Details

analyze548.0ms (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
37.5%	62.4%	0.1%	7
42.1%	57.8%	0.1%	8
54.6%	45.3%	0.1%	9
57.4%	42.5%	0.1%	10
64.4%	35.5%	0.1%	11
65.9%	34%	0.1%	12
69.6%	30.3%	0.1%	13
70.3%	29.6%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.6s (60.1%)

Results

711.0ms	6281×	body	128	valid
317.0ms	669×	body	2048	valid
304.0ms	531×	body	4096	valid
153.0ms	426×	body	1024	valid
71.0ms	238×	body	512	valid
21.0ms	111×	body	256	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess21.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

10×	`fma-def_binary64`
7×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`
4×	`distribute-rgt-in_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	30
1	45	30
2	55	30
3	59	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 re (hypot.f64 re im)))))
(.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 im (hypot.f64 re im)))))

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	34	15
3	36	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 re (hypot.f64 re im)))))

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

14.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.4b	(+.f64 re (hypot.f64 re im))

series38.0ms (1.4%)

Counts

2 → 32

Calls

12 calls:

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

rewrite42.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`log1p-expm1-u_binary64`
844×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
88×	`pow1_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	178	19
2	2361	19

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

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

Outputs

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

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

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
387×	`associate-r_binary64`
306×	`associate-l_binary64`
236×	`cancel-sign-sub-inv_binary64`
223×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	860
1	345	810
2	1133	762

Stop Event

1×	node limit

Counts

92 → 105

Calls

Call 1

Inputs
im
(+.f64 re im)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im)) (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))))
(*.f64 2 re)
(+.f64 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
(-.f64 (+.f64 (.f64 2 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 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(*.f64 -1/2 (/.f64 (pow.f64 im 2) re))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 1/2 (/.f64 (pow.f64 im 2) re))))
(-.f64 (+.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 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))
(*.f64 2 re)
(+.f64 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
(-.f64 (+.f64 (.f64 2 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 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))) (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
im
(+.f64 re im)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im)) (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))))
(*.f64 -1 im)
(-.f64 re im)
(-.f64 re (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) 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 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 1/2 (.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 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))) (.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 3)) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re))
(+.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re)) (.f64 1/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (pow.f64 im 2))))
(-.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re)) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (pow.f64 im 2)))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (pow.f64 im 4))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 7)))))))
(-.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re)) (+.f64 (.f64 1/128 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 (sqrt.f64 2) 4)) (sqrt.f64 (/.f64 1 (pow.f64 re 11))))) (+.f64 (.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (pow.f64 im 2))) (+.f64 (.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 11))) (pow.f64 im 6))) (.f64 1/64 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 11))))))))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (pow.f64 im 4))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 7)))))))

Outputs
im
(+.f64 re im)
(+.f64 im re)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im))
(fma.f64 1/2 (/.f64 (*.f64 re re) im) (+.f64 im re))
(fma.f64 1/2 (/.f64 re (/.f64 im re)) (+.f64 im re))
(+.f64 im (fma.f64 1/2 (*.f64 (/.f64 re im) re) re))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im)) (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 re re) im) (+.f64 im re)) (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))))
(+.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) (+.f64 im re)) (*.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 (+.f64 im (fma.f64 1/2 (*.f64 (/.f64 re im) re) re)))
(*.f64 2 re)
(*.f64 re 2)
(+.f64 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
(fma.f64 2 re (.f64 1/2 (/.f64 (.f64 im im) re)))
(fma.f64 re 2 (/.f64 1/2 (/.f64 re (*.f64 im im))))
(fma.f64 re 2 (.f64 1/2 (.f64 (/.f64 im re) im)))
(-.f64 (+.f64 (.f64 2 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 2 re (.f64 1/2 (/.f64 (.f64 im im) re))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 re 2 (fma.f64 1/2 (/.f64 im (/.f64 re im)) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))
(fma.f64 re 2 (fma.f64 1/2 (*.f64 (/.f64 im re) im) (/.f64 -1/8 (/.f64 (pow.f64 re 3) (pow.f64 im 4)))))
(-.f64 (+.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 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (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 -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 re 2 (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 re 2 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (.f64 (/.f64 im re) im)))))
(*.f64 -1/2 (/.f64 (pow.f64 im 2) re))
(.f64 (/.f64 (.f64 im im) re) -1/2)
(/.f64 -1/2 (/.f64 re (*.f64 im im)))
(.f64 (.f64 (/.f64 im re) im) -1/2)
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 (/.f64 (*.f64 im im) re) -1/2))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (/.f64 -1/2 (/.f64 re (*.f64 im im))))
(fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (.f64 (/.f64 im re) im) -1/2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (*.f64 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 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 (.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 (.f64 (/.f64 im re) im) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16)))
(-.f64 (+.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 (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))
(-.f64 (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)))) (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (/.f64 (*.f64 im im) re))))
(-.f64 (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 1/2 (/.f64 im (/.f64 re im)) (/.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 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (fma.f64 (.f64 (/.f64 im re) im) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))
(*.f64 2 re)
(*.f64 re 2)
(+.f64 (.f64 2 re) (.f64 1/2 (/.f64 (pow.f64 im 2) re)))
(fma.f64 2 re (.f64 1/2 (/.f64 (.f64 im im) re)))
(fma.f64 re 2 (/.f64 1/2 (/.f64 re (*.f64 im im))))
(fma.f64 re 2 (.f64 1/2 (.f64 (/.f64 im re) im)))
(-.f64 (+.f64 (.f64 2 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 2 re (.f64 1/2 (/.f64 (.f64 im im) re))) (*.f64 -1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(fma.f64 re 2 (fma.f64 1/2 (/.f64 im (/.f64 re im)) (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))
(fma.f64 re 2 (fma.f64 1/2 (*.f64 (/.f64 im re) im) (/.f64 -1/8 (/.f64 (pow.f64 re 3) (pow.f64 im 4)))))
(-.f64 (+.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 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))))
(+.f64 (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 -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 re 2 (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 re 2 (fma.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) (.f64 1/2 (.f64 (/.f64 im re) im)))))
im
(+.f64 re im)
(+.f64 im re)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im))
(fma.f64 1/2 (/.f64 (*.f64 re re) im) (+.f64 im re))
(fma.f64 1/2 (/.f64 re (/.f64 im re)) (+.f64 im re))
(+.f64 im (fma.f64 1/2 (*.f64 (/.f64 re im) re) re))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im)) (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 re re) im) (+.f64 im re)) (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))))
(+.f64 (fma.f64 1/2 (/.f64 re (/.f64 im re)) (+.f64 im re)) (*.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 (+.f64 im (fma.f64 1/2 (*.f64 (/.f64 re im) re) re)))
(*.f64 -1 im)
(neg.f64 im)
(-.f64 re im)
(-.f64 re (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(-.f64 re (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(-.f64 re (fma.f64 1/2 (/.f64 re (/.f64 im re)) im))
(-.f64 re (fma.f64 1/2 (*.f64 (/.f64 re im) re) im))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) re) (+.f64 (.f64 1/2 (/.f64 (pow.f64 re 2) im)) im))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re) (fma.f64 1/2 (/.f64 (*.f64 re re) im) im))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) re) (fma.f64 1/2 (/.f64 re (/.f64 im re)) im))
(fma.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3)) (-.f64 re (fma.f64 1/2 (*.f64 (/.f64 re im) 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)))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 im) (.f64 1/2 (.f64 (sqrt.f64 2) (*.f64 re (sqrt.f64 (/.f64 1 im))))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 re (sqrt.f64 (/.f64 1 im)))) (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 1/2 (sqrt.f64 (/.f64 1 im))))))
(+.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 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im))))))
(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 1/2 (.f64 (sqrt.f64 2) (.f64 re (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 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) (+.f64 (sqrt.f64 im) (.f64 (.f64 re re) (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))))
(-.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 1/2 (.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))))) (.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 re 3)) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))
(+.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 1/2 (.f64 (sqrt.f64 2) (.f64 re (sqrt.f64 (/.f64 1 im))))))) (.f64 -1/16 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 re 3) (sqrt.f64 (/.f64 1 (pow.f64 im 5)))))))
(+.f64 (fma.f64 1/8 (.f64 (.f64 re re) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (pow.f64 im 3))))) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 re (sqrt.f64 (/.f64 1 im)))) (.f64 (sqrt.f64 2) (sqrt.f64 im)))) (.f64 (.f64 -1/16 (sqrt.f64 2)) (*.f64 (pow.f64 re 3) (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))
(+.f64 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 (.f64 re re) (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 im 3))))))) (.f64 (sqrt.f64 2) (-.f64 (.f64 re (.f64 1/2 (sqrt.f64 (/.f64 1 im)))) (.f64 (pow.f64 re 3) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 im 5))))))))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re))
(*.f64 2 (sqrt.f64 re))
(+.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re)) (.f64 1/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (pow.f64 im 2))))
(fma.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re) (.f64 1/4 (.f64 (*.f64 im im) (sqrt.f64 (/.f64 1 (pow.f64 re 3))))))
(fma.f64 2 (sqrt.f64 re) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (.f64 (*.f64 im im) 1/4)))
(fma.f64 2 (sqrt.f64 re) (.f64 1/4 (.f64 (*.f64 im im) (sqrt.f64 (/.f64 1 (pow.f64 re 3))))))
(-.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re)) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (pow.f64 im 2)))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (pow.f64 im 4))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 7)))))))
(-.f64 (fma.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re) (.f64 1/4 (.f64 (.f64 im im) (sqrt.f64 (/.f64 1 (pow.f64 re 3)))))) (fma.f64 1/16 (.f64 (pow.f64 im 4) (sqrt.f64 (/.f64 1 (pow.f64 re 7)))) (.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (/.f64 (pow.f64 im 4) (pow.f64 (sqrt.f64 2) 2))))))
(fma.f64 2 (sqrt.f64 re) (-.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (.f64 (.f64 im im) 1/4)) (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (/.f64 (pow.f64 im 4) 2)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (.f64 (pow.f64 im 4) 1/16)))))
(-.f64 (fma.f64 2 (sqrt.f64 re) (.f64 1/4 (.f64 (.f64 im im) (sqrt.f64 (/.f64 1 (pow.f64 re 3)))))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (+.f64 (.f64 (pow.f64 im 4) 1/16) (.f64 1/32 (/.f64 (pow.f64 im 4) 2)))))
(-.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re)) (+.f64 (.f64 1/128 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 (sqrt.f64 2) 4)) (sqrt.f64 (/.f64 1 (pow.f64 re 11))))) (+.f64 (.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 3))) (pow.f64 im 2))) (+.f64 (.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 11))) (pow.f64 im 6))) (.f64 1/64 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 11))))))))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (pow.f64 im 4))) (.f64 1/32 (*.f64 (/.f64 (pow.f64 im 4) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (/.f64 1 (pow.f64 re 7)))))))
(-.f64 (fma.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 re) (fma.f64 1/128 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 (sqrt.f64 2) 4)) (sqrt.f64 (/.f64 1 (pow.f64 re 11)))) (fma.f64 1/4 (.f64 (.f64 im im) (sqrt.f64 (/.f64 1 (pow.f64 re 3)))) (fma.f64 1/32 (.f64 (pow.f64 im 6) (sqrt.f64 (/.f64 1 (pow.f64 re 11)))) (.f64 1/64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 11))) (/.f64 (pow.f64 im 6) (pow.f64 (sqrt.f64 2) 2)))))))) (fma.f64 1/16 (.f64 (pow.f64 im 4) (sqrt.f64 (/.f64 1 (pow.f64 re 7)))) (.f64 1/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (/.f64 (pow.f64 im 4) (pow.f64 (sqrt.f64 2) 2))))))
(-.f64 (fma.f64 2 (sqrt.f64 re) (fma.f64 1/128 (.f64 (/.f64 (pow.f64 im 6) 4) (sqrt.f64 (/.f64 1 (pow.f64 re 11)))) (fma.f64 1/4 (.f64 (.f64 im im) (sqrt.f64 (/.f64 1 (pow.f64 re 3)))) (fma.f64 1/64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 11))) (/.f64 (pow.f64 im 6) 2)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 11))) (.f64 (pow.f64 im 6) 1/32)))))) (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (/.f64 (pow.f64 im 4) 2)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (*.f64 (pow.f64 im 4) 1/16))))
(+.f64 (/.f64 (.f64 (pow.f64 im 6) (sqrt.f64 (/.f64 1 (pow.f64 re 11)))) 512) (-.f64 (fma.f64 2 (sqrt.f64 re) (fma.f64 (.f64 im im) (.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 re 3)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 11))) (+.f64 (.f64 (pow.f64 im 6) 1/32) (.f64 1/64 (/.f64 (pow.f64 im 6) 2)))))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 7))) (+.f64 (.f64 (pow.f64 im 4) 1/16) (*.f64 1/32 (/.f64 (pow.f64 im 4) 2))))))

prune64.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

4.7b

Counts

106 → 6

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	47.5b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 2193 to 1479 computations (32.6% saved)

localize3.0ms (0.1%)

prune7.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Error

4.7b

Counts

6 → 6

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	47.5b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 110 to 92 computations (16.4% saved)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	2	2
Total	6	6

Error

4.7b

Counts

6 → 6

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	47.5b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
▶	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 102 to 85 computations (16.7% saved)

localize4.0ms (0.2%)

prune3.0ms (0.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	3	3
Total	6	6

Error

4.7b

Counts

6 → 6

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	47.5b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
✓	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 65 to 54 computations (16.9% saved)

regimes154.0ms (5.8%)

Accuracy

Total 5.3b remaining (50.1%)

Threshold costs 0b (0%)

Counts

15 → 2

Compiler

Compiled 1583 to 1263 computations (20.2% saved)

bsearch43.0ms (1.6%)

Algorithm

1×	binary-search

Calls

1 calls:

43.0ms

re

Steps

Iters	Point		Range
-1.15e+47	∈ [	-1.522969168136182e+49	,	-5.920415498340677e+45	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	28	39

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 re -114999999999999992872826187992760441414564708352) (.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2)))) (.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))))

Outputs

(if (<=.f64 re -114999999999999992872826187992760441414564708352) (*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 (/.f64 im re) im) -1/2)))) (*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

(if (<=.f64 re -114999999999999992872826187992760441414564708352) (*.f64 1/2 (sqrt.f64 (*.f64 2 (*.f64 (*.f64 im (/.f64 im re)) -1/2)))) (*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

end75.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 121 to 96 computations (20.7% saved)

Details

analyze548.0ms (20.7%)

sample1.6s (60.1%)

preprocess21.0ms (0.8%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series38.0ms (1.4%)

rewrite42.0ms (1.6%)

simplify26.0ms (1%)

prune64.0ms (2.4%)

localize3.0ms (0.1%)

prune7.0ms (0.3%)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

localize4.0ms (0.2%)

prune3.0ms (0.1%)

regimes154.0ms (5.8%)

bsearch43.0ms (1.6%)

simplify2.0ms (0.1%)

end75.0ms (2.8%)

Profiling