Metrics for math.log/2 on complex, imaginary part

analyze210.0ms (2.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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: 127.0ms

ival-mult: 48.0ms (37.9% of total)

ival-log: 30.0ms (23.7% of total)

ival-add: 12.0ms (9.5% of total)

ival-atan2: 11.0ms (8.7% of total)

ival-sqrt: 9.0ms (7.1% of total)

ival-div: 7.0ms (5.5% of total)

ival-sub: 7.0ms (5.5% of total)

const: 1.0ms (0.8% of total)

backward-pass: 1.0ms (0.8% of total)

sample1.8s (17.3%)

Results

1.3s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-mult: 313.0ms (31.1% of total)

ival-log: 238.0ms (23.7% of total)

ival-div: 107.0ms (10.6% of total)

ival-atan2: 100.0ms (9.9% of total)

ival-add: 84.0ms (8.3% of total)

ival-sub: 75.0ms (7.5% of total)

ival-sqrt: 73.0ms (7.3% of total)

const: 12.0ms (1.2% of total)

backward-pass: 3.0ms (0.3% of total)

Bogosity

preprocess198.0ms (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)

Iter	Nodes	Cost
0	79	121
1	275	111
2	579	86
3	1261	69
4	2350	69
5	4388	69
6	7668	69
0	18	11
1	45	10
2	75	8
3	105	6
4	135	6
5	215	6
6	603	6
7	1808	6
8	3054	6
9	4452	6
10	5502	6
11	7293	6
0	8172	6

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))

explain295.0ms (2.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	2	(4.4809336851054647e-160 3.603779725660597e-192 2.1104365518085965e-259)	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	0	-	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`
0	-	0	-	`base`
0	-	0	-	`(*.f64 im im)`
0	-	0	-	`(*.f64 (log.f64 base) (log.f64 base))`
0	-	0	-	`(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))`
0	-	0	-	`#s(literal 0 binary64)`
0	-	0	-	`(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))`
0	-	0	-	`(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))`
0	-	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)))`
0	-	0	-	`re`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	0	-	`(*.f64 (atan2.f64 im re) (log.f64 base))`
0	-	0	-	`im`
0	-	0	-	`(atan2.f64 im re)`
0	-	0	-	`(*.f64 re re)`
0	-	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))))`
0	-	0	-	`(log.f64 base)`

Results

202.0ms

512×

valid

Compiler

Compiled 277 to 56 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

ival-div: 102.0ms (68.5% of total)

ival-mult: 17.0ms (11.4% of total)

ival-log: 13.0ms (8.7% of total)

ival-add: 5.0ms (3.4% of total)

ival-atan2: 5.0ms (3.4% of total)

ival-sqrt: 4.0ms (2.7% of total)

ival-sub: 3.0ms (2% of total)

const: 1.0ms (0.7% of total)

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

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune4.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (atan2.f64 im re) (log.f64 base))
▶	46.5%	(/.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))))

Status

Accuracy

Program

▶

99.5%

(/.f64 (atan2.f64 im re) (log.f64 base))

▶

46.5%

(/.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))))

Compiler

Compiled 40 to 24 computations (40% saved)

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	0	(/.f64 (atan2.f64 im re) (log.f64 base))
✓	cost-diff	320	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
✓	cost-diff	13312	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
✓	cost-diff	13440	(-.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-diff	26752	(/.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

2190×	`-lowering-.f32`
2190×	`-lowering-.f64`
1996×	`fmsub-define`
1972×	`fmm-def`
1964×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	77
1	46	73
2	75	69
3	105	65
4	135	65
5	215	65
6	603	65
7	1809	65
8	3061	65
9	4468	65
10	5521	65
11	7314	65
0	8017	65

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

localize108.0ms (1.1%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(atan2.f64 im re)
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.5%	(/.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.5%	(*.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.5%	(/.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))))
✓	accuracy	99.2%	(*.f64 (log.f64 base) (log.f64 base))
✓	accuracy	50.3%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Results

73.0ms

256×

valid

Compiler

Compiled 137 to 20 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 27.0ms (53.9% of total)

ival-log: 11.0ms (21.9% of total)

ival-div: 3.0ms (6% of total)

ival-add: 3.0ms (6% of total)

ival-atan2: 2.0ms (4% of total)

ival-sqrt: 2.0ms (4% of total)

ival-sub: 1.0ms (2% of total)

const: 0.0ms (0% of total)

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

series98.0ms (1%)

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:

Time	Variable		Point	Expression
28.0ms	im	@	0	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))
20.0ms	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)))
13.0ms	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)))

rewrite339.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4236×	`-lowering-.f32`
4236×	`-lowering-.f64`
3188×	`/-lowering-/.f32`
3188×	`/-lowering-/.f64`
912×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	52
1	116	48
2	810	40
3	7923	40
0	8027	40

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 #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) (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 #s(literal 0 binary64) (*.f64 (atan2.f64 im re) (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 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (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 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (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 #s(literal 0 binary64) (*.f64 (atan2.f64 im re) (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 #s(literal 0 binary64) (*.f64 (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 (/.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 #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 #s(literal -1 binary64) (/.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (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 #s(literal 0 binary64) (*.f64 (atan2.f64 im re) (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 (atan2.f64 im re) (.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64)))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.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))))
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(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base))) (log.f64 base)) (.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base))) (.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)))) (log.f64 base))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base))) (.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 #s(literal 0 binary64) (.f64 (atan2.f64 im re) (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 #s(literal 0 binary64) (.f64 (atan2.f64 im re) (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)))

simplify283.0ms (2.8%)

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)

Iter	Nodes	Cost
0	204	2000
1	580	1846
2	1913	1798
3	6783	1798
0	8138	1798

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))
(*.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))))
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im
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re
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(pow (log base) 2)
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(pow (log base) 2)
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(pow (log base) 2)
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(pow (log (/ 1 base)) 2)
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(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))))

eval157.0ms (1.5%)

Compiler: Compiled 35015 to 2320 computations (93.4% saved)

prune139.0ms (1.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	1331	15	1346
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1332	16	1348

Accuracy

100.0%

Counts

1348 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
✓	99.5%	(/.f64 (atan2.f64 im re) (log.f64 base))
	48.8%	(/.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)))
▶	99.2%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	85.8%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))) (.f64 (atan2.f64 im re) (log.f64 base)))
	99.3%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
▶	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
	99.3%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
▶	99.5%	(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
	99.0%	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
	99.3%	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
	86.6%	(.f64 (/.f64 (.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
	99.1%	(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -4 binary64))))
	99.2%	(.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 (atan2.f64 im re) (log.f64 base))))
▶	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))

Compiler

Compiled 495 to 322 computations (34.9% saved)

simplify491.0ms (4.8%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
✓	cost-diff	192	(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
✓	cost-diff	13568	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	cost-diff	13120	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	cost-diff	0	(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re))
✓	cost-diff	12992	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	128	(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))

Rules

4326×	`fma-define`
3824×	`fma-lowering-fma.f32`
3824×	`fma-lowering-fma.f64`
2968×	`sum3-define`
2946×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	146
1	48	141
2	97	141
3	243	140
4	682	140
5	1746	140
6	3121	140
7	3333	140
8	3686	140
9	4200	140
10	4862	140
11	5174	140
12	5808	140
0	8639	140

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (atan2 im re) (/ 1 (log base)))
(atan2 im re)
im
re
(/ 1 (log base))
1
(log base)
base
(/ 1 (/ (log base) (atan2 im re)))
1
(/ (log base) (atan2 im re))
(log base)
base
(atan2 im re)
im
re
(* (* (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 (log base) -2) (/ 1 (* (atan2 im re) (log base))))
(pow (log base) -2)
(log base)
base
-2
(/ 1 (* (atan2 im re) (log base)))
1
(* (atan2 im re) (log base))
(atan2 im re)
im
re
(/ (/ 1 (/ 1 (* (atan2 im re) (log base)))) (+ (* (log base) (log base)) (* 0 0)))
(/ 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
(+ (* (log base) (log base)) (* 0 0))
(* (log base) (log base))
(* 0 0)
0

Outputs
(* (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
(/ 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
(* (* (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 (log base) -2) (/ 1 (* (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)
(/ 1 (* (atan2 im re) (log base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
1
#s(literal 1 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 (* (atan2 im re) (log base)))) (+ (* (log base) (log base)) (* 0 0)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ 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 (/.f64 #s(literal 1 binary64) (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
(+ (* (log base) (log base)) (* 0 0))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(* (log base) (log base))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(* 0 0)
#s(literal 0 binary64)
0
#s(literal 0 binary64)

localize127.0ms (1.2%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓	accuracy	99.5%	(*.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.5%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓	accuracy	99.2%	(*.f64 (log.f64 base) (log.f64 base))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base)))
✓	accuracy	99.5%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
✓	accuracy	99.5%	(*.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.2%	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.5%	(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re))
✓	accuracy	99.4%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓	accuracy	99.2%	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	accuracy	100.0%	(atan2.f64 im re)
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.5%	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	accuracy	100.0%	(atan2.f64 im re)
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.5%	(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))

Results

85.0ms

256×

valid

Compiler

Compiled 192 to 24 computations (87.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-div: 14.0ms (34.9% of total)

ival-pow: 10.0ms (24.9% of total)

ival-mult: 8.0ms (19.9% of total)

ival-log: 4.0ms (10% of total)

ival-atan2: 3.0ms (7.5% of total)

ival-add: 1.0ms (2.5% of total)

const: 1.0ms (2.5% of total)

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

series33.0ms (0.3%)

Counts

17 → 444

Calls

Call 1

Inputs
#<alt (* (atan2 im re) (/ 1 (log base)))>
#<alt (atan2 im re)>
#<alt (/ 1 (log base))>
#<alt (log base)>
#<alt (/ 1 (/ (log base) (atan2 im re)))>
#<alt (/ (log base) (atan2 im re))>
#<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 (log base) -2) (/ 1 (* (atan2 im re) (log base))))>
#<alt (/ 1 (* (atan2 im re) (log base)))>
#<alt (/ (/ 1 (/ 1 (* (atan2 im re) (log base)))) (+ (* (log base) (log base)) (* 0 0)))>
#<alt (/ 1 (/ 1 (* (atan2 im re) (log base))))>
#<alt (+ (* (log base) (log base)) (* 0 0))>
#<alt (* 0 0)>
#<alt (* (atan2 im re) (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))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (atan2 im re) (log base))>
#<alt (/ (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 (/ 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)>
#<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 (* -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))>
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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 (/ (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 (/ (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)))))>
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#<alt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 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))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (log base) (atan2 im re)))>
#<alt (/ 1 (* (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 (/ 1 (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re)))>
#<alt (/ 1 (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re)))>
#<alt (/ 1 (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re)))>
#<alt (/ 1 (* (+ (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 (/ (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))>
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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 (* (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 (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))>
#<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

111 calls:

Time	Variable		Point	Expression
13.0ms	im	@	inf	(/ 1 (* (atan2 im re) (log base)))
1.0ms	base	@	-inf	(/ 1 (log base))
1.0ms	base	@	-inf	(/ 1 (* (atan2 im re) (log base)))
1.0ms	base	@	-inf	(* (pow (log base) -2) (atan2 im re))
1.0ms	im	@	-inf	(/ 1 (* (atan2 im re) (log base)))

rewrite390.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2644×	`-lowering-.f32`
2644×	`-lowering-.f64`
1920×	`/-lowering-/.f32`
1920×	`/-lowering-/.f64`
1680×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	82
1	118	82
2	692	81
3	4896	81
0	8895	81

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 2045

Calls

Call 1

Inputs
(* (atan2 im re) (/ 1 (log base)))
(atan2 im re)
(/ 1 (log base))
(log base)
(/ 1 (/ (log base) (atan2 im re)))
(/ (log base) (atan2 im re))
(* (* (pow (log base) -2) (atan2 im re)) (log base))
(* (pow (log base) -2) (atan2 im re))
(pow (log base) -2)
(/ (pow (log base) -2) (/ 1 (* (atan2 im re) (log base))))
(/ 1 (* (atan2 im re) (log base)))
(/ (/ 1 (/ 1 (* (atan2 im re) (log base)))) (+ (* (log base) (log base)) (* 0 0)))
(/ 1 (/ 1 (* (atan2 im re) (log base))))
(+ (* (log base) (log base)) (* 0 0))
(* 0 0)
(* (atan2 im re) (log base))
(* (log base) (log base))

Outputs
(+.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (/.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 6 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 (.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 (/.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) #s(literal 0 binary64)) (/.f64 (atan2.f64 im re) (log.f64 base)))
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(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (-.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 4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal -4 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (log.f64 base)) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal -4 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal -4 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (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)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (log.f64 base)))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal -4 binary64))))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 (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)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (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)) (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 6 binary64)) (pow.f64 (log.f64 base) #s(literal 10 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (pow.f64 (log.f64 base) #s(literal 12 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal -4 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 4 binary64)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))

simplify244.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1872×	`fma-lowering-fma.f32`
1872×	`fma-lowering-fma.f64`
1788×	`sum5-define`
1528×	`fnmadd-define`
1498×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	2916
1	78	2784
2	140	2784
3	344	2784
4	936	2784
5	2372	2784
6	4748	2784
0	8050	2784

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

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)))))
(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)))))
(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))
(* -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))
(/ (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 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (log base) (atan2 im re)))
(/ 1 (* (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)))
(/ 1 (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re)))
(/ 1 (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re)))
(/ 1 (* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re)))
(/ 1 (* (+ (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)))))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log 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))
(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))
(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))))
(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))
(/ 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))))
(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))
(* -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))
(/ (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))
(/ (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))
(/ (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) (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))
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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))
(* (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))))
(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))))
(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))

eval517.0ms (5.1%)

Compiler: Compiled 70114 to 5188 computations (92.6% saved)

prune649.0ms (6.4%)

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	3656	9	3665
Fresh	5	5	10
Picked	2	3	5
Done	0	1	1
Total	3663	18	3681

Accuracy

100.0%

Counts

3681 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.2%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
▶	99.1%	(/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
	99.2%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
✓	99.5%	(/.f64 (atan2.f64 im re) (log.f64 base))
	48.8%	(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
	99.0%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base)))) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64)))
	85.8%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))) (.f64 (atan2.f64 im re) (log.f64 base)))
▶	99.3%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
✓	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
▶	99.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base)))
	99.3%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
	99.2%	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
	99.2%	(*.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) (/.f64 #s(literal 1 binary64) (log.f64 base)))
	48.9%	(.f64 (atan2.f64 im re) (exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (log.f64 base)))))
	99.3%	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
▶	99.1%	(.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (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)) (atan2.f64 im re)) (log.f64 base))

Compiler

Compiled 485 to 325 computations (33% saved)

simplify301.0ms (3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	0	(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))
✓	cost-diff	13248	(/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	0	(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re))
✓	cost-diff	13120	(.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	cost-diff	0	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))
✓	cost-diff	12928	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (atan2.f64 im re))
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (atan2.f64 im re))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))

Rules

8180×	`-lowering-.f32`
8180×	`-lowering-.f64`
2196×	`unswap-sqr`
2194×	`cube-prod`
1534×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	159
1	44	144
2	82	144
3	192	144
4	291	143
5	929	143
6	1971	143
7	2153	143
8	2383	143
9	2766	143
10	3340	143
11	4176	143
12	4761	143
13	5138	143
14	5382	143
15	5595	143
16	5682	143
17	7571	143
18	7792	143
0	8061	143

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ 1 (log base)) (/ 1 (atan2 im re)))
(/ 1 (log base))
1
(log base)
base
(/ 1 (atan2 im re))
(atan2 im re)
im
re
(/ 1 (* (/ 1 (atan2 im re)) (log base)))
1
(* (/ 1 (atan2 im re)) (log base))
(/ 1 (atan2 im re))
(atan2 im re)
im
re
(log base)
base
(pow (pow (/ (log base) (atan2 im re)) -1/2) 2)
(pow (/ (log base) (atan2 im re)) -1/2)
(/ (log base) (atan2 im re))
(log base)
base
(atan2 im re)
im
re
-1/2
2
(* (* (pow (/ 1 (log base)) 2) (atan2 im re)) (log base))
(* (pow (/ 1 (log base)) 2) (atan2 im re))
(pow (/ 1 (log base)) 2)
(/ 1 (log base))
1
(log base)
base
2
(atan2 im re)
im
re
(/ (pow (/ 1 (log base)) 2) (/ 1 (* (atan2 im re) (log base))))
(pow (/ 1 (log base)) 2)
(/ 1 (log base))
1
(log base)
base
2
(/ 1 (* (atan2 im re) (log base)))
(* (atan2 im re) (log base))
(atan2 im re)
im
re

Outputs
(/ (/ 1 (log base)) (/ 1 (atan2 im re)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
1
#s(literal 1 binary64)
(log base)
(log.f64 base)
base
(/ 1 (atan2 im re))
(/.f64 #s(literal 1 binary64) (atan2.f64 im re))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ 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))
(/ 1 (atan2 im re))
(/.f64 #s(literal 1 binary64) (atan2.f64 im re))
(atan2 im re)
(atan2.f64 im re)
im
re
(log base)
(log.f64 base)
base
(pow (pow (/ (log base) (atan2 im re)) -1/2) 2)
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow (/ (log base) (atan2 im re)) -1/2)
(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 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
-1/2
#s(literal -1/2 binary64)
2
#s(literal 2 binary64)
(* (* (pow (/ 1 (log base)) 2) (atan2 im re)) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* (pow (/ 1 (log base)) 2) (atan2 im re))
(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)))
(pow (/ 1 (log base)) 2)
(pow.f64 (/.f64 #s(literal 1 binary64) (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)
(atan2.f64 im re)
im
re
(/ (pow (/ 1 (log base)) 2) (/ 1 (* (atan2 im re) (log base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow (/ 1 (log base)) 2)
(pow.f64 (/.f64 #s(literal 1 binary64) (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)
(/ 1 (* (atan2 im re) (log base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(* (atan2 im re) (log base))
(*.f64 (log.f64 base) (atan2.f64 im re))
(atan2 im re)
(atan2.f64 im re)
im
re

localize158.0ms (1.6%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.7%	(*.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.7%	(/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
✓	accuracy	99.6%	(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))
✓	accuracy	99.8%	(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.7%	(.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (atan2.f64 im re)) (log.f64 base))
✓	accuracy	99.6%	(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.7%	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	accuracy	99.7%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	accuracy	95.5%	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (atan2.f64 im re))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base)))
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (atan2.f64 im re))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))

Results

42.0ms	135×	0	valid
33.0ms	121×	0	invalid

Compiler

Compiled 190 to 23 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-div: 13.0ms (37.4% of total)

ival-pow: 9.0ms (25.9% of total)

ival-mult: 6.0ms (17.3% of total)

ival-log: 4.0ms (11.5% of total)

ival-atan2: 2.0ms (5.8% of total)

const: 1.0ms (2.9% of total)

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

series13.0ms (0.1%)

Counts

15 → 444

Calls

Call 1

Inputs
#<alt (/ (/ 1 (log base)) (/ 1 (atan2 im re)))>
#<alt (/ 1 (log base))>
#<alt (log base)>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (* (/ 1 (atan2 im re)) (log base)))>
#<alt (* (/ 1 (atan2 im re)) (log base))>
#<alt (atan2 im re)>
#<alt (pow (pow (/ (log base) (atan2 im re)) -1/2) 2)>
#<alt (pow (/ (log base) (atan2 im re)) -1/2)>
#<alt (/ (log base) (atan2 im re))>
#<alt (* (* (pow (/ 1 (log base)) 2) (atan2 im re)) (log base))>
#<alt (* (pow (/ 1 (log base)) 2) (atan2 im re))>
#<alt (pow (/ 1 (log base)) 2)>
#<alt (/ (pow (/ 1 (log base)) 2) (/ 1 (* (atan2 im re) (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 (* -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 (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)>
#<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 (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (atan2 im re))>
#<alt (/ 1 (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))>
#<alt (/ (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)>
#<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) (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 (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (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 (/ (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 (* (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

111 calls:

Time	Variable		Point	Expression
1.0ms	base	@	inf	(pow (/ (log base) (atan2 im re)) -1/2)
1.0ms	base	@	-inf	(pow (/ (log base) (atan2 im re)) -1/2)
1.0ms	base	@	0	(pow (/ (log base) (atan2 im re)) -1/2)
0.0ms	re	@	inf	(/ 1 (atan2 im re))
0.0ms	re	@	inf	(pow (/ (log base) (atan2 im re)) -1/2)

rewrite494.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1500×	`-lowering-.f32`
1500×	`-lowering-.f64`
1332×	`+-lowering-+.f64`
1332×	`+-lowering-+.f32`
1302×	`frac-times`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	87
1	109	80
2	513	79
3	3356	78
0	8623	78

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 1310

Calls

Call 1

Inputs
(/ (/ 1 (log base)) (/ 1 (atan2 im re)))
(/ 1 (log base))
(log base)
(/ 1 (atan2 im re))
(/ 1 (* (/ 1 (atan2 im re)) (log base)))
(* (/ 1 (atan2 im re)) (log base))
(atan2 im re)
(pow (pow (/ (log base) (atan2 im re)) -1/2) 2)
(pow (/ (log base) (atan2 im re)) -1/2)
(/ (log base) (atan2 im re))
(* (* (pow (/ 1 (log base)) 2) (atan2 im re)) (log base))
(* (pow (/ 1 (log base)) 2) (atan2 im re))
(pow (/ 1 (log base)) 2)
(/ (pow (/ 1 (log base)) 2) (/ 1 (* (atan2 im re) (log base))))
(* (atan2 im re) (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 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 4 binary64))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))
(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 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64)) #s(literal 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 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (+.f64 (log.f64 (log.f64 base)) (-.f64 (*.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))))))
(exp.f64 (+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (*.f64 (log.f64 (atan2.f64 im re)) #s(literal 1 binary64))))
(exp.f64 (+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (-.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))))))
(exp.f64 (+.f64 (*.f64 (log.f64 (atan2.f64 im re)) #s(literal 1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (.f64 (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))
(exp.f64 (+.f64 (.f64 (.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64)) (.f64 (.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/4 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) (.f64 (log.f64 (*.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (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 (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 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)) (log.f64 (.f64 (log.f64 base) (atan2.f64 im re)))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -1 binary64)) (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -1 binary64)) (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -1 binary64)) (log.f64 (*.f64 (log.f64 base) (atan2.f64 im re)))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64)) (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64)) (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64)) (log.f64 (*.f64 (log.f64 base) (atan2.f64 im re)))))
(exp.f64 (+.f64 (-.f64 (*.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))) (log.f64 (log.f64 base))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)) (*.f64 #s(literal -2 binary64) (log.f64 (log.f64 base)))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)) (*.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)) (.f64 (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64)) (.f64 #s(literal -2 binary64) (log.f64 (log.f64 base)))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64)) (.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64)) (.f64 (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64)) (.f64 (*.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64))))
(exp.f64 (+.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64))))
(exp.f64 (+.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (.f64 (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (.f64 (*.f64 #s(literal -2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal 1/2 binary64)) (*.f64 #s(literal -3/4 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))
(exp.f64 (+.f64 (.f64 (.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -3/4 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))
(exp.f64 (+.f64 (.f64 #s(literal -3/4 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal -3/4 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)) #s(literal 1 binary64))))
(exp.f64 (+.f64 (-.f64 (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))) (log.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))))
(-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(-.f64 (/.f64 #s(literal 0 binary64) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(neg.f64 (/.f64 (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) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.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 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(/.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -1 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64)))
(/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal -1/2 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 -1/8 binary64)) #s(literal 8 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 4 binary64)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (*.f64 (exp.f64 #s(literal -1/2 binary64)) (exp.f64 #s(literal -1/2 binary64))) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
(pow.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64))) #s(literal -1/4 binary64))
(pow.f64 (*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64)) (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
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(/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal -1/2 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 -1/8 binary64)) #s(literal 8 binary64))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 4 binary64)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
(pow.f64 (*.f64 (exp.f64 #s(literal -1/2 binary64)) (exp.f64 #s(literal -1/2 binary64))) (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
(pow.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64))) #s(literal -1/4 binary64))
(pow.f64 (*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64)) (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (neg.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re)))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64))))
(.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) (.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (pow.f64 (.f64 (atan2.f64 im re) (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 1/2 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 (atan2.f64 im re) #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) (.f64 (pow.f64 (atan2.f64 im re) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64))))
(.f64 (pow.f64 (atan2.f64 im re) #s(literal 1/4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -1 binary64))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/8 binary64)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -7/8 binary64)))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) (neg.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) (/.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (log.f64 base) (atan2.f64 im re))))
(*.f64 (pow.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
(*.f64 (neg.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64))) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)))
(*.f64 (neg.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64))) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64))) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 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 (pow.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (atan2.f64 im re)) #s(literal 1/2 binary64)) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) (pow.f64 (log.f64 base) #s(literal -1/4 binary64))) (pow.f64 (atan2.f64 im re) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -3/4 binary64)) (pow.f64 (atan2.f64 im re) #s(literal 1/4 binary64))) (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -7/8 binary64)) (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) #s(literal -1/4 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (log.f64 (log.f64 base)))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (atan2.f64 im re)))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (atan2.f64 im re)))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (log.f64 base)))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (log.f64 (log.f64 base)) #s(literal -1/2 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) #s(literal -1/2 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (log.f64 base)) #s(literal -1/2 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 (log.f64 base) (atan2.f64 im re)))
(exp.f64 (log.f64 (*.f64 (log.f64 base) (atan2.f64 im re))))
(exp.f64 (.f64 (log.f64 (.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #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 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (log.f64 base)) (*.f64 (log.f64 (atan2.f64 im re)) #s(literal 1 binary64))))
(exp.f64 (+.f64 (log.f64 (log.f64 base)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (atan2.f64 im re)) #s(literal 1 binary64)) (log.f64 (log.f64 base))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re))) #s(literal -1 binary64)) (log.f64 (log.f64 base))))
(-.f64 #s(literal 0 binary64) (*.f64 (log.f64 base) (atan2.f64 im re)))
(neg.f64 (*.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.f64 (log.f64 base) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
(/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 1 binary64))
(/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)))
(/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (/.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 (log.f64 base) (atan2.f64 im re))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (.f64 (log.f64 base) (atan2.f64 im re)))
(pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re)) #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 (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (log.f64 base) (atan2.f64 im re))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 (log.f64 base) (atan2.f64 im re)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 1 binary64))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (log.f64 base) (atan2.f64 im re)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)) (/.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64))) (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (sqrt.f64 (*.f64 (log.f64 base) (atan2.f64 im re))))

simplify260.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1824×	`fma-lowering-fma.f32`
1824×	`fma-lowering-fma.f64`
1788×	`sum5-define`
1498×	`fnmadd-define`
1474×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	2884
1	78	2784
2	136	2784
3	319	2784
4	864	2784
5	2297	2784
6	4610	2784
0	8041	2784

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

Inputs
(/ (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 (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)
(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))))
(/ 1 (atan2 im re))
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(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (atan2 im re))
(/ 1 (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))
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(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 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))))
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(/ (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))
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(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
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(/ (log base) (atan2 im re))
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(/ (log base) (atan2 im re))
(/ (log base) (atan2 im re))
(/ (log 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)
(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))
(/ (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))
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(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(/ (atan2 im re) (log base))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (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))
(/ (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))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log 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))
(* -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))
(/ 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))))
(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))))
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eval633.0ms (6.2%)

Compiler: Compiled 41166 to 3429 computations (91.7% saved)

prune282.0ms (2.8%)

Pruning

19 alts after pruning (12 fresh and 7 done)

	Pruned	Kept	Total
New	2667	4	2671
Fresh	1	8	9
Picked	2	3	5
Done	0	4	4
Total	2670	19	2689

Accuracy

100.0%

Counts

2689 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.9%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) #s(literal 4 binary64))
✓	55.2%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
▶	55.1%	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
	99.2%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
✓	99.5%	(/.f64 (atan2.f64 im re) (log.f64 base))
▶	48.8%	(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
	85.8%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))) (.f64 (atan2.f64 im re) (log.f64 base)))
	56.6%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
	56.1%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
✓	99.3%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
✓	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	99.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base)))
▶	99.3%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
	99.2%	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
▶	99.2%	(*.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) (/.f64 #s(literal 1 binary64) (log.f64 base)))
	48.9%	(.f64 (atan2.f64 im re) (exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (log.f64 base)))))
▶	99.3%	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
✓	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))

Compiler

Compiled 452 to 313 computations (30.8% saved)

simplify136.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	12992	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	cost-diff	13120	(*.f64 (atan2.f64 im re) (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓	cost-diff	0	(*.f64 (atan2.f64 im re) (log.f64 base))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	cost-diff	12992	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	128	(*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))
✓	cost-diff	12928	(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
✓	cost-diff	12928	(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	0	(/.f64 (atan2.f64 im re) (log.f64 base))
✓	cost-diff	0	(sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
✓	cost-diff	12864	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
✓	cost-diff	0	(pow.f64 (log.f64 base) #s(literal 2 binary64))
✓	cost-diff	0	(atan2.f64 im re)
✓	cost-diff	0	(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
✓	cost-diff	12992	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))

Rules

1350×	`-lowering-.f32`
1350×	`-lowering-.f64`
1284×	`sum4-define`
1246×	`fma-lowering-fma.f32`
1246×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	169
1	45	159
2	69	135
3	113	127
4	157	127
5	463	127
6	1449	127
7	2815	127
8	5880	127
0	8014	127

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (/ (atan2 im re) (pow (log base) 2)) (log base))
(/ (atan2 im re) (pow (log base) 2))
(atan2 im re)
im
re
(pow (log base) 2)
(log base)
base
2
(pow (sqrt (/ (atan2 im re) (log base))) 2)
(sqrt (/ (atan2 im re) (log base)))
(/ (atan2 im re) (log base))
(atan2 im re)
im
re
(log base)
base
2
(/ (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
(* (atan2 im re) (/ (pow (log base) -2) (/ 1 (log base))))
(atan2 im re)
im
re
(/ (pow (log base) -2) (/ 1 (log base)))
(pow (log base) -2)
(log base)
base
-2
(/ 1 (log base))
1

Outputs
(* (/ (atan2 im re) (pow (log base) 2)) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ (atan2 im re) (pow (log base) 2))
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(atan2 im re)
(atan2.f64 im re)
im
re
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(log base)
(log.f64 base)
base
2
#s(literal 2 binary64)
(pow (sqrt (/ (atan2 im re) (log base))) 2)
(/.f64 (atan2.f64 im re) (log.f64 base))
(sqrt (/ (atan2 im re) (log base)))
(sqrt.f64 (/.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
2
#s(literal 2 binary64)
(/ (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
(* (atan2 im re) (/ (pow (log base) -2) (/ 1 (log base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
im
re
(/ (pow (log base) -2) (/ 1 (log base)))
(/.f64 #s(literal 1 binary64) (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)
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
1
#s(literal 1 binary64)

localize135.0ms (1.3%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(*.f64 (atan2.f64 im re) (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.8%	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	accuracy	99.8%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.9%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
✓	accuracy	99.9%	(*.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.8%	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	100.0%	(log.f64 (log.f64 base))
✓	accuracy	99.9%	(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
✓	accuracy	99.5%	(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.9%	(/.f64 (atan2.f64 im re) (log.f64 base))
✓	accuracy	99.8%	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
✓	accuracy	97.0%	(sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.9%	(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
✓	accuracy	99.8%	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
✓	accuracy	99.8%	(pow.f64 (log.f64 base) #s(literal 2 binary64))

Results

61.0ms	184×	0	invalid
31.0ms	72×	0	valid

Compiler

Compiled 170 to 25 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-pow: 14.0ms (29.4% of total)

ival-div: 12.0ms (25.2% of total)

ival-mult: 8.0ms (16.8% of total)

ival-log: 6.0ms (12.6% of total)

ival-atan2: 3.0ms (6.3% of total)

ival-exp: 2.0ms (4.2% of total)

ival-sqrt: 2.0ms (4.2% of total)

const: 1.0ms (2.1% of total)

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

series155.0ms (1.5%)

Counts

18 → 444

Calls

Call 1

Inputs
#<alt (* (/ (atan2 im re) (pow (log base) 2)) (log base))>
#<alt (/ (atan2 im re) (pow (log base) 2))>
#<alt (atan2 im re)>
#<alt (pow (log base) 2)>
#<alt (pow (sqrt (/ (atan2 im re) (log base))) 2)>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (/ (atan2 im re) (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 (log base)>
#<alt (* (atan2 im re) (log base))>
#<alt (* (atan2 im re) (/ (pow (log base) -2) (/ 1 (log base))))>
#<alt (/ (pow (log base) -2) (/ 1 (log base)))>
#<alt (log (log base))>
#<alt (/ 1 (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 (/ (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 (/ (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)>
#<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 (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))))>
#<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 (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (sqrt (/ (atan2 im re) (log base)))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (sqrt (/ (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) (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) (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 (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)>
#<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 (* (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))>
#<alt (/ (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 (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 (/ 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)))))>

Calls

111 calls:

Time	Variable		Point	Expression
109.0ms	base	@	0	(* (log (log base)) 1)
20.0ms	base	@	-inf	(* (log (log base)) 1)
18.0ms	base	@	inf	(* (log (log base)) 1)
0.0ms	im	@	inf	(sqrt (/ (atan2 im re) (log base)))
0.0ms	im	@	-inf	(sqrt (/ (atan2 im re) (log base)))

rewrite179.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1528×	`-lowering-.f32`
1528×	`-lowering-.f64`
996×	`/-lowering-/.f32`
996×	`/-lowering-/.f64`
758×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	128
1	96	82
2	411	82
0	3075	82

Stop Event

1×	iter limit
1×	iter limit
1×	node limit

Counts

18 → 1470

Calls

Call 1

Inputs
(* (/ (atan2 im re) (pow (log base) 2)) (log base))
(/ (atan2 im re) (pow (log base) 2))
(atan2 im re)
(pow (log base) 2)
(pow (sqrt (/ (atan2 im re) (log base))) 2)
(sqrt (/ (atan2 im re) (log base)))
(/ (atan2 im re) (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)
(log base)
(* (atan2 im re) (log base))
(* (atan2 im re) (/ (pow (log base) -2) (/ 1 (log base))))
(/ (pow (log base) -2) (/ 1 (log base)))
(log (log base))
(/ 1 (log base))

Outputs
(exp.f64 (log.f64 (/.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 (log.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(fabs.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
(-.f64 #s(literal 0 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))))
(sqrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 2 binary64)))
(neg.f64 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(neg.f64 (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (log.f64 base)))
(neg.f64 (*.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(neg.f64 (/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re))))
(/.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)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (log.f64 base)) (/.f64 (atan2.f64 im re) (sqrt.f64 (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 #s(literal 1 binary64) (atan2.f64 im re)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (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 #s(literal -1 binary64) (*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (-.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 (log.f64 (/.f64 #s(literal 1 binary64) base)) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (atan2.f64 im re))))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -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 #s(literal 0 binary64) (/.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) (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal -1 binary64))
(/.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (log.f64 base))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (neg.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (log.f64 base))))
(/.f64 (neg.f64 (/.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
(/.f64 (/.f64 (atan2.f64 im re) #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (/.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base)) (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 -2 binary64))) (log.f64 base))
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(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (sqrt.f64 (log.f64 base))) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (sqrt.f64 (log.f64 base))))
(.f64 (.f64 (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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))

simplify224.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

2212×	`sum4-define`
1786×	`sum5-define`
1348×	`fma-define`
1336×	`fnmadd-define`
1268×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	2848
1	72	2720
2	125	2720
3	278	2720
4	731	2720
5	1985	2720
6	4006	2720
7	7894	2720
0	8270	2720

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

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)))))
(/ (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))
(/ (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)
(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)
(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)))))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(sqrt (/ (atan2 im re) (log base)))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ (atan2 im re) (log (/ 1 base)))) (sqrt -1))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt (/ (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))
(/ (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) (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)
(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 base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log base) (atan2 im re))
(* (log 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)))))
(/ 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 (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)))))
(/ 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)))))

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))
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(/.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))))
(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))))
(/ 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))))

eval343.0ms (3.4%)

Compiler: Compiled 42136 to 3486 computations (91.7% saved)

prune312.0ms (3.1%)

Pruning

21 alts after pruning (10 fresh and 11 done)

	Pruned	Kept	Total
New	2755	4	2759
Fresh	1	6	7
Picked	1	4	5
Done	0	7	7
Total	2757	21	2778

Accuracy

100.0%

Counts

2778 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.9%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) #s(literal 4 binary64))
✓	55.2%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	55.1%	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
	99.2%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
	49.2%	(/.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
	48.6%	(/.f64 (atan2.f64 im re) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓	99.5%	(/.f64 (atan2.f64 im re) (log.f64 base))
	48.8%	(/.f64 (atan2.f64 im re) (exp.f64 (log.f64 (log.f64 base))))
	85.8%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))) (.f64 (atan2.f64 im re) (log.f64 base)))
	56.6%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
✓	99.3%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))
✓	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	99.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base)))
	99.0%	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
✓	99.3%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
	99.2%	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
✓	99.2%	(*.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) (/.f64 #s(literal 1 binary64) (log.f64 base)))
	48.9%	(.f64 (atan2.f64 im re) (exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (log.f64 base)))))
✓	99.3%	(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
✓	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))

Compiler

Compiled 724 to 312 computations (56.9% saved)

regimes59.0ms (0.6%)

Accuracy

Total -55.9b remaining (-18590.4%)

Threshold costs -55.9b (-18590.4%)

Counts

34 → 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 (/.f64 #s(literal 1 binary64) (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) (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)))
(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64))
(.f64 (atan2.f64 im re) (exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (log.f64 base)))))
(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (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 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) #s(literal -1/4 binary64)) #s(literal 4 binary64))
(.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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (pow.f64 (atan2.f64 im re) #s(literal -1/2 binary64)) #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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (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 #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) (pow.f64 (pow.f64 (atan2.f64 im re) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
(/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (atan2.f64 im re) (log.f64 base)))) (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) (atan2.f64 im re)) (/.f64 #s(literal 1 binary64) (atan2.f64 im re)))) (.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 im re) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal -4 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 -2 binary64)))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -4 binary64))))
(.f64 (/.f64 (.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (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:

18.0ms	(log.f64 base)
10.0ms	base
10.0ms	re
9.0ms	(/.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))))
9.0ms	im

Results

Accuracy	Segments	Branch
99.5%	1	`re`
99.5%	1	`im`
99.5%	1	`base`
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)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6

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))

soundness289.0ms (2.8%)

Rules

2532×	`-lowering-.f32`
2532×	`-lowering-.f64`
1996×	`fmsub-define`
1972×	`fmm-def`
1964×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	11
1	45	10
2	75	8
3	105	6
4	135	6
5	215	6
6	603	6
7	1808	6
8	3054	6
9	4452	6
10	5502	6
11	7293	6
0	8172	6

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess34.0ms (0.3%)

Compiler: Compiled 80 to 48 computations (40% saved)

analyze210.0ms (2.1%)

sample1.8s (17.3%)

preprocess198.0ms (1.9%)

explain295.0ms (2.9%)

eval0.0ms (0%)

prune4.0ms (0%)

simplify116.0ms (1.1%)

localize108.0ms (1.1%)

series98.0ms (1%)

rewrite339.0ms (3.3%)

simplify283.0ms (2.8%)

eval157.0ms (1.5%)

prune139.0ms (1.4%)

simplify491.0ms (4.8%)

localize127.0ms (1.2%)

series33.0ms (0.3%)

rewrite390.0ms (3.8%)

simplify244.0ms (2.4%)

eval517.0ms (5.1%)

prune649.0ms (6.4%)

simplify301.0ms (3%)

localize158.0ms (1.6%)

series13.0ms (0.1%)

rewrite494.0ms (4.9%)

simplify260.0ms (2.6%)

eval633.0ms (6.2%)

prune282.0ms (2.8%)

simplify136.0ms (1.3%)

localize135.0ms (1.3%)

series155.0ms (1.5%)

rewrite179.0ms (1.8%)

simplify224.0ms (2.2%)

eval343.0ms (3.4%)

prune312.0ms (3.1%)

regimes59.0ms (0.6%)

simplify8.0ms (0.1%)

soundness289.0ms (2.8%)

preprocess34.0ms (0.3%)

end0.0ms (0%)

Profiling