64 1/2 (/.f64 im (sqrt.f64 re))) (.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

Outputs
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re) 0) (.f64 1/2 (/.f64 im (sqrt.f64 re))) (.f64 1/2 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

end137.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 183 to 140 computations (23.5% 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

analyze630.0ms (17.2%)

sample2.0s (55.9%)

preprocess39.0ms (1.1%)

simplify23.0ms (0.6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series22.0ms (0.6%)

rewrite49.0ms (1.3%)

simplify38.0ms (1%)

prune83.0ms (2.3%)

localize9.0ms (0.2%)

series15.0ms (0.4%)

rewrite52.0ms (1.4%)

simplify8.0ms (0.2%)

prune56.0ms (1.5%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite35.0ms (1%)

simplify7.0ms (0.2%)

prune24.0ms (0.7%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite33.0ms (0.9%)

simplify7.0ms (0.2%)

prune13.0ms (0.4%)

regimes299.0ms (8.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end137.0ms (3.7%)

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