math.log/2 on complex, imaginary part

Time bar (total: 10.0s)

analyze233.0ms (2.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
0%0%99.9%0.1%0%0%0%3
0%0%49.9%0.1%0%49.9%0%4
0%0%49.9%0.1%0%49.9%0%5
0%0%49.9%0.1%0%49.9%0%6
9.4%4.7%45.2%0.1%0%49.9%0%7
17.2%8.6%41.3%0.1%0%49.9%0%8
27.3%13.7%36.3%0.1%0%49.9%0%9
41%20.5%29.4%0.1%0%49.9%0%10
48.6%24.3%25.6%0.1%0%49.9%0%11
57.1%28.5%21.4%0.1%0%49.9%0%12
Compiler

Compiled 32 to 19 computations (40.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 152.0ms
ival-mult: 64.0ms (42.2% of total)
ival-log: 39.0ms (25.7% of total)
ival-add: 12.0ms (7.9% of total)
ival-atan2: 11.0ms (7.3% of total)
ival-sqrt: 9.0ms (5.9% of total)
ival-sub: 8.0ms (5.3% of total)
ival-div: 6.0ms (4% of total)
const: 1.0ms (0.7% of total)
backward-pass: 0.0ms (0% of total)

sample1.8s (18.5%)

Results
1.5s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-mult: 382.0ms (35% of total)
ival-log: 296.0ms (27.1% of total)
ival-atan2: 112.0ms (10.3% of total)
ival-add: 85.0ms (7.8% of total)
ival-div: 77.0ms (7.1% of total)
ival-sqrt: 76.0ms (7% of total)
ival-sub: 48.0ms (4.4% of total)
const: 13.0ms (1.2% of total)
backward-pass: 4.0ms (0.4% of total)
Bogosity

preprocess186.0ms (1.9%)

Algorithm
2×egg-herbie
Rules
2532×*-lowering-*.f32
2532×*-lowering-*.f64
2034×fnmadd-define
1996×fmsub-define
1972×fmm-def
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
079143
1266133
257086
3125069
4234569
5438569
6766669
01813
14212
2728
31026
41326
52126
66006
717776
830346
944266
1054776
1172506
081066
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
Outputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/.f64 (atan2.f64 im re) (log.f64 base))
Call 2
Inputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (- (* (atan2 im (neg re)) (log base)) (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (- (* (atan2 (neg im) re) (log base)) (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (- (* (atan2 im re) (log (neg base))) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0)))
(neg (/ (- (* (atan2 im (neg re)) (log base)) (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))))
(neg (/ (- (* (atan2 (neg im) re) (log base)) (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) 0)) (+ (* (log base) (log base)) (* 0 0))))
(neg (/ (- (* (atan2 im re) (log (neg base))) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0))))
(/ (- (* (atan2 re im) (log base)) (* (log (sqrt (+ (* im im) (* re re)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (- (* (atan2 im base) (log re)) (* (log (sqrt (+ (* base base) (* im im)))) 0)) (+ (* (log re) (log re)) (* 0 0)))
(/ (- (* (atan2 base re) (log im)) (* (log (sqrt (+ (* re re) (* base base)))) 0)) (+ (* (log im) (log im)) (* 0 0)))
Outputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (atan2 im re) (log base))
(/ (- (* (atan2 im (neg re)) (log base)) (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (atan2 im (neg re)) (log base))
(/ (- (* (atan2 (neg im) re) (log base)) (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (atan2 (neg im) re) (log base))
(/ (- (* (atan2 im re) (log (neg base))) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0)))
(/ (atan2 im re) (log (neg base)))
(neg (/ (- (* (atan2 im (neg re)) (log base)) (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))))
(/ (atan2 im (neg re)) (neg (log base)))
(neg (/ (- (* (atan2 (neg im) re) (log base)) (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) 0)) (+ (* (log base) (log base)) (* 0 0))))
(/ (atan2 (neg im) re) (neg (log base)))
(neg (/ (- (* (atan2 im re) (log (neg base))) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0))))
(/ (neg (atan2 im re)) (log (neg base)))
(/ (- (* (atan2 re im) (log base)) (* (log (sqrt (+ (* im im) (* re re)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (atan2 re im) (log base))
(/ (- (* (atan2 im base) (log re)) (* (log (sqrt (+ (* base base) (* im im)))) 0)) (+ (* (log re) (log re)) (* 0 0)))
(/ (atan2 im base) (log re))
(/ (- (* (atan2 base re) (log im)) (* (log (sqrt (+ (* re re) (* base base)))) 0)) (+ (* (log im) (log im)) (* 0 0)))
(/ (atan2 base re) (log im))

explain189.0ms (1.9%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1300-1(-1.411899779896759e-156 -1.2465278240021204e-175 1.2599415106285716e+106)(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
10-1(1.3708212427325895e+268 2.6426259397715717e-49 6.640480992922485e+80)(*.f64 (atan2.f64 im re) (log.f64 base))
00-0-(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
00-0-base
00-0-(*.f64 im im)
00-0-(*.f64 (log.f64 base) (log.f64 base))
00-0-(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
00-0-#s(literal 0 binary64)
00-0-(+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
00-0-(*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
00-0-(-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64)))
00-0-re
00-0-(+.f64 (*.f64 re re) (*.f64 im im))
00-0-im
00-0-(atan2.f64 im re)
00-0-(*.f64 re re)
00-0-(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
00-0-(log.f64 base)
Results
116.0ms512×0valid
Compiler

Compiled 277 to 56 computations (79.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 77.0ms
ival-sub: 26.0ms (33.8% of total)
ival-mult: 19.0ms (24.7% of total)
ival-log: 13.0ms (16.9% of total)
ival-add: 5.0ms (6.5% of total)
ival-atan2: 5.0ms (6.5% of total)
ival-sqrt: 4.0ms (5.2% of total)
ival-div: 3.0ms (3.9% of total)
const: 1.0ms (1.3% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(/.f64 (atan2.f64 im re) (log.f64 base))
▶49.2%
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
Compiler

Compiled 40 to 24 computations (40% saved)

simplify116.0ms (1.2%)

Algorithm
1×egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(log.f64 base)
✓cost-diff0
(atan2.f64 im re)
✓cost-diff0
(/.f64 (atan2.f64 im re) (log.f64 base))
✓cost-diff320
(log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))))
✓cost-diff13312
(*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
✓cost-diff13440
(-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64)))
✓cost-diff26752
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
Rules
2532×*-lowering-*.f32
2532×*-lowering-*.f64
1996×fmsub-define
1972×fmm-def
1964×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01988
14384
27276
310272
413272
521272
660072
7177872
8303672
9445772
10549972
11727072
0811972
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0))
(* (atan2 im re) (log base))
(atan2 im re)
im
re
(log base)
base
(* (log (sqrt (+ (* re re) (* im im)))) 0)
(log (sqrt (+ (* re re) (* im im))))
(sqrt (+ (* re re) (* im im)))
(+ (* re re) (* im im))
(* re re)
(* im im)
0
(+ (* (log base) (log base)) (* 0 0))
(* (log base) (log base))
(* 0 0)
(/ (atan2 im re) (log base))
(atan2 im re)
im
re
(log base)
base
Outputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (atan2 im re) (log base))
(*.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(log base)
(log.f64 base)
base
(* (log (sqrt (+ (* re re) (* im im)))) 0)
#s(literal 0 binary64)
(log (sqrt (+ (* re re) (* im im))))
(log.f64 (hypot.f64 im re))
(sqrt (+ (* re re) (* im im)))
(hypot.f64 im re)
(+ (* re re) (* im im))
(+.f64 (*.f64 re re) (*.f64 im im))
(* re re)
(*.f64 re re)
(* im im)
(*.f64 im im)
0
#s(literal 0 binary64)
(+ (* (log base) (log base)) (* 0 0))
(*.f64 (log.f64 base) (log.f64 base))
(* (log base) (log base))
(*.f64 (log.f64 base) (log.f64 base))
(* 0 0)
#s(literal 0 binary64)
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(log base)
(log.f64 base)
base

localize78.0ms (0.8%)

Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(atan2.f64 im re)
✓accuracy100.0%
(log.f64 base)
✓accuracy99.5%
(/.f64 (atan2.f64 im re) (log.f64 base))
✓accuracy99.5%
(*.f64 (atan2.f64 im re) (log.f64 base))
✓accuracy99.5%
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓accuracy99.2%
(*.f64 (log.f64 base) (log.f64 base))
✓accuracy53.1%
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Results
54.0ms256×0valid
Compiler

Compiled 137 to 20 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-mult: 9.0ms (32.1% of total)
ival-log: 6.0ms (21.4% of total)
ival-div: 3.0ms (10.7% of total)
ival-add: 3.0ms (10.7% of total)
ival-sub: 2.0ms (7.1% of total)
ival-atan2: 2.0ms (7.1% of total)
ival-sqrt: 2.0ms (7.1% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series92.0ms (0.9%)

Counts
10 → 264
Calls
Call 1
Inputs
#<alt (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))>
#<alt (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0))>
#<alt (* (log (sqrt (+ (* re re) (* im im)))) 0)>
#<alt (log (sqrt (+ (* re re) (* im im))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (atan2 im re)>
#<alt (log base)>
#<alt (sqrt (+ (* re re) (* im im)))>
#<alt (* (log base) (log base))>
#<alt (* (atan2 im re) (log base))>
Outputs
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (log im)>
#<alt (+ (log im) (* 1/2 (/ (pow re 2) (pow im 2))))>
#<alt (+ (log im) (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (pow im 4))) (* 1/2 (/ 1 (pow im 2))))))>
#<alt (+ (log im) (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (pow im 6))) (* 1/4 (/ 1 (pow im 4))))) (* 1/2 (/ 1 (pow im 2))))))>
#<alt (* -1 (log (/ 1 re)))>
#<alt (+ (* -1 (log (/ 1 re))) (* 1/2 (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -1 (log (/ 1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))>
#<alt (+ (* -1 (log (/ 1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))>
#<alt (* -1 (log (/ -1 re)))>
#<alt (+ (* -1 (log (/ -1 re))) (* 1/2 (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -1 (log (/ -1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))>
#<alt (+ (* -1 (log (/ -1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))>
#<alt (log re)>
#<alt (+ (log re) (* 1/2 (/ (pow im 2) (pow re 2))))>
#<alt (+ (log re) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 4))) (* 1/2 (/ 1 (pow re 2))))))>
#<alt (+ (log re) (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (pow re 6))) (* 1/4 (/ 1 (pow re 4))))) (* 1/2 (/ 1 (pow re 2))))))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (+ (* -1 (log (/ 1 im))) (* 1/2 (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -1 (log (/ 1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))>
#<alt (+ (* -1 (log (/ 1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))>
#<alt (* -1 (log (/ -1 im)))>
#<alt (+ (* -1 (log (/ -1 im))) (* 1/2 (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))>
#<alt (+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt im>
#<alt (+ im (* 1/2 (/ (pow re 2) im)))>
#<alt (+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))>
#<alt (+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))>
#<alt re>
#<alt (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))>
#<alt (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))>
#<alt (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))>
#<alt (* -1 re)>
#<alt (* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))>
#<alt (* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))>
#<alt (* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))>
#<alt re>
#<alt (+ re (* 1/2 (/ (pow im 2) re)))>
#<alt (+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))>
#<alt (+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))>
#<alt im>
#<alt (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))>
#<alt (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))>
#<alt (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))>
#<alt (* -1 im)>
#<alt (* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))>
#<alt (* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))>
#<alt (* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
Calls

66 calls:

TimeVariablePointExpression
28.0ms
im
@0
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
21.0ms
base
@0
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
14.0ms
base
@-inf
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
6.0ms
base
@inf
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
6.0ms
re
@0
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))

rewrite347.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
4236×*-lowering-*.f32
4236×*-lowering-*.f64
3188×/-lowering-/.f32
3188×/-lowering-/.f64
1164×sum5-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01955
111351
280341
3793241
0851441
Stop Event
1×iter limit
1×node limit
Counts
10 → 964
Calls
Call 1
Inputs
(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
(- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0))
(* (log (sqrt (+ (* re re) (* im im)))) 0)
(log (sqrt (+ (* re re) (* im im))))
(/ (atan2 im re) (log base))
(atan2 im re)
(log base)
(sqrt (+ (* re re) (* im im)))
(* (log base) (log base))
(* (atan2 im re) (log base))
Outputs
(+.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 0 binary64))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 #s(literal 0 binary64) (/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))))
(+.f64 (*.f64 #s(literal 0 binary64) (/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(-.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 0 binary64))
(-.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(-.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
(fma.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 0 binary64))
(neg.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re))))
(neg.f64 (/.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base)))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (*.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (neg.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 6 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 6 binary64)) (*.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 4 binary64))))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 4 binary64)) (*.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)))
(/.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 9 binary64)) (*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 6 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (neg.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)))
(/.f64 (/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal -4 binary64)))
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (*.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
(/.f64 (neg.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (neg.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (neg.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base)))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 (*.f64 (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base))) (*.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
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(*.f64 (/.f64 (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (/.f64 (log.f64 base) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(*.f64 (/.f64 (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
(*.f64 (/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (atan2.f64 im re) (*.f64 (atan2.f64 im re) (log.f64 base))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))))
(*.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)) (atan2.f64 im re)) (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)) (log.f64 base)) (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))))
(*.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)) (*.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)))) (log.f64 base))
(*.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)) (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (atan2.f64 im re))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(*.f64 (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(*.f64 (/.f64 (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 6 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 4 binary64)))
(*.f64 (/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -2 binary64))))

simplify259.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
4250×*-lowering-*.f32
4250×*-lowering-*.f64
2740×fma-lowering-fma.f32
2740×fma-lowering-fma.f64
1804×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02042000
15801936
219081914
367421914
080951914
Stop Event
1×iter limit
1×node limit
Counts
264 → 264
Calls
Call 1
Inputs
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(log im)
(+ (log im) (* 1/2 (/ (pow re 2) (pow im 2))))
(+ (log im) (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (pow im 4))) (* 1/2 (/ 1 (pow im 2))))))
(+ (log im) (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (pow im 6))) (* 1/4 (/ 1 (pow im 4))))) (* 1/2 (/ 1 (pow im 2))))))
(* -1 (log (/ 1 re)))
(+ (* -1 (log (/ 1 re))) (* 1/2 (/ (pow im 2) (pow re 2))))
(+ (* -1 (log (/ 1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))
(+ (* -1 (log (/ 1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (log (/ -1 re)))
(+ (* -1 (log (/ -1 re))) (* 1/2 (/ (pow im 2) (pow re 2))))
(+ (* -1 (log (/ -1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))
(+ (* -1 (log (/ -1 re))) (+ (* -1/4 (/ (pow im 4) (pow re 4))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(log re)
(+ (log re) (* 1/2 (/ (pow im 2) (pow re 2))))
(+ (log re) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (pow re 4))) (* 1/2 (/ 1 (pow re 2))))))
(+ (log re) (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (pow re 6))) (* 1/4 (/ 1 (pow re 4))))) (* 1/2 (/ 1 (pow re 2))))))
(* -1 (log (/ 1 im)))
(+ (* -1 (log (/ 1 im))) (* 1/2 (/ (pow re 2) (pow im 2))))
(+ (* -1 (log (/ 1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))
(+ (* -1 (log (/ 1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (log (/ -1 im)))
(+ (* -1 (log (/ -1 im))) (* 1/2 (/ (pow re 2) (pow im 2))))
(+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))
(+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
re
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
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(*.f64 im (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im)) (/.f64 (*.f64 re (*.f64 re (*.f64 re (*.f64 re #s(literal -1/8 binary64))))) (*.f64 im (*.f64 im (*.f64 im im))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(*.f64 im (+.f64 (/.f64 (*.f64 re (*.f64 re (*.f64 re (*.f64 re #s(literal -1/8 binary64))))) (*.f64 im (*.f64 im (*.f64 im im)))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im)) (/.f64 (*.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 im #s(literal 6 binary64))))))
(* -1 im)
(-.f64 #s(literal 0 binary64) im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 im (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im)) (/.f64 (*.f64 re (*.f64 re (*.f64 re (*.f64 re #s(literal -1/8 binary64))))) (*.f64 im (*.f64 im (*.f64 im im))))) (-.f64 #s(literal 0 binary64) im))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(-.f64 #s(literal 0 binary64) (*.f64 im (+.f64 (/.f64 (*.f64 re (*.f64 re (*.f64 re (*.f64 re #s(literal -1/8 binary64))))) (*.f64 im (*.f64 im (*.f64 im im)))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im)) (/.f64 (*.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 im #s(literal 6 binary64)))))))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))

eval185.0ms (1.9%)

Compiler

Compiled 35014 to 2321 computations (93.4% saved)

prune137.0ms (1.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New1327191346
Fresh000
Picked112
Done000
Total1328201348
Accuracy
100.0%
Counts
1348 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.4%
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
53.5%
(/.f64 (atan2.f64 im re) (*.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
✓99.5%
(/.f64 (atan2.f64 im re) (log.f64 base))
▶53.1%
(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
99.2%
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
▶98.9%
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
99.1%
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
99.3%
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
99.3%
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
99.3%
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (atan2.f64 im re) (log.f64 base))) (log.f64 base))
99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
84.6%
(*.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (/.f64 (log.f64 base) (atan2.f64 im re)))
99.1%
(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
▶99.3%
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
▶99.4%
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
99.2%
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
99.3%
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
99.2%
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
99.3%
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (atan2.f64 im re))
49.9%
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1 binary64)))
Compiler

Compiled 577 to 382 computations (33.8% saved)

simplify132.0ms (1.3%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
✓cost-diff320
(+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
✓cost-diff13568
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓cost-diff0
(*.f64 (atan2.f64 im re) (log.f64 base))
✓cost-diff0
(log.f64 base)
✓cost-diff0
(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓cost-diff12992
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff128
(*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))
✓cost-diff12928
(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
✓cost-diff12928
(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
✓cost-diff0
(log.f64 base)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (log.f64 base))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff128
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (log.f64 base))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓cost-diff256
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
Rules
2212×fma-lowering-fma.f32
2212×fma-lowering-fma.f64
2046×fma-define
1880×sum3-define
1790×fnmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025129
153129
2110127
3285127
41000127
52325127
65324127
77239127
08543127
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (atan2 im re) (/ 1 (/ 1 (log base))))
(atan2 im re)
im
re
(/ 1 (/ 1 (log base)))
1
(/ 1 (log base))
(log base)
base
(* (atan2 im re) (/ 1 (log base)))
(atan2 im re)
im
re
(/ 1 (log base))
1
(log base)
base
(/ (atan2 im re) (exp (* (log (log base)) 1)))
(atan2 im re)
im
re
(exp (* (log (log base)) 1))
(* (log (log base)) 1)
(log (log base))
(log base)
base
1
(* (pow (log base) -2) (* (atan2 im re) (log base)))
(pow (log base) -2)
(log base)
base
-2
(* (atan2 im re) (log base))
(atan2 im re)
im
re
(/ (/ 1 (/ (/ 1 (log base)) (atan2 im re))) (+ (* (log base) (log base)) (* 0 0)))
(/ 1 (/ (/ 1 (log base)) (atan2 im re)))
1
(/ (/ 1 (log base)) (atan2 im re))
(/ 1 (log base))
(log base)
base
(atan2 im re)
im
re
(+ (* (log base) (log base)) (* 0 0))
(* (log base) (log base))
(* 0 0)
0
Outputs
(/ (atan2 im re) (/ 1 (/ 1 (log base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ 1 (/ 1 (log base)))
(log.f64 base)
1
#s(literal 1 binary64)
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(log base)
(log.f64 base)
base
(* (atan2 im re) (/ 1 (log base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
1
#s(literal 1 binary64)
(log base)
(log.f64 base)
base
(/ (atan2 im re) (exp (* (log (log base)) 1)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(exp (* (log (log base)) 1))
(log.f64 base)
(* (log (log base)) 1)
(log.f64 (log.f64 base))
(log (log base))
(log.f64 (log.f64 base))
(log base)
(log.f64 base)
base
1
#s(literal 1 binary64)
(* (pow (log base) -2) (* (atan2 im re) (log base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow (log base) -2)
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log base)
(log.f64 base)
base
-2
#s(literal -2 binary64)
(* (atan2 im re) (log base))
(*.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ (/ 1 (/ (/ 1 (log base)) (atan2 im re))) (+ (* (log base) (log base)) (* 0 0)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ 1 (/ (/ 1 (log base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
1
#s(literal 1 binary64)
(/ (/ 1 (log base)) (atan2 im re))
(/.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(log base)
(log.f64 base)
base
(atan2 im re)
(atan2.f64 im re)
im
re
(+ (* (log base) (log base)) (* 0 0))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(* (log base) (log base))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(* 0 0)
#s(literal 0 binary64)
0
#s(literal 0 binary64)

localize139.0ms (1.4%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (log.f64 base))
✓accuracy99.7%
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓accuracy99.6%
(*.f64 (log.f64 base) (log.f64 base))
✓accuracy99.4%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
✓accuracy100.0%
(log.f64 base)
✓accuracy99.7%
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓accuracy99.7%
(*.f64 (atan2.f64 im re) (log.f64 base))
✓accuracy99.5%
(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓accuracy100.0%
(log.f64 base)
✓accuracy100.0%
(log.f64 (log.f64 base))
✓accuracy99.7%
(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
✓accuracy99.1%
(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
✓accuracy100.0%
(atan2.f64 im re)
✓accuracy100.0%
(log.f64 base)
✓accuracy99.8%
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (log.f64 base))
✓accuracy100.0%
(log.f64 base)
✓accuracy99.7%
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (log.f64 base))
Results
51.0ms138×0valid
41.0ms118×0invalid
Compiler

Compiled 186 to 26 computations (86% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-mult: 12.0ms (24.6% of total)
ival-log: 12.0ms (24.6% of total)
ival-div: 11.0ms (22.6% of total)
ival-pow: 7.0ms (14.4% of total)
ival-atan2: 3.0ms (6.2% of total)
ival-exp: 2.0ms (4.1% of total)
ival-add: 1.0ms (2.1% of total)
const: 1.0ms (2.1% of total)
backward-pass: 0.0ms (0% of total)

series110.0ms (1.1%)

Counts
18 → 384
Calls
Call 1
Inputs
#<alt (/ (atan2 im re) (/ 1 (/ 1 (log base))))>
#<alt (/ 1 (/ 1 (log base)))>
#<alt (atan2 im re)>
#<alt (/ 1 (log base))>
#<alt (* (atan2 im re) (/ 1 (log base)))>
#<alt (log base)>
#<alt (/ (atan2 im re) (exp (* (log (log base)) 1)))>
#<alt (exp (* (log (log base)) 1))>
#<alt (* (log (log base)) 1)>
#<alt (* (pow (log base) -2) (* (atan2 im re) (log base)))>
#<alt (pow (log base) -2)>
#<alt (* (atan2 im re) (log base))>
#<alt (/ (/ 1 (/ (/ 1 (log base)) (atan2 im re))) (+ (* (log base) (log base)) (* 0 0)))>
#<alt (+ (* (log base) (log base)) (* 0 0))>
#<alt (/ 1 (/ (/ 1 (log base)) (atan2 im re)))>
#<alt (* 0 0)>
#<alt (log (log base))>
#<alt (* (log base) (log base))>
Outputs
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
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#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
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#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log base)>
#<alt (log base)>
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#<alt (* -1 (log (/ 1 base)))>
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#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
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#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
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#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
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#<alt (/ (atan2 im re) (log base))>
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#<alt (/ (atan2 im re) (log base))>
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#<alt (/ (atan2 im re) (log base))>
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#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
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#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
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#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
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#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
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#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
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#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
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#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
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#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
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#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
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#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
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#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
Calls

96 calls:

TimeVariablePointExpression
46.0ms
base
@inf
(* (log (log base)) 1)
36.0ms
base
@0
(* (log (log base)) 1)
17.0ms
base
@-inf
(* (log (log base)) 1)
2.0ms
base
@-inf
(pow (log base) -2)
1.0ms
base
@-inf
(/ 1 (log base))

rewrite334.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
2858×*-lowering-*.f32
2858×*-lowering-*.f64
2068×/-lowering-/.f32
2068×/-lowering-/.f64
1756×fma-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02573
112273
272873
3508673
0867273
Stop Event
1×iter limit
1×node limit
Counts
18 → 2032
Calls
Call 1
Inputs
(/ (atan2 im re) (/ 1 (/ 1 (log base))))
(/ 1 (/ 1 (log base)))
(atan2 im re)
(/ 1 (log base))
(* (atan2 im re) (/ 1 (log base)))
(log base)
(/ (atan2 im re) (exp (* (log (log base)) 1)))
(exp (* (log (log base)) 1))
(* (log (log base)) 1)
(* (pow (log base) -2) (* (atan2 im re) (log base)))
(pow (log base) -2)
(* (atan2 im re) (log base))
(/ (/ 1 (/ (/ 1 (log base)) (atan2 im re))) (+ (* (log base) (log base)) (* 0 0)))
(+ (* (log base) (log base)) (* 0 0))
(/ 1 (/ (/ 1 (log base)) (atan2 im re)))
(* 0 0)
(log (log base))
(* (log base) (log base))
Outputs
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 5 binary64))) #s(literal 0 binary64)))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal 0 binary64)))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))))
(+.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 5 binary64))) #s(literal 0 binary64)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal 0 binary64)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))))))
(exp.f64 (+.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))) (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64))))
(exp.f64 (-.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))) (*.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
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simplify208.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
2020×sum4-define
1924×fma-lowering-fma.f32
1924×fma-lowering-fma.f64
1868×sum3-define
1786×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0362304
1632240
21102240
32452240
45992240
515842240
634332240
771422240
081962240
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
Calls
Call 1
Inputs
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(log (log base))
(log (log base))
(log (log base))
(log (log base))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(log (log base))
(log (log base))
(log (log base))
(log (log base))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
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(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(log (log base))
(log.f64 (log.f64 base))
(log (log base))
(log.f64 (log.f64 base))
(log (log base))
(log.f64 (log.f64 base))
(log (log base))
(log.f64 (log.f64 base))
(log (* -1 (log (/ 1 base))))
(log.f64 (log.f64 base))
(log (* -1 (log (/ 1 base))))
(log.f64 (log.f64 base))
(log (* -1 (log (/ 1 base))))
(log.f64 (log.f64 base))
(log (* -1 (log (/ 1 base))))
(log.f64 (log.f64 base))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))

eval475.0ms (4.8%)

Compiler

Compiled 71198 to 5550 computations (92.2% saved)

prune380.0ms (3.8%)

Pruning

21 alts after pruning (18 fresh and 3 done)

PrunedKeptTotal
New3764113775
Fresh7714
Picked325
Done011
Total3774213795
Accuracy
100.0%
Counts
3795 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.5%
(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
52.9%
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
▶99.3%
(/.f64 (atan2.f64 im re) (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base))))
✓99.4%
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
99.3%
(/.f64 (atan2.f64 im re) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓99.5%
(/.f64 (atan2.f64 im re) (log.f64 base))
53.1%
(/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (log.f64 base))))
99.2%
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
99.0%
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64)))
99.1%
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
99.3%
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
99.2%
(/.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)))
▶99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
84.6%
(*.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (/.f64 (log.f64 base) (atan2.f64 im re)))
▶99.1%
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
56.7%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
53.5%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
99.3%
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓99.4%
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
▶99.2%
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
49.9%
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1 binary64)))
Compiler

Compiled 549 to 377 computations (31.3% saved)

simplify96.0ms (1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(log.f64 base)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (log.f64 base))
✓cost-diff128
(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))
✓cost-diff13120
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓cost-diff0
(log.f64 base)
✓cost-diff0
(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re))
✓cost-diff12992
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓cost-diff0
(sqrt.f64 (log.f64 base))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff12864
(pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))
✓cost-diff12864
(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff0
(log.f64 base)
✓cost-diff0
(/.f64 (log.f64 base) (atan2.f64 im re))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓cost-diff0
(/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff13248
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
✓cost-diff13248
(/.f64 (atan2.f64 im re) (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base))))
Rules
1602×/-lowering-/.f32
1602×/-lowering-/.f64
1490×*-lowering-*.f32
1490×*-lowering-*.f64
1400×fnmadd-define
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
026225
146225
296189
3268160
41024129
54035129
08511129
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (atan2 im re) (/ (/ -1 (pow (log base) -2)) (- 0 (log base))))
(atan2 im re)
im
re
(/ (/ -1 (pow (log base) -2)) (- 0 (log base)))
(/ -1 (pow (log base) -2))
-1
(pow (log base) -2)
(log base)
base
-2
(- 0 (log base))
0
(/ 1 (/ (log base) (atan2 im re)))
1
(/ (log base) (atan2 im re))
(log base)
base
(atan2 im re)
im
re
(/ (atan2 im re) (pow (sqrt (log base)) 2))
(atan2 im re)
im
re
(pow (sqrt (log base)) 2)
(sqrt (log base))
(log base)
base
2
(* (* (pow (log base) -2) (atan2 im re)) (log base))
(* (pow (log base) -2) (atan2 im re))
(pow (log base) -2)
(log base)
base
-2
(atan2 im re)
im
re
(* (pow (/ 1 (log base)) 2) (* (atan2 im re) (log base)))
(pow (/ 1 (log base)) 2)
(/ 1 (log base))
1
(log base)
base
2
(* (atan2 im re) (log base))
(atan2 im re)
im
re
Outputs
(/ (atan2 im re) (/ (/ -1 (pow (log base) -2)) (- 0 (log base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ (/ -1 (pow (log base) -2)) (- 0 (log base)))
(log.f64 base)
(/ -1 (pow (log base) -2))
(/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
-1
#s(literal -1 binary64)
(pow (log base) -2)
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log base)
(log.f64 base)
base
-2
#s(literal -2 binary64)
(- 0 (log base))
(-.f64 #s(literal 0 binary64) (log.f64 base))
0
#s(literal 0 binary64)
(/ 1 (/ (log base) (atan2 im re)))
(/.f64 (atan2.f64 im re) (log.f64 base))
1
#s(literal 1 binary64)
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(log base)
(log.f64 base)
base
(atan2 im re)
(atan2.f64 im re)
im
re
(/ (atan2 im re) (pow (sqrt (log base)) 2))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(pow (sqrt (log base)) 2)
(log.f64 base)
(sqrt (log base))
(sqrt.f64 (log.f64 base))
(log base)
(log.f64 base)
base
2
#s(literal 2 binary64)
(* (* (pow (log base) -2) (atan2 im re)) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* (pow (log base) -2) (atan2 im re))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(pow (log base) -2)
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log base)
(log.f64 base)
base
-2
#s(literal -2 binary64)
(atan2 im re)
(atan2.f64 im re)
im
re
(* (pow (/ 1 (log base)) 2) (* (atan2 im re) (log base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow (/ 1 (log base)) 2)
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
1
#s(literal 1 binary64)
(log base)
(log.f64 base)
base
2
#s(literal 2 binary64)
(* (atan2 im re) (log base))
(*.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re

localize138.0ms (1.4%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (log.f64 base))
✓accuracy99.7%
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓accuracy99.7%
(*.f64 (atan2.f64 im re) (log.f64 base))
✓accuracy99.6%
(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))
✓accuracy100.0%
(log.f64 base)
✓accuracy99.7%
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re))
✓accuracy99.6%
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓accuracy99.5%
(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓accuracy100.0%
(log.f64 base)
✓accuracy99.9%
(sqrt.f64 (log.f64 base))
✓accuracy99.7%
(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
✓accuracy99.6%
(pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))
✓accuracy100.0%
(atan2.f64 im re)
✓accuracy100.0%
(log.f64 base)
✓accuracy99.7%
(/.f64 (log.f64 base) (atan2.f64 im re))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓accuracy99.8%
(/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
✓accuracy99.7%
(/.f64 (atan2.f64 im re) (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base))))
✓accuracy99.6%
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
✓accuracy99.5%
(pow.f64 (log.f64 base) #s(literal -2 binary64))
Results
53.0ms138×0valid
35.0ms118×0invalid
Compiler

Compiled 175 to 27 computations (84.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-pow: 12.0ms (29.2% of total)
ival-div: 11.0ms (26.8% of total)
ival-mult: 6.0ms (14.6% of total)
ival-log: 5.0ms (12.2% of total)
ival-atan2: 3.0ms (7.3% of total)
ival-sqrt: 2.0ms (4.9% of total)
ival-sub: 1.0ms (2.4% of total)
const: 1.0ms (2.4% of total)
backward-pass: 0.0ms (0% of total)

series21.0ms (0.2%)

Counts
17 → 408
Calls
Call 1
Inputs
#<alt (/ (atan2 im re) (/ (/ -1 (pow (log base) -2)) (- 0 (log base))))>
#<alt (/ (/ -1 (pow (log base) -2)) (- 0 (log base)))>
#<alt (atan2 im re)>
#<alt (/ -1 (pow (log base) -2))>
#<alt (/ 1 (/ (log base) (atan2 im re)))>
#<alt (/ (log base) (atan2 im re))>
#<alt (log base)>
#<alt (/ (atan2 im re) (pow (sqrt (log base)) 2))>
#<alt (pow (sqrt (log base)) 2)>
#<alt (sqrt (log base))>
#<alt (* (* (pow (log base) -2) (atan2 im re)) (log base))>
#<alt (* (pow (log base) -2) (atan2 im re))>
#<alt (pow (log base) -2)>
#<alt (* (pow (/ 1 (log base)) 2) (* (atan2 im re) (log base)))>
#<alt (pow (/ 1 (log base)) 2)>
#<alt (/ 1 (log base))>
#<alt (* (atan2 im re) (log base))>
Outputs
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (* -1 (pow (log base) 2))>
#<alt (* -1 (pow (log base) 2))>
#<alt (* -1 (pow (log base) 2))>
#<alt (* -1 (pow (log base) 2))>
#<alt (* -1 (pow (log (/ 1 base)) 2))>
#<alt (* -1 (pow (log (/ 1 base)) 2))>
#<alt (* -1 (pow (log (/ 1 base)) 2))>
#<alt (* -1 (pow (log (/ 1 base)) 2))>
#<alt (* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (sqrt (log base))>
#<alt (sqrt (log base))>
#<alt (sqrt (log base))>
#<alt (sqrt (log base))>
#<alt (* (sqrt (log (/ 1 base))) (sqrt -1))>
#<alt (* (sqrt (log (/ 1 base))) (sqrt -1))>
#<alt (* (sqrt (log (/ 1 base))) (sqrt -1))>
#<alt (* (sqrt (log (/ 1 base))) (sqrt -1))>
#<alt (sqrt (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (sqrt (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (sqrt (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (sqrt (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log (/ 1 base)) 2))>
#<alt (/ (atan2 im re) (pow (log (/ 1 base)) 2))>
#<alt (/ (atan2 im re) (pow (log (/ 1 base)) 2))>
#<alt (/ (atan2 im re) (pow (log (/ 1 base)) 2))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log base) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (log (/ 1 base)) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
Calls

102 calls:

TimeVariablePointExpression
1.0ms
base
@-inf
(* (pow (log base) -2) (atan2 im re))
0.0ms
im
@-inf
(/ (log base) (atan2 im re))
0.0ms
base
@0
(* (pow (log base) -2) (atan2 im re))
0.0ms
base
@-inf
(/ (log base) (atan2 im re))
0.0ms
re
@inf
(/ (log base) (atan2 im re))

rewrite318.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
2704×*-lowering-*.f32
2704×*-lowering-*.f64
1820×/-lowering-/.f32
1820×/-lowering-/.f64
1008×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026143
112178
270178
3606778
0811878
Stop Event
1×iter limit
1×node limit
Counts
17 → 2329
Calls
Call 1
Inputs
(/ (atan2 im re) (/ (/ -1 (pow (log base) -2)) (- 0 (log base))))
(/ (/ -1 (pow (log base) -2)) (- 0 (log base)))
(atan2 im re)
(/ -1 (pow (log base) -2))
(/ 1 (/ (log base) (atan2 im re)))
(/ (log base) (atan2 im re))
(log base)
(/ (atan2 im re) (pow (sqrt (log base)) 2))
(pow (sqrt (log base)) 2)
(sqrt (log base))
(* (* (pow (log base) -2) (atan2 im re)) (log base))
(* (pow (log base) -2) (atan2 im re))
(pow (log base) -2)
(* (pow (/ 1 (log base)) 2) (* (atan2 im re) (log base)))
(pow (/ 1 (log base)) 2)
(/ 1 (log base))
(* (atan2 im re) (log base))
Outputs
(+.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 0 binary64))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64)))
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
(+.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(+.f64 (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(fma.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(fma.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(neg.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 #s(literal -1 binary64) (/.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))))
(/.f64 (log.f64 base) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (atan2.f64 im re)))
(/.f64 (-.f64 #s(literal 0 binary64) (log.f64 base)) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(/.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (atan2.f64 im re)))
(/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (atan2.f64 im re)))
(/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))) #s(literal -1 binary64))
(/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (log.f64 base))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(/.f64 (neg.f64 (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (neg.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base))) (*.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base)))) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (*.f64 (atan2.f64 im re) (log.f64 base))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 base))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (log.f64 base))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 base)) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (*.f64 (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (log.f64 base))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (pow.f64 (log.f64 base) #s(literal 1/4 binary64))) (pow.f64 (log.f64 base) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1 binary64))
(pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1 binary64))
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (log.f64 base) (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (log.f64 base) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 base)) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))))
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(/.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (log.f64 base))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 9 binary64)))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 6 binary64)))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(*.f64 (log.f64 base) (atan2.f64 im re))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(*.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (atan2.f64 im re)))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)))
(*.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))))
(*.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(*.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(*.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))

simplify200.0ms (2%)

Algorithm
1×egg-herbie
Rules
2664×sum4-define
1514×fnmadd-define
1322×fma-lowering-fma.f32
1322×fma-lowering-fma.f64
1138×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0482596
1852532
21492532
33842532
411342532
539752532
080862532
Stop Event
1×iter limit
1×node limit
Counts
408 → 408
Calls
Call 1
Inputs
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(* -1 (pow (log base) 2))
(* -1 (pow (log base) 2))
(* -1 (pow (log base) 2))
(* -1 (pow (log base) 2))
(* -1 (pow (log (/ 1 base)) 2))
(* -1 (pow (log (/ 1 base)) 2))
(* -1 (pow (log (/ 1 base)) 2))
(* -1 (pow (log (/ 1 base)) 2))
(* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* -1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(sqrt (log base))
(sqrt (log base))
(sqrt (log base))
(sqrt (log base))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(sqrt (+ (log -1) (* -1 (log (/ -1 base)))))
(sqrt (+ (log -1) (* -1 (log (/ -1 base)))))
(sqrt (+ (log -1) (* -1 (log (/ -1 base)))))
(sqrt (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
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(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (log base) (atan2 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))

eval698.0ms (7%)

Compiler

Compiled 87577 to 7956 computations (90.9% saved)

prune602.0ms (6%)

Pruning

21 alts after pruning (15 fresh and 6 done)

PrunedKeptTotal
New465544659
Fresh21113
Picked235
Done033
Total4659214680
Accuracy
100.0%
Counts
4680 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.3%
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓53.5%
(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
▶52.9%
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓99.4%
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
99.3%
(/.f64 (atan2.f64 im re) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓99.5%
(/.f64 (atan2.f64 im re) (log.f64 base))
53.1%
(/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (log.f64 base))))
99.2%
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
99.1%
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
▶99.3%
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
99.2%
(/.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)))
✓99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
▶99.2%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
▶56.7%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
53.5%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
▶99.3%
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓99.4%
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
99.0%
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓99.2%
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
99.1%
(*.f64 (neg.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (log.f64 base))
49.9%
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1 binary64)))
Compiler

Compiled 486 to 343 computations (29.4% saved)

simplify341.0ms (3.4%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(log.f64 base)
✓cost-diff0
(atan2.f64 im re)
✓cost-diff0
(*.f64 (atan2.f64 im re) (log.f64 base))
✓cost-diff12992
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
✓cost-diff0
(pow.f64 (log.f64 base) #s(literal 2 binary64))
✓cost-diff0
(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff0
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓cost-diff0
(E.f64)
✓cost-diff0
(pow.f64 (E.f64) (log.f64 (log.f64 base)))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff0
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓cost-diff0
(atan2.f64 im re)
✓cost-diff0
(/.f64 (atan2.f64 im re) (log.f64 base))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
✓cost-diff0
(log.f64 base)
✓cost-diff0
(atan2.f64 im re)
✓cost-diff12864
(/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
✓cost-diff12992
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
Rules
7418×*-lowering-*.f32
7418×*-lowering-*.f64
2728×cube-prod
2094×pow-lowering-pow.f64
2094×pow-lowering-pow.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
022155
135155
254131
376130
4203130
5953130
61894130
72160130
82273130
92467130
102768130
113248130
124494130
135426130
145554130
155655130
165765130
175884130
187440130
08049130
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (atan2 im re) (/ (log base) (pow (log base) 2)))
(atan2 im re)
im
re
(/ (log base) (pow (log base) 2))
(log base)
base
(pow (log base) 2)
2
(/ 1 (/ 1 (/ (atan2 im re) (log base))))
1
(/ 1 (/ (atan2 im re) (log base)))
(/ (atan2 im re) (log base))
(atan2 im re)
im
re
(log base)
base
(/ (atan2 im re) (pow (E) (log (log base))))
(atan2 im re)
im
re
(pow (E) (log (log base)))
(E)
(log (log base))
(log base)
base
(* (atan2 im re) (pow (pow (log base) 2) -1/2))
(atan2 im re)
im
re
(pow (pow (log base) 2) -1/2)
(pow (log base) 2)
(log base)
base
2
-1/2
(/ (* (atan2 im re) (log base)) (pow (log base) 2))
(* (atan2 im re) (log base))
(atan2 im re)
im
re
(log base)
base
(pow (log base) 2)
2
Outputs
(* (atan2 im re) (/ (log base) (pow (log base) 2)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ (log base) (pow (log base) 2))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(log base)
(log.f64 base)
base
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 1 (/ 1 (/ (atan2 im re) (log base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
1
#s(literal 1 binary64)
(/ 1 (/ (atan2 im re) (log base)))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(log base)
(log.f64 base)
base
(/ (atan2 im re) (pow (E) (log (log base))))
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
(atan2 im re)
(atan2.f64 im re)
im
re
(pow (E) (log (log base)))
(pow.f64 (E.f64) (log.f64 (log.f64 base)))
(E)
(E.f64)
(log (log base))
(log.f64 (log.f64 base))
(log base)
(log.f64 base)
base
(* (atan2 im re) (pow (pow (log base) 2) -1/2))
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(atan2 im re)
(atan2.f64 im re)
im
re
(pow (pow (log base) 2) -1/2)
(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(log base)
(log.f64 base)
base
2
#s(literal 2 binary64)
-1/2
#s(literal -1/2 binary64)
(/ (* (atan2 im re) (log base)) (pow (log base) 2))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* (atan2 im re) (log base))
(*.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(log base)
(log.f64 base)
base
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
2
#s(literal 2 binary64)

localize312.0ms (3.1%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(log.f64 base)
✓accuracy99.7%
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
✓accuracy99.7%
(*.f64 (atan2.f64 im re) (log.f64 base))
✓accuracy99.6%
(pow.f64 (log.f64 base) #s(literal 2 binary64))
✓accuracy100.0%
(log.f64 base)
✓accuracy99.9%
(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64))
✓accuracy99.8%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓accuracy99.6%
(pow.f64 (log.f64 base) #s(literal 2 binary64))
✓accuracy100.0%
(log.f64 (log.f64 base))
✓accuracy99.7%
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓accuracy98.9%
(pow.f64 (E.f64) (log.f64 (log.f64 base)))
✓accuracy55.3%
(E.f64)
✓accuracy100.0%
(log.f64 base)
✓accuracy99.7%
(/.f64 (atan2.f64 im re) (log.f64 base))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
✓accuracy100.0%
(log.f64 base)
✓accuracy99.8%
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓accuracy99.7%
(/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
✓accuracy99.6%
(pow.f64 (log.f64 base) #s(literal 2 binary64))
Results
204.0ms118×0invalid
72.0ms138×0valid
Compiler

Compiled 154 to 23 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 45.0ms
ival-pow: 17.0ms (37.8% of total)
ival-div: 10.0ms (22.2% of total)
ival-log: 7.0ms (15.5% of total)
ival-mult: 5.0ms (11.1% of total)
ival-atan2: 3.0ms (6.7% of total)
ival-e: 2.0ms (4.4% of total)
const: 1.0ms (2.2% of total)
backward-pass: 0.0ms (0% of total)

series165.0ms (1.7%)

Counts
16 → 384
Calls
Call 1
Inputs
#<alt (* (atan2 im re) (/ (log base) (pow (log base) 2)))>
#<alt (/ (log base) (pow (log base) 2))>
#<alt (atan2 im re)>
#<alt (log base)>
#<alt (/ 1 (/ 1 (/ (atan2 im re) (log base))))>
#<alt (/ 1 (/ (atan2 im re) (log base)))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (pow (E) (log (log base))))>
#<alt (pow (E) (log (log base)))>
#<alt (E)>
#<alt (* (atan2 im re) (pow (pow (log base) 2) -1/2))>
#<alt (pow (pow (log base) 2) -1/2)>
#<alt (pow (log base) 2)>
#<alt (/ (* (atan2 im re) (log base)) (pow (log base) 2))>
#<alt (* (atan2 im re) (log base))>
#<alt (log (log base))>
Outputs
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (atan2 im re)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (log base)>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (* -1 (log (/ 1 base)))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (+ (log -1) (* -1 (log (/ -1 base))))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (/ (log base) (atan2 im re))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (/ (log (/ 1 base)) (atan2 im re)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
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#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (log base) (log (E))))>
#<alt (/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))>
#<alt (/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))>
#<alt (/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))>
#<alt (/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))>
#<alt (/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))>
#<alt (pow (log base) (log (E)))>
#<alt (pow (log base) (log (E)))>
#<alt (pow (log base) (log (E)))>
#<alt (pow (log base) (log (E)))>
#<alt (pow (* -1 (log (/ 1 base))) (log (E)))>
#<alt (pow (* -1 (log (/ 1 base))) (log (E)))>
#<alt (pow (* -1 (log (/ 1 base))) (log (E)))>
#<alt (pow (* -1 (log (/ 1 base))) (log (E)))>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ 1 (log base))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ -1 (log (/ 1 base)))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log base) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (log (/ 1 base)) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
#<alt (* -1 (/ (atan2 im re) (log (/ 1 base))))>
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#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
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#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* (log base) (atan2 im re))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* -1 (* (log (/ 1 base)) (atan2 im re)))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (log base))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (* -1 (log (/ 1 base))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 base)))))>
Calls

96 calls:

TimeVariablePointExpression
107.0ms
re
@0
(/ (atan2 im re) (pow (E) (log (log base))))
26.0ms
base
@0
(/ (atan2 im re) (pow (E) (log (log base))))
21.0ms
im
@0
(/ (atan2 im re) (pow (E) (log (log base))))
1.0ms
im
@inf
(/ (atan2 im re) (log base))
1.0ms
base
@inf
(/ (atan2 im re) (pow (E) (log (log base))))

rewrite320.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
2404×*-lowering-*.f32
2404×*-lowering-*.f64
2314×pow-lowering-pow.f64
2314×pow-lowering-pow.f32
1710×prod-diff
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
022108
1110107
253169
3325369
0913869
Stop Event
1×iter limit
1×node limit
Counts
16 → 1408
Calls
Call 1
Inputs
(* (atan2 im re) (/ (log base) (pow (log base) 2)))
(/ (log base) (pow (log base) 2))
(atan2 im re)
(log base)
(/ 1 (/ 1 (/ (atan2 im re) (log base))))
(/ 1 (/ (atan2 im re) (log base)))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (pow (E) (log (log base))))
(pow (E) (log (log base)))
(E)
(* (atan2 im re) (pow (pow (log base) 2) -1/2))
(pow (pow (log base) 2) -1/2)
(pow (log base) 2)
(/ (* (atan2 im re) (log base)) (pow (log base) 2))
(* (atan2 im re) (log base))
(log (log base))
Outputs
(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
(exp.f64 (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(-.f64 (/.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) base))) (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(neg.f64 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)))
(/.f64 (log.f64 base) (*.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) (log.f64 base)))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))))
(/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (*.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (*.f64 (/.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))) (log.f64 base)))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (*.f64 (log.f64 base) (/.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (atan2.f64 im re)))))
(/.f64 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal -1 binary64))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (atan2.f64 im re)))
(/.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -1/2 binary64)))
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (log.f64 base)) (log.f64 base))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))) (log.f64 base)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base)))) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 3/2 binary64)))
(/.f64 (*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (pow.f64 (log.f64 base) #s(literal 3/2 binary64)))
(/.f64 (neg.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (atan2.f64 im re) (exp.f64 (*.f64 #s(literal 2/3 binary64) (log.f64 (log.f64 base))))) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1/3 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 im re)) #s(literal 1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (*.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (atan2.f64 im re) (log.f64 base))) (log.f64 base))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (atan2.f64 im re))) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1/3 binary64)))) (exp.f64 (*.f64 #s(literal 1/6 binary64) (log.f64 (log.f64 base)))))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))) (pow.f64 (log.f64 base) #s(literal 1/4 binary64))) (pow.f64 (log.f64 base) #s(literal 1/4 binary64)))
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(-.f64 (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) (log.f64 (log.f64 base)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))
(-.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) (/.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)))
(-.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) (log.f64 base))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)))))
(-.f64 (log.f64 (log.f64 (/.f64 #s(literal 1 binary64) base))) (log.f64 #s(literal -1 binary64)))
(-.f64 (log.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (log.f64 (log.f64 (/.f64 #s(literal 1 binary64) base))))
(-.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64))) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(-.f64 (log.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(-.f64 (log.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 2/3 binary64) (log.f64 (log.f64 base)))))) (*.f64 (log.f64 (log.f64 base)) #s(literal 1/3 binary64)))
(-.f64 (log.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))) (log.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))))
(-.f64 (log.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) (log.f64 (log.f64 base)) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))
(fma.f64 #s(literal 1 binary64) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(fma.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))
(fma.f64 (log.f64 (log.f64 base)) #s(literal 1/2 binary64) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(fma.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 1 binary64) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (log.f64 base)) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) #s(literal -1/2 binary64) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))
(/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))))
(/.f64 (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal 2 binary64))
(/.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)) #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal 4 binary64) (log.f64 (log.f64 base))) #s(literal 4 binary64))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base)))) (*.f64 (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) (log.f64 (log.f64 base)))) (*.f64 (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal -2 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))) (*.f64 (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -2 binary64)))
(/.f64 (+.f64 (*.f64 (log.f64 (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base)))))
(/.f64 (+.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)) (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64))) #s(literal -4 binary64))
(/.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base)))) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (log.f64 (log.f64 base)))))
(/.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))) #s(literal 4 binary64))
(/.f64 (+.f64 (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (log.f64 (log.f64 base)))
(*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))))
(*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal 1/2 binary64))
(*.f64 (/.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))))
(*.f64 #s(literal -2 binary64) (*.f64 (log.f64 (log.f64 base)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (log.f64 base))) #s(literal 3 binary64))
(*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (log.f64 base))) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 4 binary64) (log.f64 (log.f64 base))))

simplify226.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
2100×sum4-define
1788×sum5-define
1394×fnmadd-define
1364×fma-define
1308×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0452340
1762284
21242284
32762284
46992284
518492284
639702284
778992284
082162284
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
Calls
Call 1
Inputs
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(atan2 im re)
(log base)
(log base)
(log base)
(log base)
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (log base) (log (E))))
(/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (atan2 im re) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(pow (log base) (log (E)))
(pow (log base) (log (E)))
(pow (log base) (log (E)))
(pow (log base) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ -1 (log (/ 1 base)))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(log (log base))
(log (log base))
(log (log base))
(log (log base))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (* -1 (log (/ 1 base))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64))))
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(atan2 im re)
(atan2.f64 im re)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (log base) (atan2 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(/.f64 (log.f64 base) (atan2.f64 im re))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(/.f64 (log.f64 base) (atan2.f64 im re))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(/.f64 (log.f64 base) (atan2.f64 im re))
(* -1 (/ (log (/ 1 base)) (atan2 im re)))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (atan2.f64 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (atan2.f64 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (atan2.f64 im re))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (atan2.f64 im re))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (atan2 im re) (pow (log base) (log (E))))
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eval352.0ms (3.5%)

Compiler

Compiled 43162 to 3985 computations (90.8% saved)

prune314.0ms (3.1%)

Pruning

23 alts after pruning (12 fresh and 11 done)

PrunedKeptTotal
New282152826
Fresh3710
Picked055
Done066
Total2824232847
Accuracy
100.0%
Counts
2847 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.5%
(pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
53.3%
(/.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
✓53.5%
(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
✓52.9%
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓99.4%
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
99.3%
(/.f64 (atan2.f64 im re) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓99.5%
(/.f64 (atan2.f64 im re) (log.f64 base))
53.1%
(/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (log.f64 base))))
99.2%
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
99.1%
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
✓99.3%
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
99.2%
(/.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)))
✓99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓99.2%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
✓56.7%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
53.2%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal 4 binary64)))
53.5%
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
99.2%
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64))))
✓99.3%
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓99.4%
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
99.0%
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓99.2%
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
52.5%
(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
Compiler

Compiled 789 to 335 computations (57.5% saved)

regimes66.0ms (0.7%)

Accuracy

Total -56.2b remaining (-18203.4%)

Threshold costs -56.2b (-18203.4%)

Counts
41 → 1
Calls
Call 1
Inputs
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (log.f64 base))))
(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal 4 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
(/.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (atan2.f64 im re))
(*.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)))
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re)) (log.f64 base))
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(*.f64 (neg.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (log.f64 base))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (atan2.f64 im re) (log.f64 base))) (log.f64 base))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 (atan2.f64 im re) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 (atan2.f64 im re) (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (atan2.f64 im re) (*.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
Outputs
(/.f64 (atan2.f64 im re) (log.f64 base))
Calls

5 calls:

16.0ms
im
15.0ms
(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
11.0ms
(log.f64 base)
11.0ms
base
11.0ms
re
Results
AccuracySegmentsBranch
99.5%1re
99.5%1im
99.5%1base
99.5%1(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
99.5%1(log.f64 base)
Compiler

Compiled 48 to 31 computations (35.4% saved)

simplify13.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (atan2.f64 im re) (log.f64 base))
Outputs
(/.f64 (atan2.f64 im re) (log.f64 base))

soundness309.0ms (3.1%)

Rules
2532×*-lowering-*.f32
2532×*-lowering-*.f64
1996×fmsub-define
1972×fmm-def
1964×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01813
14212
2728
31026
41326
52126
66006
717776
830346
944266
1054776
1172506
081066
Stop Event
1×fuel
1×iter limit
1×node limit
Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess36.0ms (0.4%)

Compiler

Compiled 80 to 48 computations (40% saved)

end0.0ms (0%)

Profiling

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