Details

analyze475.0ms (16.6%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.7s (60.4%)

Results

787.0ms	6259×	body	128	valid
345.0ms	684×	body	2048	valid
344.0ms	577×	body	4096	valid
153.0ms	394×	body	1024	valid
65.0ms	232×	body	512	valid
23.0ms	110×	body	256	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess20.0ms (0.7%)

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)

simplify6.0ms (0.2%)

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

13.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.1b	(.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
✓	0.0b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	1.0b	(+.f64 re (hypot.f64 re im))

series18.0ms (0.6%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	re	@	-inf	(+.f64 re (hypot.f64 re im))
2.0ms	im	@	0	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	im	@	inf	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	re	@	inf	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	re	@	-inf	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))

rewrite44.0ms (1.5%)

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 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 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 log1p.f64 (expm1.f64 (+.f64 re (hypot.f64 re im))))))) (#(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 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 log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))))) (#(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 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 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 log1p.f64 (expm1.f64 (+.f64 re (hypot.f64 re im))))))) (#(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 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 log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))))))))

simplify27.0ms (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))))))

prune78.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

4.9b

Counts

106 → 7

Alt Table

Status	Error	Program
	46.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	15.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
✓	13.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	45.8b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	48.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 2227 to 1499 computations (32.7% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (hypot.f64 re im))
✓	0.0b	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)))
✓	15.7b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)

series19.0ms (0.7%)

Counts

3 → 26

Calls

18 calls:

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

rewrite41.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

774×	`pow1_binary64`
711×	`log1p-expm1-u_binary64`
711×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	180	25
2	2001	25

Stop Event

1×	node limit

Counts

3 → 71

Calls

Call 1

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

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

Outputs

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

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

simplify31.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

508×	`associate-r_binary64`
504×	`fma-def_binary64`
411×	`associate-l_binary64`
273×	`cancel-sign-sub-inv_binary64`
200×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	807
1	370	759
2	1237	707

Stop Event

1×	node limit

Counts

97 → 116

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

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

prune104.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	154	7	161

Error

4.9b

Counts

161 → 7

Alt Table

Status	Error	Program
	46.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
✓	13.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	45.8b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	48.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 3474 to 2194 computations (36.8% saved)

localize4.0ms (0.1%)

prune5.0ms (0.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	2	2
Total	7	7

Error

4.9b

Counts

7 → 7

Alt Table

Status	Error	Program
▶	46.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
✓	13.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	45.8b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	48.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 127 to 102 computations (19.7% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	3	3
Total	7	7

Error

4.9b

Counts

7 → 7

Alt Table

Status	Error	Program
✓	46.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	15.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
✓	13.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	45.8b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	48.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 82 to 64 computations (22% saved)

regimes138.0ms (4.8%)

Accuracy

Total 4.0b remaining (40.6%)

Threshold costs 0b (0%)

Counts

20 → 3

Compiler

Compiled 317 to 214 computations (32.5% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Steps

Iters	Point		Range
0.0	∈ [	0.0	,	2.5756484948594707e-282	]
-5e-287	∈ [	-6.090132441363868e-287	,	0.0	]

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	88
1	38	88

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re) -8572068857490139/171441377149802771351748007849600289689824769872885377191000062139256168179989779598911740610511337300415147666808503492029943245710770246975753241195177196862953084397187695766737193680997938270047266914448743599737311060278380280946648703137233006633139143642984674682566877306441990189395290689110016) (*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (if (<=.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re) 0) (*.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 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re) -8572068857490139/171441377149802771351748007849600289689824769872885377191000062139256168179989779598911740610511337300415147666808503492029943245710770246975753241195177196862953084397187695766737193680997938270047266914448743599737311060278380280946648703137233006633139143642984674682566877306441990189395290689110016) (*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (if (<=.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re) 0) (*.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 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) -8572068857490139/171441377149802771351748007849600289689824769872885377191000062139256168179989779598911740610511337300415147666808503492029943245710770246975753241195177196862953084397187695766737193680997938270047266914448743599737311060278380280946648703137233006633139143642984674682566877306441990189395290689110016) (*.f64 1/2 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))) (if (<=.f64 (+.f64 re (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0) (*.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)))))))

end98.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 202 to 132 computations (34.7% saved)

Details

analyze475.0ms (16.6%)

sample1.7s (60.4%)

preprocess20.0ms (0.7%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series18.0ms (0.6%)

rewrite44.0ms (1.5%)

simplify27.0ms (1%)

prune78.0ms (2.7%)

localize7.0ms (0.3%)

series19.0ms (0.7%)

rewrite41.0ms (1.4%)

simplify31.0ms (1.1%)

prune104.0ms (3.6%)

localize4.0ms (0.1%)

prune5.0ms (0.2%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

regimes138.0ms (4.8%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end98.0ms (3.4%)

Profiling