Metrics for math.square on complex, imaginary part

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-add: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample928.0ms (59.9%)

Results

731.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

ival-mult: 175.0ms (73.9% of total)

ival-add: 52.0ms (22% of total)

const: 7.0ms (3% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess57.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

223×	`fma-define`
93×	`fma-neg`
34×	`distribute-lft-neg-in`
30×	`associate-r`
28×	`unsub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	205
1	50	141
2	92	133
3	239	133
4	465	133
5	718	133
6	720	133

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 re im) (.f64 im re))
(+.f64 (.f64 re im) (.f64 im re))
(+.f64 (.f64 (neg.f64 re) im) (.f64 im (neg.f64 re)))
(+.f64 (.f64 re (neg.f64 im)) (.f64 (neg.f64 im) re))
(neg.f64 (+.f64 (.f64 (neg.f64 re) im) (.f64 im (neg.f64 re))))
(neg.f64 (+.f64 (.f64 re (neg.f64 im)) (.f64 (neg.f64 im) re)))
(+.f64 (.f64 im re) (.f64 re im))

Outputs
(+.f64 (.f64 re im) (.f64 im re))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(+.f64 (.f64 re im) (.f64 im re))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(+.f64 (.f64 (neg.f64 re) im) (.f64 im (neg.f64 re)))
(fma.f64 re (neg.f64 im) (*.f64 re (neg.f64 im)))
(.f64 #s(literal 2 binary64) (.f64 re (neg.f64 im)))
(.f64 re (.f64 im #s(literal -2 binary64)))
(+.f64 (.f64 re (neg.f64 im)) (.f64 (neg.f64 im) re))
(fma.f64 re (neg.f64 im) (*.f64 re (neg.f64 im)))
(.f64 #s(literal 2 binary64) (.f64 re (neg.f64 im)))
(.f64 re (.f64 im #s(literal -2 binary64)))
(neg.f64 (+.f64 (.f64 (neg.f64 re) im) (.f64 im (neg.f64 re))))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(neg.f64 (+.f64 (.f64 re (neg.f64 im)) (.f64 (neg.f64 im) re)))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))
(+.f64 (.f64 im re) (.f64 re im))
(fma.f64 re im (*.f64 re im))
(.f64 #s(literal 2 binary64) (.f64 re im))
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 im (.f64 re #s(literal 2 binary64)))

Symmetry

(negabs re)

(negabs im)

(sort re im)

explain57.0ms (3.7%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`im`
-	-	`re`
-	-	`(+.f64 (.f64 re im) (.f64 im re))`
-	-	`(*.f64 re im)`
-	-	`(*.f64 im re)`

Results

29.0ms

512×

valid

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 8.0ms (69.5% of total)

ival-add: 3.0ms (26.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler: Compiled 23 to 10 computations (56.5% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 re (.f64 #s(literal 2 binary64) im))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize27.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) im)
✓	cost-diff	0	(.f64 re (.f64 #s(literal 2 binary64) im))
✓	accuracy	100.0%	(.f64 re (.f64 #s(literal 2 binary64) im))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) im)

Rules

5×	`*-commutative`
3×	`associate-r`
3×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	14	38
2	21	38
3	23	38

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 re (.f64 #s(literal 2 binary64) im))
re
(*.f64 #s(literal 2 binary64) im)
#s(literal 2 binary64)
im

Outputs
(.f64 re (.f64 #s(literal 2 binary64) im))
(.f64 (.f64 re im) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 re im))
re
(*.f64 #s(literal 2 binary64) im)
#s(literal 2 binary64)
im

Results

13.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 4.0ms (94.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.5%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (*.f64 #s(literal 2 binary64) im)>
#<alt (.f64 re (.f64 #s(literal 2 binary64) im))>

Outputs
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>
#<alt (.f64 #s(literal 2 binary64) (.f64 im re))>

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	re	@	0	(* re (* 2 im))
1.0ms	re	@	inf	(* re (* 2 im))
1.0ms	im	@	0	(* re (* 2 im))
1.0ms	im	@	inf	(* re (* 2 im))
1.0ms	im	@	-inf	(* 2 im)

rewrite189.0ms (12.2%)

Algorithm

1×	batch-egg-rewrite

Rules

409×	`unpow-prod-down`
361×	`log1p-expm1-u`
361×	`expm1-log1p-u`
346×	`add-exp-log`
334×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	88	29
2	1006	29

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) im)
(.f64 re (.f64 #s(literal 2 binary64) im))

Outputs
(+.f64 im im)
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) im))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) im)) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) im) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 im #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 2 binary64) im)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im)))) (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))))
(sqrt.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 im #s(literal 3 binary64)) #s(literal 8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) im)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) im)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) im)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (*.f64 #s(literal 2 binary64) im))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (.f64 im re)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)) re))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 1 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 im re)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 3 binary64))
(pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))) (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))))
(sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))
(cbrt.f64 (.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) #s(literal 8 binary64)))
(expm1.f64 (log1p.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(log1p.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (*.f64 im re)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 im re)))) #s(literal 2 binary64)))

simplify168.0ms (10.8%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-neg`
499×	`exp-sum`
405×	`associate-r`
366×	`times-frac`
333×	`associate--l+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1368
1	215	1362
2	415	1356
3	940	1356
4	2900	1356
5	5095	1356

Stop Event

1×	node limit

Counts

67 → 63

Calls

Call 1

Inputs
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(+.f64 im im)
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) im))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) im)) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) im) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 im #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 2 binary64) im)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im)))) (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))))
(sqrt.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 im #s(literal 3 binary64)) #s(literal 8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) im)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) im)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) im)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (*.f64 #s(literal 2 binary64) im))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (.f64 im re)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)) re))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 1 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 im re)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 3 binary64))
(pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))) (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))))
(sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))
(cbrt.f64 (.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) #s(literal 8 binary64)))
(expm1.f64 (log1p.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(log1p.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (*.f64 im re)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 im re)))) #s(literal 2 binary64)))

Outputs
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
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(.f64 im (.f64 #s(literal 2 binary64) re))
(.f64 #s(literal 2 binary64) (.f64 im re))
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(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 im (.f64 #s(literal 2 binary64) re))
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(*.f64 #s(literal 2 binary64) (log.f64 (fabs.f64 (exp.f64 im))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) im)) #s(literal 1 binary64))
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(pow.f64 (*.f64 #s(literal 2 binary64) im) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) im)
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 3 binary64))
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(pow.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) im)
(pow.f64 (*.f64 (pow.f64 im #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1/3 binary64))
(*.f64 #s(literal 2 binary64) im)
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) im)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) im)
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 2 binary64) im)))
(*.f64 #s(literal 2 binary64) im)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im)))) (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) im))))
(sqrt.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) #s(literal 4 binary64)))
(*.f64 #s(literal 2 binary64) im)
(log.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) im)
(cbrt.f64 (*.f64 (pow.f64 im #s(literal 3 binary64)) #s(literal 8 binary64)))
(*.f64 #s(literal 2 binary64) im)
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) im)))
(*.f64 #s(literal 2 binary64) im)
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) im)))
(*.f64 #s(literal 2 binary64) im)
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) im)))
(*.f64 #s(literal 2 binary64) im)
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 3 binary64)))
(*.f64 #s(literal 2 binary64) im)
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (*.f64 #s(literal 2 binary64) im))) #s(literal 1/3 binary64)))
(*.f64 #s(literal 2 binary64) im)
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) im))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) im)
(+.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (.f64 im re)))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)) re))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)) re))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) im) re))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 4 binary64)) re))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 im) (*.f64 #s(literal 2 binary64) re)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(*.f64 #s(literal 2 binary64) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))))
(*.f64 #s(literal 2 binary64) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) im) re))))
(.f64 #s(literal 2 binary64) (log.f64 (fabs.f64 (exp.f64 (.f64 im re)))))
(*.f64 #s(literal 2 binary64) (log.f64 (fabs.f64 (pow.f64 (exp.f64 im) re))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 im re)) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 3 binary64))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1/3 binary64))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 im re))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (E.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) im) re))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) im) re))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 im (.f64 re #s(literal 2 binary64))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 im (.f64 re #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 im (.f64 #s(literal 2 binary64) re)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 im (.f64 #s(literal 2 binary64) re)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))) (sqrt.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) im) re)))) (sqrt.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) im) re))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 im (.f64 re #s(literal 2 binary64)))))) (sqrt.f64 (log.f64 (.f64 im (.f64 re #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 im (.f64 #s(literal 2 binary64) re))))) (sqrt.f64 (log.f64 (.f64 im (.f64 #s(literal 2 binary64) re)))))
(sqrt.f64 (.f64 #s(literal 4 binary64) (pow.f64 (.f64 im re) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(log.f64 (pow.f64 (pow.f64 (exp.f64 im) #s(literal 2 binary64)) re))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(cbrt.f64 (.f64 (pow.f64 (.f64 re im) #s(literal 3 binary64)) #s(literal 8 binary64)))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(expm1.f64 (log1p.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(log1p.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re))))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (*.f64 im re)))) #s(literal 3 binary64)))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 im re)))) #s(literal 1/3 binary64)))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 im re)))) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) im) re)
(.f64 im (.f64 re #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 im re))
(.f64 im (.f64 #s(literal 2 binary64) re))

eval8.0ms (0.5%)

Compiler: Compiled 645 to 201 computations (68.8% saved)

prune9.0ms (0.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	1	64

Accuracy

100.0%

Counts

64 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 re (.f64 #s(literal 2 binary64) im))

Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes4.0ms (0.3%)

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 re (.f64 #s(literal 2 binary64) im))
(+.f64 (.f64 re im) (.f64 im re))

Outputs
(.f64 re (.f64 #s(literal 2 binary64) im))

Calls

3 calls:

1.0ms	re
1.0ms	(+.f64 (.f64 re im) (.f64 im re))
1.0ms	im

Results

Accuracy	Segments	Branch
100.0%	1	`re`
100.0%	1	`im`
100.0%	1	`(+.f64 (.f64 re im) (.f64 im re))`

Compiler

Compiled 15 to 9 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	12	19

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 re (.f64 #s(literal 2 binary64) im))

Outputs
(.f64 re (.f64 #s(literal 2 binary64) im))

soundness38.0ms (2.4%)

Rules

223×	`fma-define`
93×	`fma-neg`
34×	`distribute-lft-neg-in`
30×	`associate-r`
28×	`unsub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	205
1	50	141
2	92	133
3	239	133
4	465	133
5	718	133
6	720	133

Stop Event

1×	done
1×	saturated

Compiler

Compiled 33 to 16 computations (51.5% saved)

preprocess54.0ms (3.5%)

Remove

(sort re im)

(negabs im)

(negabs re)

Compiler

Compiled 116 to 80 computations (31% saved)

math.square on complex, imaginary part

analyze0.0ms (0%)

sample928.0ms (59.9%)

preprocess57.0ms (3.6%)

explain57.0ms (3.7%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize27.0ms (1.7%)

series8.0ms (0.5%)

rewrite189.0ms (12.2%)

simplify168.0ms (10.8%)

eval8.0ms (0.5%)

prune9.0ms (0.6%)

regimes4.0ms (0.3%)

simplify2.0ms (0.1%)

soundness38.0ms (2.4%)

preprocess54.0ms (3.5%)

end0.0ms (0%)

Profiling