math.abs on complex

Time bar (total: 1.2s)

analyze0.0ms (0%)

Memory
0.5MiB live, 0.4MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 10 to 5 computations (50% saved)

sample439.0ms (35.7%)

Memory
3.1MiB live, 873.7MiB allocated
Samples
304.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 151.0ms
ival-hypot: 143.0ms (94.6% of total)
ival-true: 5.0ms (3.3% of total)
ival-assert: 3.0ms (2% of total)
Bogosity

preprocess50.0ms (4.1%)

Memory
1.3MiB live, 78.2MiB allocated
Algorithm
1×egg-herbie
Rules
52×fmm-def
45×fma-define
16×distribute-lft-neg-in
15×neg-sub0
12×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02499
15199
29899
318799
428499
532399
633399
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im)))
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im))))
(neg.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im))))
(neg.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im)))))
(sqrt.f64 (+.f64 (*.f64 im im) (*.f64 re re)))
Outputs
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im))))
(hypot.f64 re im)
(neg.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im))))
(neg.f64 (hypot.f64 re im))
(neg.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im)))))
(neg.f64 (hypot.f64 re im))
(sqrt.f64 (+.f64 (*.f64 im im) (*.f64 re re)))
(hypot.f64 re im)
Symmetry

(abs re)

(abs im)

(sort re im)

explain81.0ms (6.6%)

Memory
1.1MiB live, 176.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1240-3(1.6729303685758587e-287 9.616185688697886e-157)(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
00-0-(+.f64 (*.f64 re re) (*.f64 im im))
00-0-(*.f64 re re)
00-0-re
00-0-(*.f64 im im)
00-0-im
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))oflow-rescue1030
↳(+.f64 (*.f64 re re) (*.f64 im im))overflow103
↳(*.f64 re re)overflow11
↳(*.f64 im im)overflow103
sqrt.f64(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))uflow-rescue180
↳(+.f64 (*.f64 re re) (*.f64 im im))underflow18
↳(*.f64 re re)underflow119
↳(*.f64 im im)underflow18
Confusion
Predicted +Predicted -
+1213
-0132
Precision
1.0
Recall
0.9758064516129032
Confusion?
Predicted +Predicted MaybePredicted -
+12103
-00132
Precision?
1.0
Recall?
0.9758064516129032
Freqs
test
numberfreq
0135
1121
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
31.0ms512×0valid
Compiler

Compiled 70 to 28 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-hypot: 9.0ms (49.3% of total)
ival-mult: 7.0ms (38.3% of total)
ival-add: 2.0ms (11% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Compiler

Compiled 5 to 3 computations (40% saved)

prune1.0ms (0.1%)

Memory
2.1MiB live, 2.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 re im)
Compiler

Compiled 5 to 3 computations (40% saved)

simplify6.0ms (0.5%)

Memory
13.8MiB live, 13.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(hypot.f64 re im)
Rules
2×fma-define
1×hypot-define
1×hypot-undefine
1×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
11321
21621
31821
Stop Event
1×saturated
Calls
Call 1
Inputs
(hypot.f64 re im)
re
im
Outputs
(hypot.f64 re im)
re
im

localize15.0ms (1.2%)

Memory
-10.4MiB live, 30.8MiB allocated
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(hypot.f64 re im)
Samples
9.0ms256×0valid
Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-hypot: 4.0ms (93.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.3%)

Memory
10.2MiB live, 10.2MiB allocated
Counts
1 → 24
Calls
Call 1
Inputs
#<alt (hypot.f64 re im)>
Outputs
#<alt im>
#<alt (+.f64 im (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) im)))>
#<alt (+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) im)))))>
#<alt (+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 (*.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) im)))))>
#<alt re>
#<alt (*.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))>
#<alt (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))>
#<alt (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))>
#<alt (*.f64 #s(literal -1 binary64) re)>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))>
#<alt re>
#<alt (+.f64 re (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) re)))>
#<alt (+.f64 re (*.f64 (pow.f64 im #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) re)))))>
#<alt (+.f64 re (*.f64 (pow.f64 im #s(literal 2 binary64)) (+.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) re)))))>
#<alt im>
#<alt (*.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))>
#<alt (*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))>
#<alt (*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))>
#<alt (*.f64 #s(literal -1 binary64) im)>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))>
Calls

6 calls:

TimeVariablePointExpression
1.0ms
re
@0
(sqrt (+ (* re re) (* im im)))
1.0ms
re
@inf
(sqrt (+ (* re re) (* im im)))
1.0ms
im
@inf
(sqrt (+ (* re re) (* im im)))
1.0ms
im
@0
(sqrt (+ (* re re) (* im im)))
0.0ms
re
@-inf
(sqrt (+ (* re re) (* im im)))

rewrite294.0ms (23.9%)

Memory
-6.6MiB live, 347.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
425×log1p-expm1-u
294×associate-*r*
244×expm1-log1p-u
242×associate-*l*
232×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
16613
269613
3764813
Stop Event
1×node limit
Counts
1 → 58
Calls
Call 1
Inputs
(hypot.f64 re im)
Outputs
(+.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (hypot.f64 re im))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 re im))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 re im)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 re im)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 re im)))))
(-.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (hypot.f64 re im) #s(literal 1 binary64))
(*.f64 (hypot.f64 re im) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 re im))
(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 re im)))
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64))) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 re im))))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (sqrt.f64 (hypot.f64 re im))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 re im))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (hypot.f64 re im)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 5 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (hypot.f64 re im))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 5/2 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 5 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 re #s(literal 4 binary64)) (-.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 (*.f64 re im) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) (+.f64 (hypot.f64 re im) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (hypot.f64 re im) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) (+.f64 (hypot.f64 re im) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 1 binary64)))
(pow.f64 (hypot.f64 re im) #s(literal 1 binary64))
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (hypot.f64 re im)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (hypot.f64 re im)))
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 re im)) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (hypot.f64 re im))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))
(sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 2 binary64)))
(fabs.f64 (hypot.f64 re im))
(log.f64 (exp.f64 (hypot.f64 re im)))
(cbrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (hypot.f64 re im)))
(log1p.f64 (expm1.f64 (hypot.f64 re im)))
(exp.f64 (log.f64 (hypot.f64 re im)))
(exp.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (hypot.f64 re im))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)))

simplify108.0ms (8.7%)

Memory
7.9MiB live, 133.0MiB allocated
Algorithm
1×egg-herbie
Rules
724×fma-define
466×distribute-lft-in
435×distribute-rgt-in
255×fmm-def
245×*-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02513078
15603018
217102984
357812898
Stop Event
1×node limit
Counts
82 → 164
Calls
Call 1
Inputs
im
(+.f64 im (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) im)))
(+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) im)))))
(+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 (*.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) im)))))
re
(*.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
(*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
(*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) re)
(*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
(*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
re
(+.f64 re (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) re)))
(+.f64 re (*.f64 (pow.f64 im #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) re)))))
(+.f64 re (*.f64 (pow.f64 im #s(literal 2 binary64)) (+.f64 (*.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) re)))))
im
(*.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
(*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
(*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) im)
(*.f64 #s(literal -1 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
(*.f64 #s(literal -1 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
(*.f64 #s(literal -1 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
(+.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (hypot.f64 re im))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 re im))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 re im)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 re im)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 re im)))))
(-.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (hypot.f64 re im) #s(literal 1 binary64))
(*.f64 (hypot.f64 re im) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 re im))
(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 re im)))
(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64))) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)) (cbrt.f64 (hypot.f64 re im))))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)) (sqrt.f64 (hypot.f64 re im))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 re im))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (hypot.f64 re im)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 5 binary64)) #s(literal 1/2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (hypot.f64 re im))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 5/2 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (sqrt.f64 (hypot.f64 re im)) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3/2 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 5 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64)))) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 re #s(literal 4 binary64)) (-.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 (*.f64 re im) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) (+.f64 (hypot.f64 re im) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (hypot.f64 re im) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) (+.f64 (hypot.f64 re im) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 1 binary64)))
(pow.f64 (hypot.f64 re im) #s(literal 1 binary64))
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (hypot.f64 re im)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (hypot.f64 re im)))
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 re im)) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (hypot.f64 re im))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))
(sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 2 binary64)))
(fabs.f64 (hypot.f64 re im))
(log.f64 (exp.f64 (hypot.f64 re im)))
(cbrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (hypot.f64 re im)))
(log1p.f64 (expm1.f64 (hypot.f64 re im)))
(exp.f64 (log.f64 (hypot.f64 re im)))
(exp.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (hypot.f64 re im))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)))
Outputs
im
(+.f64 im (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) im)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) im) im)
(+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) im)))))
(+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) im))))
(fma.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) im)) im)
(+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 (*.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 im #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) im)))))
(+.f64 im (*.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (pow.f64 im #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) im))))
(fma.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) im)) im)
(fma.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 3 binary64)))) (pow.f64 re #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) im) im))
(fma.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 im #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) im)) im)
re
(*.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
(*.f64 re (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))) #s(literal 1 binary64)))
(+.f64 re (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) re))))
(*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
(*.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
(*.f64 re (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 4 binary64))) (pow.f64 re #s(literal 4 binary64)))))
(*.f64 re (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) #s(literal 1 binary64))))
(*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
(*.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
(*.f64 re (+.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))) #s(literal 1 binary64))))
(fma.f64 re (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))))) re)
(*.f64 #s(literal -1 binary64) re)
(neg.f64 re)
(*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
(*.f64 (neg.f64 re) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
(*.f64 re (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))) #s(literal 1 binary64))))
(-.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) re))) re)
(*.f64 #s(literal -1 binary64) (*.f64 re (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
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(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 4 binary64))) (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64))))
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(*.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))
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(hypot.f64 im re)
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) #s(literal 2 binary64)) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64))) (pow.f64 (hypot.f64 re im) #s(literal 1/6 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)
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(/.f64 (sqrt.f64 (+.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 re #s(literal 4 binary64)) (-.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 (*.f64 re im) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 re #s(literal 4 binary64)) (-.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 (*.f64 im re) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 (hypot.f64 re im) #s(literal 1 binary64)) (+.f64 (hypot.f64 re im) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (hypot.f64 re im) #s(literal 1 binary64)))))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (hypot.f64 re im)) #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 (+.f64 #s(literal 1 binary64) (hypot.f64 re im)) (+.f64 #s(literal 1 binary64) (hypot.f64 re im)) (+.f64 (hypot.f64 re im) #s(literal 2 binary64))))
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(hypot.f64 im re)
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(hypot.f64 re im)
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(hypot.f64 re im)
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(hypot.f64 re im)
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(hypot.f64 re im)
(hypot.f64 im re)
(pow.f64 (pow.f64 (hypot.f64 re im) #s(literal 4 binary64)) #s(literal 1/4 binary64))
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(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (hypot.f64 im re))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 im re)))) (sqrt.f64 (log.f64 (hypot.f64 im re))))
(sqrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 2 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)
(fabs.f64 (hypot.f64 re im))
(hypot.f64 re im)
(hypot.f64 im re)
(log.f64 (exp.f64 (hypot.f64 re im)))
(hypot.f64 re im)
(hypot.f64 im re)
(cbrt.f64 (pow.f64 (hypot.f64 re im) #s(literal 3 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)
(expm1.f64 (log1p.f64 (hypot.f64 re im)))
(hypot.f64 re im)
(hypot.f64 im re)
(log1p.f64 (expm1.f64 (hypot.f64 re im)))
(hypot.f64 re im)
(hypot.f64 im re)
(exp.f64 (log.f64 (hypot.f64 re im)))
(hypot.f64 re im)
(hypot.f64 im re)
(exp.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 re im)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) #s(literal 3 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (hypot.f64 re im))) #s(literal 1/3 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 re im))) #s(literal 2 binary64)))
(hypot.f64 re im)
(hypot.f64 im re)

eval64.0ms (5.2%)

Memory
-24.7MiB live, 53.0MiB allocated
Compiler

Compiled 2 682 to 462 computations (82.8% saved)

prune20.0ms (1.6%)

Memory
27.4MiB live, 66.3MiB allocated
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1631164
Fresh000
Picked011
Done000
Total1632165
Accuracy
100.0%
Counts
165 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 re im)
▶99.3%
im
Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify7.0ms (0.6%)

Memory
-29.0MiB live, 13.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044
Stop Event
1×saturated
Calls
Call 1
Inputs
im
Outputs
im

localize6.0ms (0.5%)

Memory
16.2MiB live, 16.2MiB allocated
Samples
4.0ms256×0valid
Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Accuracy
100.0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 re im)
✓99.3%
im
Compiler

Compiled 22 to 12 computations (45.5% saved)

regimes22.0ms (1.8%)

Memory
-1.1MiB live, 37.9MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
im
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Outputs
(hypot.f64 re im)
Calls

6 calls:

13.0ms
(*.f64 re re)
2.0ms
re
2.0ms
im
2.0ms
(*.f64 im im)
2.0ms
(+.f64 (*.f64 re re) (*.f64 im im))
Results
AccuracySegmentsBranch
100.0%1re
100.0%1im
100.0%1(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
100.0%1(+.f64 (*.f64 re re) (*.f64 im im))
100.0%1(*.f64 re re)
100.0%1(*.f64 im im)
Compiler

Compiled 35 to 21 computations (40% saved)

regimes3.0ms (0.3%)

Memory
-30.0MiB live, 9.6MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
im
Outputs
im
Calls

2 calls:

2.0ms
re
1.0ms
im
Results
AccuracySegmentsBranch
99.3%1re
99.3%1im
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify2.0ms (0.1%)

Memory
3.1MiB live, 3.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
Stop Event
1×saturated
Calls
Call 1
Inputs
(hypot.f64 re im)
im
Outputs
(hypot.f64 re im)
im

soundness23.0ms (1.9%)

Memory
0.6MiB live, 39.6MiB allocated
Rules
52×fmm-def
45×fma-define
16×distribute-lft-neg-in
15×neg-sub0
12×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02499
15199
29899
318799
428499
532399
633399
Stop Event
1×done
1×saturated
Compiler

Compiled 19 to 10 computations (47.4% saved)

preprocess84.0ms (6.9%)

Memory
5.3MiB live, 86.1MiB allocated
Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 122 to 72 computations (41% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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