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

analyze239.0ms (1.8%)

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: 135.0ms

ival-mult: 52.0ms (38.6% of total)

ival-log: 34.0ms (25.2% of total)

ival-add: 18.0ms (13.4% of total)

ival-atan2: 12.0ms (8.9% of total)

ival-sqrt: 10.0ms (7.4% of total)

ival-div: 7.0ms (5.2% of total)

const: 2.0ms (1.5% of total)

backward-pass: 1.0ms (0.7% of total)

sample2.0s (14.7%)

Results

1.6s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 357.0ms (29% of total)

ival-mult: 299.0ms (24.3% of total)

ival-log: 232.0ms (18.8% of total)

ival-add: 168.0ms (13.6% of total)

ival-atan2: 99.0ms (8% of total)

ival-div: 61.0ms (5% of total)

const: 12.0ms (1% of total)

backward-pass: 3.0ms (0.2% of total)

Bogosity

preprocess321.0ms (2.4%)

Algorithm

2×	egg-herbie

Rules

4332×	`-lowering-.f32`
4332×	`-lowering-.f64`
2560×	`cube-prod`
2266×	`/-lowering-/.f32`
2266×	`/-lowering-/.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	79	127
1	186	117
2	319	117
3	630	89
4	1291	75
5	2362	75
6	7180	75
0	18	12
1	33	11
2	42	11
3	54	9
4	63	7
5	65	7
6	118	7
7	334	7
8	1447	7
9	2552	7
10	3732	7
11	3941	7
12	4230	7
13	4638	7
14	5161	7
15	6434	7
16	6861	7
17	7091	7
18	7262	7
19	7432	7
20	7626	7
0	8394	7

Stop Event

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

Calls

Call 1

Inputs
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

Outputs
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Call 2

Inputs
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (+ (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) (log base)) (* (atan2 im (neg re)) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (+ (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) (log base)) (* (atan2 (neg im) re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log (neg base))) (* (atan2 im re) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0)))
(neg (/ (+ (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) (log base)) (* (atan2 im (neg re)) 0)) (+ (* (log base) (log base)) (* 0 0))))
(neg (/ (+ (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) (log base)) (* (atan2 (neg im) re) 0)) (+ (* (log base) (log base)) (* 0 0))))
(neg (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log (neg base))) (* (atan2 im re) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0))))
(/ (+ (* (log (sqrt (+ (* im im) (* re re)))) (log base)) (* (atan2 re im) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (+ (* (log (sqrt (+ (* base base) (* im im)))) (log re)) (* (atan2 im base) 0)) (+ (* (log re) (log re)) (* 0 0)))
(/ (+ (* (log (sqrt (+ (* re re) (* base base)))) (log im)) (* (atan2 base re) 0)) (+ (* (log im) (log im)) (* 0 0)))

Outputs
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (log (hypot re im)) (log base))
(/ (+ (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) (log base)) (* (atan2 im (neg re)) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (log (hypot re im)) (log base))
(/ (+ (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) (log base)) (* (atan2 (neg im) re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (log (hypot re im)) (log base))
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log (neg base))) (* (atan2 im re) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0)))
(/ (log (hypot re im)) (log (neg base)))
(neg (/ (+ (* (log (sqrt (+ (* (neg re) (neg re)) (* im im)))) (log base)) (* (atan2 im (neg re)) 0)) (+ (* (log base) (log base)) (* 0 0))))
(/ (log (hypot re im)) (neg (log base)))
(neg (/ (+ (* (log (sqrt (+ (* re re) (* (neg im) (neg im))))) (log base)) (* (atan2 (neg im) re) 0)) (+ (* (log base) (log base)) (* 0 0))))
(/ (log (hypot re im)) (neg (log base)))
(neg (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log (neg base))) (* (atan2 im re) 0)) (+ (* (log (neg base)) (log (neg base))) (* 0 0))))
(/ (log (hypot re im)) (neg (log (neg base))))
(/ (+ (* (log (sqrt (+ (* im im) (* re re)))) (log base)) (* (atan2 re im) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/ (log (hypot re im)) (log base))
(/ (+ (* (log (sqrt (+ (* base base) (* im im)))) (log re)) (* (atan2 im base) 0)) (+ (* (log re) (log re)) (* 0 0)))
(/ (log (hypot im base)) (log re))
(/ (+ (* (log (sqrt (+ (* re re) (* base base)))) (log im)) (* (atan2 base re) 0)) (+ (* (log im) (log im)) (* 0 0)))
(/ (log (hypot re base)) (log im))

Symmetry

(abs re)

(abs im)

(sort re im)

explain271.0ms (2%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
132	-	2	(8.790373554289603e-231 1.7461598390281372e-161 8.23815456561582e-26)	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	0	-	`base`
0	-	0	-	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`
0	-	0	-	`(*.f64 im im)`
0	-	0	-	`(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))`
0	-	0	-	`(*.f64 (log.f64 base) (log.f64 base))`
0	-	0	-	`(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))`
0	-	0	-	`(*.f64 (atan2.f64 im re) #s(literal 0 binary64))`
0	-	0	-	`#s(literal 0 binary64)`
0	-	0	-	`(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #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 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64)))`
0	-	0	-	`re`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	0	-	`im`
0	-	0	-	`(atan2.f64 im re)`
0	-	0	-	`(*.f64 re re)`
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: 68.0ms

ival-mult: 30.0ms (43.9% of total)

ival-add: 13.0ms (19% of total)

ival-log: 12.0ms (17.6% of total)

ival-atan2: 4.0ms (5.9% of total)

ival-sqrt: 4.0ms (5.9% of total)

ival-div: 3.0ms (4.4% of total)

const: 1.0ms (1.5% of total)

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

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.0%	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
▶	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Status

Accuracy

Program

▶

50.0%

(/.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))

▶

99.4%

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

Compiler

Compiled 41 to 25 computations (39% saved)

simplify528.0ms (3.9%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	320	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
✓	cost-diff	6592	(*.f64 (atan2.f64 im re) #s(literal 0 binary64))
✓	cost-diff	7040	(+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64)))
✓	cost-diff	20352	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(hypot.f64 re im)
✓	cost-diff	0	(log.f64 (hypot.f64 re im))
✓	cost-diff	0	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Rules

4332×	`-lowering-.f32`
4332×	`-lowering-.f64`
2548×	`cube-prod`
2266×	`/-lowering-/.f32`
2266×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	75
1	34	73
2	43	73
3	54	73
4	63	73
5	65	73
6	118	73
7	335	73
8	1431	73
9	2542	73
10	3771	73
11	3981	73
12	4270	73
13	4678	73
14	5198	73
15	6468	73
16	6895	73
17	7125	73
18	7296	73
19	7466	73
20	7660	73
0	8423	73

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
(log (sqrt (+ (* re re) (* im im))))
(sqrt (+ (* re re) (* im im)))
re
im
(log base)
base
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0))
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
(log (sqrt (+ (* re re) (* im im))))
(sqrt (+ (* re re) (* im im)))
(+ (* re re) (* im im))
(* re re)
re
(* im im)
im
(log base)
base
(* (atan2 im re) 0)
(atan2 im re)
0
(+ (* (log base) (log base)) (* 0 0))
(* (log base) (log base))
(* 0 0)

Outputs
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(log (sqrt (+ (* re re) (* im im))))
(log.f64 (hypot.f64 re im))
(sqrt (+ (* re re) (* im im)))
(hypot.f64 re im)
re
im
(log base)
(log.f64 base)
base
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0))
(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(log (sqrt (+ (* re re) (* im im))))
(log.f64 (hypot.f64 re im))
(sqrt (+ (* re re) (* im im)))
(hypot.f64 re im)
(+ (* re re) (* im im))
(+.f64 (.f64 re re) (.f64 im im))
(* re re)
(*.f64 re re)
re
(* im im)
(*.f64 im im)
im
(log base)
(log.f64 base)
base
(* (atan2 im re) 0)
#s(literal 0 binary64)
(atan2 im re)
(atan2.f64 im re)
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)

localize126.0ms (0.9%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
✓	accuracy	99.4%	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
✓	accuracy	99.2%	(*.f64 (log.f64 base) (log.f64 base))
✓	accuracy	52.2%	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	accuracy	100.0%	(hypot.f64 re im)
✓	accuracy	100.0%	(log.f64 (hypot.f64 re im))
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Results

87.0ms

256×

valid

Compiler

Compiled 142 to 22 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 13.0ms (28.4% of total)

ival-log: 9.0ms (19.7% of total)

compiled-spec: 8.0ms (17.5% of total)

ival-add: 5.0ms (10.9% of total)

ival-div: 4.0ms (8.7% of total)

ival-sqrt: 4.0ms (8.7% of total)

ival-atan2: 2.0ms (4.4% of total)

const: 0.0ms (0% of total)

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

series92.0ms (0.7%)

Counts

10 → 264

Calls

Call 1

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

Outputs
#<alt (/ (log im) (log base))>
#<alt (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))>
#<alt (+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))>
#<alt (+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))>
#<alt (* -1 (/ (log (/ 1 re)) (log base)))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))>
#<alt (* -1 (/ (log (/ -1 re)) (log base)))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))>
#<alt (/ (log re) (log base))>
#<alt (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))) (/ (log re) (log base)))>
#<alt (+ (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))>
#<alt (+ (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))>
#<alt (* -1 (/ (log (/ -1 im)) (log base)))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))>
#<alt (* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))>
#<alt (* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))>
#<alt (* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))>
#<alt (* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<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)))))>
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#<alt (pow (log base) 2)>
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#<alt (pow (log base) 2)>
#<alt (pow (log (/ 1 base)) 2)>
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#<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

66 calls:

Time	Variable		Point	Expression
52.0ms	base	@	0	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms	base	@	-inf	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	base	@	inf	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	re	@	0	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	re	@	inf	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))

rewrite321.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2144×	`-lowering-.f32`
2144×	`-lowering-.f64`
1426×	`fma-lowering-fma.f32`
1426×	`fma-lowering-fma.f64`
1290×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	55	44
2	165	44
3	644	44
4	3068	44
0	8281	44

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 1027

Calls

Call 1

Inputs
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
(log (sqrt (+ (* re re) (* im im))))
(sqrt (+ (* re re) (* im im)))
(log base)
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
(+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0))
(* (atan2 im re) 0)
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
(sqrt (+ (* re re) (* im im)))
(* (log base) (log base))

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)) #s(literal 0 binary64))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 0 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
(exp.f64 (log.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)))
(-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (log.f64 base) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (log.f64 base) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 #s(literal -1 binary64) (log.f64 base))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 #s(literal -1 binary64) (log.f64 base))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(literal 0 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(fma.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 #s(literal 1/2 binary64) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 0 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(fma.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal 0 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 (/.f64 #s(literal 1 binary64) base))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base)) #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base)) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1 binary64) base)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1 binary64) base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (log.f64 base)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (log.f64 base)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (log.f64 base)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (log.f64 base)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 (/.f64 #s(literal 1 binary64) base))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (log.f64 base)) #s(literal 0 binary64))
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(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base))) (log.f64 base))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (.f64 (log.f64 base) #s(literal 1/2 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (log.f64 base))) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (log.f64 base))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(pow.f64 (pow.f64 (E.f64) (log.f64 base)) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(pow.f64 (pow.f64 (E.f64) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(pow.f64 (pow.f64 (E.f64) (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))) (log.f64 base))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(pow.f64 (pow.f64 (E.f64) (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(pow.f64 (pow.f64 (E.f64) #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(pow.f64 (pow.f64 (E.f64) (/.f64 #s(literal 1 binary64) (log.f64 base))) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
(pow.f64 (pow.f64 (E.f64) #s(literal -1 binary64)) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (E.f64) (/.f64 #s(literal -1 binary64) (log.f64 base))) (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(pow.f64 (pow.f64 (E.f64) (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(pow.f64 (pow.f64 (E.f64) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(pow.f64 (pow.f64 (E.f64) #s(literal -1/2 binary64)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (E.f64) #s(literal -1/2 binary64)) (/.f64 (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(pow.f64 (pow.f64 (E.f64) (.f64 (log.f64 base) #s(literal 1/2 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)))
(pow.f64 (pow.f64 (E.f64) (/.f64 #s(literal 1/2 binary64) (log.f64 base))) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(pow.f64 (pow.f64 (E.f64) (/.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (log.f64 base))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (E.f64) (/.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(pow.f64 (pow.f64 (E.f64) (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (log.f64 base) #s(literal 1/2 binary64)))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(pow.f64 (pow.f64 (E.f64) (.f64 (log.f64 base) (/.f64 #s(literal 1/2 binary64) (log.f64 base)))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(pow.f64 (exp.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))) (log.f64 base))
(pow.f64 (exp.f64 (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(pow.f64 (exp.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
(pow.f64 (exp.f64 (/.f64 #s(literal -1 binary64) (log.f64 base))) (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(pow.f64 (exp.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(pow.f64 (exp.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)))
(pow.f64 (exp.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base))) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(pow.f64 (exp.f64 (/.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (log.f64 base))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal 1 binary64)))
(pow.f64 (exp.f64 (/.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(pow.f64 (exp.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (log.f64 base) #s(literal 1/2 binary64)))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(pow.f64 (exp.f64 (.f64 (log.f64 base) (/.f64 #s(literal 1/2 binary64) (log.f64 base)))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
(*.f64 (hypot.f64 re im) #s(literal 1 binary64))
(.f64 (hypot.f64 re im) (pow.f64 (E.f64) (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 0 binary64))))
(.f64 (hypot.f64 re im) (exp.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 0 binary64))))
(*.f64 #s(literal 1 binary64) (hypot.f64 re im))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (hypot.f64 re im)))
(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (hypot.f64 re im)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 re im)) #s(literal -1 binary64)))
(.f64 (pow.f64 (E.f64) (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 0 binary64))) (hypot.f64 re im))
(.f64 (exp.f64 (.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 0 binary64))) (hypot.f64 re im))
(+.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(+.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) base))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(+.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) #s(literal 0 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (log.f64 base))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(-.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(fma.f64 (log.f64 base) (log.f64 base) #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (log.f64 (/.f64 #s(literal 1 binary64) base)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (log.f64 base) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (exp.f64 (log.f64 #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))))
(/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 #s(literal -1 binary64))))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (log.f64 base)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
(*.f64 (log.f64 base) (log.f64 base))
(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (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 2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base))) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base))))
(*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (log.f64 (/.f64 #s(literal 1 binary64) base)))))
(*.f64 (pow.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base))) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))

simplify330.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

4436×	`-lowering-.f32`
4436×	`-lowering-.f64`
3660×	`+-lowering-+.f64`
3660×	`+-lowering-+.f32`
1326×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	4474
1	1118	3758
2	3856	3658
0	8092	3658

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
(/ (log im) (log base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(* -1 (/ (log (/ 1 re)) (log base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(* -1 (/ (log (/ -1 re)) (log base)))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(/ (log re) (log base))
(+ (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(* -1 (/ (log (/ -1 im)) (log base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(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))))))
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))))))))
(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 im) (log base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(* -1 (/ (log (/ 1 re)) (log base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(* -1 (/ (log (/ -1 re)) (log base)))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(/ (log re) (log base))
(+ (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(* -1 (/ (log (/ -1 im)) (log base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log base) (log im))
(+ (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))) (* (log base) (log im)))
(+ (* (log base) (log im)) (* (pow re 2) (+ (* -1/4 (/ (* (pow re 2) (log base)) (pow im 4))) (* 1/2 (/ (log base) (pow im 2))))))
(+ (* (log base) (log im)) (* (pow re 2) (+ (* 1/2 (/ (log base) (pow im 2))) (* (pow re 2) (+ (* -1/4 (/ (log base) (pow im 4))) (* 1/6 (/ (* (pow re 2) (log base)) (pow im 6))))))))
(* -1 (* (log base) (log (/ 1 re))))
(+ (* -1 (* (log base) (log (/ 1 re)))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))
(+ (* -1 (* (log base) (log (/ 1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2)))))
(+ (* -1 (* (log base) (log (/ 1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow im 6)) (* 90 (pow im 6)))) (pow re 6))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))))
(* -1 (* (log base) (log (/ -1 re))))
(+ (* -1 (* (log base) (log (/ -1 re)))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))
(+ (* -1 (* (log base) (log (/ -1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2)))))
(+ (* -1 (* (log base) (log (/ -1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow im 6)) (* 90 (pow im 6)))) (pow re 6))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))))
(* (log base) (log re))
(+ (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))) (* (log base) (log re)))
(+ (* (log base) (log re)) (* (pow im 2) (+ (* -1/4 (/ (* (pow im 2) (log base)) (pow re 4))) (* 1/2 (/ (log base) (pow re 2))))))
(+ (* (log base) (log re)) (* (pow im 2) (+ (* 1/2 (/ (log base) (pow re 2))) (* (pow im 2) (+ (* -1/4 (/ (log base) (pow re 4))) (* 1/6 (/ (* (pow im 2) (log base)) (pow re 6))))))))
(* -1 (* (log base) (log (/ 1 im))))
(+ (* -1 (* (log base) (log (/ 1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))
(+ (* -1 (* (log base) (log (/ 1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2)))))
(+ (* -1 (* (log base) (log (/ 1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))))
(* -1 (* (log base) (log (/ -1 im))))
(+ (* -1 (* (log base) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))
(+ (* -1 (* (log base) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2)))))
(+ (* -1 (* (log base) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
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 base) (log im))
(+ (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))) (* (log base) (log im)))
(+ (* (log base) (log im)) (* (pow re 2) (+ (* -1/4 (/ (* (pow re 2) (log base)) (pow im 4))) (* 1/2 (/ (log base) (pow im 2))))))
(+ (* (log base) (log im)) (* (pow re 2) (+ (* 1/2 (/ (log base) (pow im 2))) (* (pow re 2) (+ (* -1/4 (/ (log base) (pow im 4))) (* 1/6 (/ (* (pow re 2) (log base)) (pow im 6))))))))
(* -1 (* (log base) (log (/ 1 re))))
(+ (* -1 (* (log base) (log (/ 1 re)))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))
(+ (* -1 (* (log base) (log (/ 1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2)))))
(+ (* -1 (* (log base) (log (/ 1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow im 6)) (* 90 (pow im 6)))) (pow re 6))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))))
(* -1 (* (log base) (log (/ -1 re))))
(+ (* -1 (* (log base) (log (/ -1 re)))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))
(+ (* -1 (* (log base) (log (/ -1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2)))))
(+ (* -1 (* (log base) (log (/ -1 re)))) (+ (* -1/4 (/ (* (pow im 4) (log base)) (pow re 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow im 6)) (* 90 (pow im 6)))) (pow re 6))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))))
(* (log base) (log re))
(+ (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))) (* (log base) (log re)))
(+ (* (log base) (log re)) (* (pow im 2) (+ (* -1/4 (/ (* (pow im 2) (log base)) (pow re 4))) (* 1/2 (/ (log base) (pow re 2))))))
(+ (* (log base) (log re)) (* (pow im 2) (+ (* 1/2 (/ (log base) (pow re 2))) (* (pow im 2) (+ (* -1/4 (/ (log base) (pow re 4))) (* 1/6 (/ (* (pow im 2) (log base)) (pow re 6))))))))
(* -1 (* (log base) (log (/ 1 im))))
(+ (* -1 (* (log base) (log (/ 1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))
(+ (* -1 (* (log base) (log (/ 1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2)))))
(+ (* -1 (* (log base) (log (/ 1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))))
(* -1 (* (log base) (log (/ -1 im))))
(+ (* -1 (* (log base) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))
(+ (* -1 (* (log base) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2)))))
(+ (* -1 (* (log base) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (log base)) (pow im 4))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (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)

Outputs
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
(+.f64 (/.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) im) im) (log.f64 base)) (/.f64 (log.f64 im) (log.f64 base)))
(+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(+.f64 (.f64 (.f64 re re) (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 re (/.f64 re (pow.f64 im #s(literal 4 binary64))))) (log.f64 base)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (log.f64 base) im) im)))) (/.f64 (log.f64 im) (log.f64 base)))
(+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(+.f64 (.f64 (.f64 re re) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (log.f64 base) im) im)) (.f64 re (.f64 re (+.f64 (.f64 (.f64 re (/.f64 re (pow.f64 im #s(literal 6 binary64)))) (/.f64 #s(literal 1/6 binary64) (log.f64 base))) (/.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (log.f64 base))))))) (/.f64 (log.f64 im) (log.f64 base)))
(* -1 (/ (log (/ 1 re)) (log base)))
(/.f64 (log.f64 re) (log.f64 base))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+.f64 (/.f64 (log.f64 re) (log.f64 base)) (/.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 im im)) re) re) (log.f64 base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
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(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+.f64 re (.f64 (.f64 im im) (+.f64 (/.f64 (.f64 (.f64 im im) #s(literal -1/8 binary64)) (.f64 re (.f64 re re))) (/.f64 #s(literal 1/2 binary64) 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)))))
(+.f64 re (.f64 (.f64 im im) (+.f64 (/.f64 #s(literal 1/2 binary64) re) (.f64 im (.f64 im (+.f64 (/.f64 (.f64 (.f64 im im) #s(literal 1/16 binary64)) (pow.f64 re #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 re (.f64 re re)))))))))
im
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(.f64 im (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im)))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(.f64 im (+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) im) im) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 im #s(literal 4 binary64))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(.f64 im (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) im) im) (+.f64 (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 im #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 im #s(literal 6 binary64)))))))
(* -1 im)
(-.f64 #s(literal 0 binary64) im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 re re)) im) im)) (-.f64 #s(literal 0 binary64) im))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(.f64 (+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) im) im) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 im #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) im))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) im) im) (+.f64 (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 im #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 im #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) im))
(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))

eval238.0ms (1.7%)

Compiler: Compiled 35436 to 2717 computations (92.3% saved)

prune177.0ms (1.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	1428	19	1447
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1429	20	1449

Accuracy

99.8%

Counts

1449 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.0%	(/.f64 (/.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 base))
	49.9%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
	50.0%	(/.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
▶	50.0%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	23.0%	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (exp.f64 (log.f64 (log.f64 base)))) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	50.1%	(/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
	98.9%	(/.f64 (.f64 (log.f64 im) (log.f64 base)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	49.7%	(/.f64 (log.f64 (pow.f64 (exp.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) base)))) (log.f64 base))
▶	99.2%	(/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	46.0%	(/.f64 (log.f64 (hypot.f64 re im)) (exp.f64 (log.f64 (log.f64 base))))
▶	99.1%	(/.f64 (log.f64 im) (log.f64 base))
	50.0%	(/.f64 (log.f64 base) (neg.f64 (.f64 (log.f64 base) (/.f64 (log.f64 base) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64))))))
	50.1%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
	50.0%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
▶	50.0%	(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
▶	50.0%	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 base))
	50.1%	(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
	50.0%	(.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
	29.1%	(exp.f64 (log.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))))

Compiler

Compiled 776 to 519 computations (33.1% saved)

simplify226.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 19 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	192	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
✓	cost-diff	13184	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (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)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
✓	cost-diff	12992	(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(log.f64 im)
✓	cost-diff	0	(/.f64 (log.f64 im) (log.f64 base))
✓	cost-diff	0	(hypot.f64 re im)
✓	cost-diff	0	(log.f64 (hypot.f64 re im))
✓	cost-diff	13120	(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	cost-diff	13120	(/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))

Rules

4832×	`-lowering-.f32`
4832×	`-lowering-.f64`
2438×	`/-lowering-/.f32`
2438×	`/-lowering-/.f64`
2234×	`cube-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	256
1	62	227
2	138	210
3	330	208
4	2102	208
5	2316	208
6	2430	208
7	2573	208
8	2760	208
9	2981	208
10	5278	208
11	5879	208
12	6568	208
13	7324	208
14	7878	208
0	8021	208

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize209.0ms (1.5%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.4%	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 base))
✓	accuracy	99.4%	(/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
✓	accuracy	50.4%	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	accuracy	99.4%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
✓	accuracy	99.4%	(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
✓	accuracy	99.1%	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	accuracy	50.4%	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	accuracy	99.6%	(/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.4%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
✓	accuracy	50.4%	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	accuracy	100.0%	(log.f64 im)
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.4%	(/.f64 (log.f64 im) (log.f64 base))
✓	accuracy	99.5%	(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓	accuracy	99.2%	(pow.f64 (log.f64 base) #s(literal 2 binary64))

Results

151.0ms

256×

valid

Compiler

Compiled 286 to 30 computations (89.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 16.0ms (25.1% of total)

ival-div: 13.0ms (20.4% of total)

ival-log: 12.0ms (18.8% of total)

ival-pow: 8.0ms (12.5% of total)

compiled-spec: 8.0ms (12.5% of total)

ival-add: 3.0ms (4.7% of total)

ival-sqrt: 2.0ms (3.1% of total)

const: 1.0ms (1.6% of total)

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

series195.0ms (1.4%)

Counts

18 → 444

Calls

Call 1

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

Outputs
#<alt (/ (log im) (log base))>
#<alt (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))>
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#<alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2))))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 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 (pow im 2))>
#<alt (+ (log (pow im 2)) (/ (pow re 2) (pow im 2)))>
#<alt (+ (log (pow im 2)) (* (pow re 2) (+ (* -1/2 (/ (pow re 2) (pow im 4))) (/ 1 (pow im 2)))))>
#<alt (+ (log (pow im 2)) (* (pow re 2) (+ (* (pow re 2) (- (* 1/3 (/ (pow re 2) (pow im 6))) (* 1/2 (/ 1 (pow im 4))))) (/ 1 (pow im 2)))))>
#<alt (* -2 (log (/ 1 re)))>
#<alt (+ (* -2 (log (/ 1 re))) (/ (pow im 2) (pow re 2)))>
#<alt (+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))>
#<alt (* -2 (log (/ -1 re)))>
#<alt (+ (* -2 (log (/ -1 re))) (/ (pow im 2) (pow re 2)))>
#<alt (+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))>
#<alt (log (pow re 2))>
#<alt (+ (log (pow re 2)) (/ (pow im 2) (pow re 2)))>
#<alt (+ (log (pow re 2)) (* (pow im 2) (+ (* -1/2 (/ (pow im 2) (pow re 4))) (/ 1 (pow re 2)))))>
#<alt (+ (log (pow re 2)) (* (pow im 2) (+ (* (pow im 2) (- (* 1/3 (/ (pow im 2) (pow re 6))) (* 1/2 (/ 1 (pow re 4))))) (/ 1 (pow re 2)))))>
#<alt (* -2 (log (/ 1 im)))>
#<alt (+ (* -2 (log (/ 1 im))) (/ (pow re 2) (pow im 2)))>
#<alt (+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))>
#<alt (* -2 (log (/ -1 im)))>
#<alt (+ (* -2 (log (/ -1 im))) (/ (pow re 2) (pow im 2)))>
#<alt (+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (pow im 2))))>
#<alt (+ (* -2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* 2 (/ (log base) (log (pow im 2)))))>
#<alt (+ (* 2 (/ (log base) (log (pow im 2)))) (* (pow re 2) (+ (* -2 (* (pow re 2) (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2))))))) (* -2 (/ (log base) (* (pow im 2) (pow (log (pow im 2)) 2)))))))>
#<alt (+ (* 2 (/ (log base) (log (pow im 2)))) (* (pow re 2) (+ (* -2 (/ (log base) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* (pow re 2) (+ (* -2 (* (pow re 2) (+ (* -1 (/ (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2))))) (* (pow im 2) (log (pow im 2))))) (+ (* 1/3 (/ (log base) (* (pow im 6) (pow (log (pow im 2)) 2)))) (* 1/2 (/ (log base) (* (pow im 6) (pow (log (pow im 2)) 3)))))))) (* -2 (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2)))))))))))>
#<alt (* -1 (/ (log base) (log (/ 1 re))))>
#<alt (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow im 6) (log base)) (pow (log (/ 1 re)) 3))) (+ (* 1/12 (/ (* (pow im 6) (log base)) (pow (log (/ 1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3))))) (log (/ 1 re)))))) (pow re 6))) (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2)))))))>
#<alt (* -1 (/ (log base) (log (/ -1 re))))>
#<alt (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow im 6) (log base)) (pow (log (/ -1 re)) 3))) (+ (* 1/12 (/ (* (pow im 6) (log base)) (pow (log (/ -1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3))))) (log (/ -1 re)))))) (pow re 6))) (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2)))))))>
#<alt (* 2 (/ (log base) (log (pow re 2))))>
#<alt (+ (* -2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (pow re 2)) 2)))) (* 2 (/ (log base) (log (pow re 2)))))>
#<alt (+ (* 2 (/ (log base) (log (pow re 2)))) (* (pow im 2) (+ (* -2 (* (pow im 2) (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2))))))) (* -2 (/ (log base) (* (pow re 2) (pow (log (pow re 2)) 2)))))))>
#<alt (+ (* 2 (/ (log base) (log (pow re 2)))) (* (pow im 2) (+ (* -2 (/ (log base) (* (pow re 2) (pow (log (pow re 2)) 2)))) (* (pow im 2) (+ (* -2 (* (pow im 2) (+ (* -1 (/ (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2))))) (* (pow re 2) (log (pow re 2))))) (+ (* 1/3 (/ (log base) (* (pow re 6) (pow (log (pow re 2)) 2)))) (* 1/2 (/ (log base) (* (pow re 6) (pow (log (pow re 2)) 3)))))))) (* -2 (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2)))))))))))>
#<alt (* -1 (/ (log base) (log (/ 1 im))))>
#<alt (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3))))) (log (/ 1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2)))))))>
#<alt (* -1 (/ (log base) (log (/ -1 im))))>
#<alt (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))>

Calls

111 calls:

Time	Variable		Point	Expression
53.0ms	im	@	0	(/ (log im) (log base))
39.0ms	im	@	0	(/ (log (sqrt (+ (* re re) (* im im)))) (* (pow (log base) 2) (/ 1 (log base))))
20.0ms	base	@	0	(/ (/ 1 (log base)) (/ 2 (log (+ (* re re) (* im im)))))
15.0ms	base	@	0	(/ (log im) (log base))
7.0ms	im	@	-inf	(/ (log im) (log base))

rewrite426.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3510×	`/-lowering-/.f32`
3510×	`/-lowering-/.f64`
3020×	`-lowering-.f32`
3020×	`-lowering-.f64`
1744×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	138
1	122	92
2	664	90
3	3439	90
0	8290	90

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1826

Calls

Call 1

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

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

simplify477.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

6552×	`-lowering-.f32`
6552×	`-lowering-.f64`
4364×	`+-lowering-+.f64`
4364×	`+-lowering-+.f32`
1952×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	879	9605
1	2829	8296
0	8679	8296

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

Inputs
(/ (log im) (log base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(* -1 (/ (log (/ 1 re)) (log base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(* -1 (/ (log (/ -1 re)) (log base)))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(/ (log re) (log base))
(+ (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(* -1 (/ (log (/ -1 im)) (log base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (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 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))))))
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))))))))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(log im)
(log im)
(log im)
(log im)
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(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))))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))
(* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(* 1/2 (/ (log (pow im 2)) (log base)))
(+ (* 1/2 (/ (log (pow im 2)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* 1/2 (/ (log (pow im 2)) (log base))) (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))))
(+ (* 1/2 (/ (log (pow im 2)) (log base))) (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))))
(* -1 (/ (log (/ 1 re)) (log base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/6 (/ (pow im 6) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(* -1 (/ (log (/ -1 re)) (log base)))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/6 (/ (pow im 6) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(* 1/2 (/ (log (pow re 2)) (log base)))
(+ (* 1/2 (/ (log (pow re 2)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* 1/2 (/ (log (pow re 2)) (log base))) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))))
(+ (* 1/2 (/ (log (pow re 2)) (log base))) (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))))
(* -1 (/ (log (/ 1 im)) (log base)))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(* -1 (/ (log (/ -1 im)) (log base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (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)))))
(/ 2 (log (pow im 2)))
(+ (* -2 (/ (pow re 2) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* 2 (/ 1 (log (pow im 2)))))
(+ (* (pow re 2) (- (* (pow re 2) (+ (/ 1 (* (pow im 4) (pow (log (pow im 2)) 2))) (* 2 (/ 1 (* (pow im 4) (pow (log (pow im 2)) 3)))))) (* 2 (/ 1 (* (pow im 2) (pow (log (pow im 2)) 2)))))) (* 2 (/ 1 (log (pow im 2)))))
(+ (* (pow re 2) (- (* (pow re 2) (+ (* -1 (* (pow re 2) (+ (* 2/3 (/ 1 (* (pow im 6) (pow (log (pow im 2)) 2)))) (+ (* 2 (/ 1 (* (pow im 6) (pow (log (pow im 2)) 3)))) (* 2 (/ 1 (* (pow im 6) (pow (log (pow im 2)) 4)))))))) (+ (* 2 (/ 1 (* (pow im 4) (pow (log (pow im 2)) 3)))) (/ 1 (* (pow im 4) (pow (log (pow im 2)) 2)))))) (* 2 (/ 1 (* (pow im 2) (pow (log (pow im 2)) 2)))))) (* 2 (/ 1 (log (pow im 2)))))
(/ -1 (log (/ 1 re)))
(- (* -1/2 (/ (pow im 2) (* (pow re 2) (pow (log (/ 1 re)) 2)))) (/ 1 (log (/ 1 re))))
(- (* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow (log (/ 1 re)) 2))) (* 1/4 (/ (pow im 4) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log (/ 1 re)) 2)))) (/ 1 (log (/ 1 re)))))
(- (* -1 (/ (+ (* -1/8 (/ (pow im 6) (pow (log (/ 1 re)) 3))) (+ (* 1/6 (/ (pow im 6) (pow (log (/ 1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/4 (/ (pow im 4) (pow (log (/ 1 re)) 2))) (* 1/4 (/ (pow im 4) (pow (log (/ 1 re)) 3))))) (log (/ 1 re)))))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (pow (log (/ 1 re)) 2)))) (+ (* 1/4 (/ (pow im 4) (* (pow re 4) (pow (log (/ 1 re)) 3)))) (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log (/ 1 re)) 2)))) (/ 1 (log (/ 1 re)))))))
(/ -1 (log (/ -1 re)))
(- (* -1/2 (/ (pow im 2) (* (pow re 2) (pow (log (/ -1 re)) 2)))) (/ 1 (log (/ -1 re))))
(- (* -1 (/ (+ (* -1/4 (/ (pow im 4) (pow (log (/ -1 re)) 2))) (* 1/4 (/ (pow im 4) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log (/ -1 re)) 2)))) (/ 1 (log (/ -1 re)))))
(- (* -1 (/ (+ (* -1/8 (/ (pow im 6) (pow (log (/ -1 re)) 3))) (+ (* 1/6 (/ (pow im 6) (pow (log (/ -1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/4 (/ (pow im 4) (pow (log (/ -1 re)) 2))) (* 1/4 (/ (pow im 4) (pow (log (/ -1 re)) 3))))) (log (/ -1 re)))))) (pow re 6))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (pow (log (/ -1 re)) 2)))) (+ (* 1/4 (/ (pow im 4) (* (pow re 4) (pow (log (/ -1 re)) 3)))) (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log (/ -1 re)) 2)))) (/ 1 (log (/ -1 re)))))))
(/ 2 (log (pow re 2)))
(+ (* -2 (/ (pow im 2) (* (pow re 2) (pow (log (pow re 2)) 2)))) (* 2 (/ 1 (log (pow re 2)))))
(+ (* (pow im 2) (- (* (pow im 2) (+ (/ 1 (* (pow re 4) (pow (log (pow re 2)) 2))) (* 2 (/ 1 (* (pow re 4) (pow (log (pow re 2)) 3)))))) (* 2 (/ 1 (* (pow re 2) (pow (log (pow re 2)) 2)))))) (* 2 (/ 1 (log (pow re 2)))))
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(+ (log (pow im 2)) (/ (pow re 2) (pow im 2)))
(+ (log (pow im 2)) (* (pow re 2) (+ (* -1/2 (/ (pow re 2) (pow im 4))) (/ 1 (pow im 2)))))
(+ (log (pow im 2)) (* (pow re 2) (+ (* (pow re 2) (- (* 1/3 (/ (pow re 2) (pow im 6))) (* 1/2 (/ 1 (pow im 4))))) (/ 1 (pow im 2)))))
(* -2 (log (/ 1 re)))
(+ (* -2 (log (/ 1 re))) (/ (pow im 2) (pow re 2)))
(+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))
(+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))
(* -2 (log (/ -1 re)))
(+ (* -2 (log (/ -1 re))) (/ (pow im 2) (pow re 2)))
(+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))
(+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))
(log (pow re 2))
(+ (log (pow re 2)) (/ (pow im 2) (pow re 2)))
(+ (log (pow re 2)) (* (pow im 2) (+ (* -1/2 (/ (pow im 2) (pow re 4))) (/ 1 (pow re 2)))))
(+ (log (pow re 2)) (* (pow im 2) (+ (* (pow im 2) (- (* 1/3 (/ (pow im 2) (pow re 6))) (* 1/2 (/ 1 (pow re 4))))) (/ 1 (pow re 2)))))
(* -2 (log (/ 1 im)))
(+ (* -2 (log (/ 1 im))) (/ (pow re 2) (pow im 2)))
(+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))
(+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))
(* -2 (log (/ -1 im)))
(+ (* -2 (log (/ -1 im))) (/ (pow re 2) (pow im 2)))
(+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))
(+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (pow im 2))))
(+ (* -2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* 2 (/ (log base) (log (pow im 2)))))
(+ (* 2 (/ (log base) (log (pow im 2)))) (* (pow re 2) (+ (* -2 (* (pow re 2) (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2))))))) (* -2 (/ (log base) (* (pow im 2) (pow (log (pow im 2)) 2)))))))
(+ (* 2 (/ (log base) (log (pow im 2)))) (* (pow re 2) (+ (* -2 (/ (log base) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* (pow re 2) (+ (* -2 (* (pow re 2) (+ (* -1 (/ (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2))))) (* (pow im 2) (log (pow im 2))))) (+ (* 1/3 (/ (log base) (* (pow im 6) (pow (log (pow im 2)) 2)))) (* 1/2 (/ (log base) (* (pow im 6) (pow (log (pow im 2)) 3)))))))) (* -2 (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2)))))))))))
(* -1 (/ (log base) (log (/ 1 re))))
(+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2)))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2))))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow im 6) (log base)) (pow (log (/ 1 re)) 3))) (+ (* 1/12 (/ (* (pow im 6) (log base)) (pow (log (/ 1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3))))) (log (/ 1 re)))))) (pow re 6))) (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2)))))))
(* -1 (/ (log base) (log (/ -1 re))))
(+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2)))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2))))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow im 6) (log base)) (pow (log (/ -1 re)) 3))) (+ (* 1/12 (/ (* (pow im 6) (log base)) (pow (log (/ -1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3))))) (log (/ -1 re)))))) (pow re 6))) (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2)))))))
(* 2 (/ (log base) (log (pow re 2))))
(+ (* -2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (pow re 2)) 2)))) (* 2 (/ (log base) (log (pow re 2)))))
(+ (* 2 (/ (log base) (log (pow re 2)))) (* (pow im 2) (+ (* -2 (* (pow im 2) (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2))))))) (* -2 (/ (log base) (* (pow re 2) (pow (log (pow re 2)) 2)))))))
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(* -1 (/ (log base) (log (/ 1 im))))
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(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3))))) (log (/ 1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2)))))))
(* -1 (/ (log base) (log (/ -1 im))))
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(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))))
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Outputs
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
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(* -1 (/ (log (/ 1 re)) (log base)))
(/.f64 (log.f64 re) (log.f64 base))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
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(/ (log re) (log base))
(/.f64 (log.f64 re) (log.f64 base))
(+ (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))) (/ (log re) (log base)))
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(* -1 (/ (log (/ -1 im)) (log base)))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
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(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 (hypot.f64 im re)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 (hypot.f64 im re)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 (hypot.f64 im re)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(log base)
(log.f64 base)
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im
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re
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re
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im
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(+.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (/.f64 (.f64 re re) im) (/.f64 (log.f64 base) im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im)))) (/.f64 (.f64 #s(literal -2 binary64) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (pow.f64 im #s(literal 4 binary64))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))
(+.f64 (.f64 #s(literal -2 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64)))) (pow.f64 im #s(literal 4 binary64))) (/.f64 (+.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) im))) (+.f64 (/.f64 (.f64 (.f64 #s(literal 1/12 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal -1/16 binary64) (log.f64 base)) (pow.f64 re #s(literal 6 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (pow.f64 im #s(literal 6 binary64))))) (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (/.f64 (*.f64 re re) im) (/.f64 (log.f64 base) im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im)))))

eval444.0ms (3.3%)

Compiler: Compiled 75588 to 5229 computations (93.1% saved)

prune380.0ms (2.8%)

Pruning

27 alts after pruning (24 fresh and 3 done)

	Pruned	Kept	Total
New	2899	21	2920
Fresh	11	3	14
Picked	3	2	5
Done	0	1	1
Total	2913	27	2940

Accuracy

100.0%

Counts

2940 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.0%	(/.f64 (/.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 base))
▶	49.9%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
✓	50.0%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	26.7%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 (.f64 (log.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal -1 binary64))))))
	98.8%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
	98.8%	(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
	98.9%	(/.f64 (*.f64 (log.f64 im) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
▶	99.3%	(/.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))))
✓	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
▶	45.8%	(/.f64 (log.f64 im) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
	98.8%	(/.f64 (log.f64 im) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	99.0%	(/.f64 (log.f64 im) (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
	99.1%	(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
✓	99.1%	(/.f64 (log.f64 im) (log.f64 base))
	46.0%	(/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base))))
	50.0%	(/.f64 (log.f64 base) (neg.f64 (.f64 (log.f64 base) (/.f64 (log.f64 base) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64))))))
	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
	50.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	49.9%	(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (pow.f64 (log.f64 base) #s(literal 2 binary64))))))
	98.9%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 im)))
▶	98.8%	(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
	98.8%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im))) (log.f64 base))
	50.0%	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
	98.9%	(*.f64 (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
▶	98.9%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
	98.8%	(.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))
	54.5%	(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 im))) #s(literal -1 binary64)))

Compiler

Compiled 818 to 566 computations (30.8% saved)

simplify214.0ms (1.6%)

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	13184	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
✓	cost-diff	13184	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	cost-diff	128	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
✓	cost-diff	13120	(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
✓	cost-diff	0	(E.f64)
✓	cost-diff	0	(pow.f64 (E.f64) (log.f64 (log.f64 base)))
✓	cost-diff	0	(log.f64 im)
✓	cost-diff	0	(/.f64 (log.f64 im) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓	cost-diff	0	(log.f64 im)
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
✓	cost-diff	13120	(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	cost-diff	13120	(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
✓	cost-diff	26240	(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
✓	cost-diff	26240	(/.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))))

Rules

5850×	`-lowering-.f32`
5850×	`-lowering-.f64`
2502×	`/-lowering-/.f32`
2502×	`/-lowering-/.f64`
1394×	`neg-mul-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	297
1	72	255
2	168	169
3	468	163
4	1719	163
5	1950	163
6	2487	163
7	5030	163
0	8125	163

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize282.0ms (2.1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
✓	accuracy	99.7%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
✓	accuracy	76.5%	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (log.f64 im))
✓	accuracy	99.7%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
✓	accuracy	99.7%	(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
✓	accuracy	99.6%	(pow.f64 (log.f64 base) #s(literal -2 binary64))
✓	accuracy	100.0%	(log.f64 (log.f64 base))
✓	accuracy	99.7%	(/.f64 (log.f64 im) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓	accuracy	99.0%	(pow.f64 (E.f64) (log.f64 (log.f64 base)))
✓	accuracy	48.5%	(E.f64)
✓	accuracy	100.0%	(log.f64 im)
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
✓	accuracy	99.8%	(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
✓	accuracy	99.8%	(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	accuracy	99.7%	(/.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))))
✓	accuracy	99.7%	(pow.f64 (log.f64 base) #s(literal 2 binary64))

Results

126.0ms	120×	0	valid
101.0ms	136×	0	invalid

Compiler

Compiled 255 to 36 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-div: 29.0ms (31% of total)

ival-log: 16.0ms (17.1% of total)

ival-pow: 16.0ms (17.1% of total)

ival-mult: 15.0ms (16% of total)

compiled-spec: 9.0ms (9.6% of total)

ival-e: 4.0ms (4.3% of total)

ival-add: 3.0ms (3.2% of total)

ival-sqrt: 2.0ms (2.1% of total)

const: 1.0ms (1.1% of total)

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

series213.0ms (1.6%)

Counts

22 → 408

Calls

Call 1

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

Outputs
#<alt (/ (log im) (log base))>
#<alt (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))>
#<alt (+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))>
#<alt (+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))>
#<alt (* -1 (/ (log (/ 1 re)) (log base)))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))>
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#<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))) (+ (* 1/6 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))>
#<alt (/ -1 (log base))>
#<alt (/ -1 (log base))>
#<alt (/ -1 (log base))>
#<alt (/ -1 (log base))>
#<alt (/ 1 (log (/ 1 base)))>
#<alt (/ 1 (log (/ 1 base)))>
#<alt (/ 1 (log (/ 1 base)))>
#<alt (/ 1 (log (/ 1 base)))>
#<alt (/ -1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ -1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ -1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ -1 (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (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 (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 im))>
#<alt (/ 1 (log im))>
#<alt (/ 1 (log im))>
#<alt (/ 1 (log im))>
#<alt (/ -1 (log (/ 1 im)))>
#<alt (/ -1 (log (/ 1 im)))>
#<alt (/ -1 (log (/ 1 im)))>
#<alt (/ -1 (log (/ 1 im)))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (/ 1 (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (log (pow im 2))>
#<alt (+ (log (pow im 2)) (/ (pow re 2) (pow im 2)))>
#<alt (+ (log (pow im 2)) (* (pow re 2) (+ (* -1/2 (/ (pow re 2) (pow im 4))) (/ 1 (pow im 2)))))>
#<alt (+ (log (pow im 2)) (* (pow re 2) (+ (* (pow re 2) (- (* 1/3 (/ (pow re 2) (pow im 6))) (* 1/2 (/ 1 (pow im 4))))) (/ 1 (pow im 2)))))>
#<alt (* -2 (log (/ 1 re)))>
#<alt (+ (* -2 (log (/ 1 re))) (/ (pow im 2) (pow re 2)))>
#<alt (+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))>
#<alt (* -2 (log (/ -1 re)))>
#<alt (+ (* -2 (log (/ -1 re))) (/ (pow im 2) (pow re 2)))>
#<alt (+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))>
#<alt (log (pow re 2))>
#<alt (+ (log (pow re 2)) (/ (pow im 2) (pow re 2)))>
#<alt (+ (log (pow re 2)) (* (pow im 2) (+ (* -1/2 (/ (pow im 2) (pow re 4))) (/ 1 (pow re 2)))))>
#<alt (+ (log (pow re 2)) (* (pow im 2) (+ (* (pow im 2) (- (* 1/3 (/ (pow im 2) (pow re 6))) (* 1/2 (/ 1 (pow re 4))))) (/ 1 (pow re 2)))))>
#<alt (* -2 (log (/ 1 im)))>
#<alt (+ (* -2 (log (/ 1 im))) (/ (pow re 2) (pow im 2)))>
#<alt (+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))>
#<alt (* -2 (log (/ -1 im)))>
#<alt (+ (* -2 (log (/ -1 im))) (/ (pow re 2) (pow im 2)))>
#<alt (+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))>
#<alt (/ -2 (* (log base) (log (pow im 2))))>
#<alt (- (* 2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (pow im 2)) 2))))) (* 2 (/ 1 (* (log base) (log (pow im 2))))))>
#<alt (- (* (pow re 2) (+ (* -1 (* (pow re 2) (+ (* 2 (/ 1 (* (pow im 4) (* (log base) (pow (log (pow im 2)) 3))))) (/ 1 (* (pow im 4) (* (log base) (pow (log (pow im 2)) 2))))))) (* 2 (/ 1 (* (pow im 2) (* (log base) (pow (log (pow im 2)) 2))))))) (* 2 (/ 1 (* (log base) (log (pow im 2))))))>
#<alt (- (* (pow re 2) (+ (* (pow re 2) (- (* (pow re 2) (- (+ (* 2/3 (/ 1 (* (pow im 6) (* (log base) (pow (log (pow im 2)) 2))))) (/ 1 (* (pow im 6) (* (log base) (pow (log (pow im 2)) 3))))) (* -1 (/ (+ (/ 1 (* (pow im 4) (* (log base) (pow (log (pow im 2)) 2)))) (* 2 (/ 1 (* (pow im 4) (* (log base) (pow (log (pow im 2)) 3)))))) (* (pow im 2) (log (pow im 2))))))) (+ (* 2 (/ 1 (* (pow im 4) (* (log base) (pow (log (pow im 2)) 3))))) (/ 1 (* (pow im 4) (* (log base) (pow (log (pow im 2)) 2))))))) (* 2 (/ 1 (* (pow im 2) (* (log base) (pow (log (pow im 2)) 2))))))) (* 2 (/ 1 (* (log base) (log (pow im 2))))))>
#<alt (/ 1 (* (log base) (log (/ 1 re))))>
#<alt (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (/ 1 re)) 2))))) (/ 1 (* (log base) (log (/ 1 re)))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (pow im 4) (* (log base) (pow (log (/ 1 re)) 3)))) (* 1/4 (/ (pow im 4) (* (log base) (pow (log (/ 1 re)) 2))))) (pow re 4))) (/ 1 (* (log base) (log (/ 1 re))))) (* -1/2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (/ 1 re)) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/6 (/ (pow im 6) (* (log base) (pow (log (/ 1 re)) 2)))) (+ (* 1/8 (/ (pow im 6) (* (log base) (pow (log (/ 1 re)) 3)))) (* 1/2 (/ (* (pow im 2) (+ (* -1/4 (/ (pow im 4) (* (log base) (pow (log (/ 1 re)) 3)))) (* 1/4 (/ (pow im 4) (* (log base) (pow (log (/ 1 re)) 2)))))) (log (/ 1 re)))))) (pow re 6))) (/ 1 (* (log base) (log (/ 1 re))))) (+ (* -1/2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (/ 1 re)) 2))))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (* (log base) (pow (log (/ 1 re)) 3))))) (* 1/4 (/ (pow im 4) (* (pow re 4) (* (log base) (pow (log (/ 1 re)) 2))))))))>
#<alt (/ 1 (* (log base) (log (/ -1 re))))>
#<alt (+ (* 1/2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (/ -1 re)) 2))))) (/ 1 (* (log base) (log (/ -1 re)))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (pow im 4) (* (log base) (pow (log (/ -1 re)) 3)))) (* 1/4 (/ (pow im 4) (* (log base) (pow (log (/ -1 re)) 2))))) (pow re 4))) (/ 1 (* (log base) (log (/ -1 re))))) (* -1/2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (/ -1 re)) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/6 (/ (pow im 6) (* (log base) (pow (log (/ -1 re)) 2)))) (+ (* 1/8 (/ (pow im 6) (* (log base) (pow (log (/ -1 re)) 3)))) (* 1/2 (/ (* (pow im 2) (+ (* -1/4 (/ (pow im 4) (* (log base) (pow (log (/ -1 re)) 3)))) (* 1/4 (/ (pow im 4) (* (log base) (pow (log (/ -1 re)) 2)))))) (log (/ -1 re)))))) (pow re 6))) (/ 1 (* (log base) (log (/ -1 re))))) (+ (* -1/2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (/ -1 re)) 2))))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (* (log base) (pow (log (/ -1 re)) 3))))) (* 1/4 (/ (pow im 4) (* (pow re 4) (* (log base) (pow (log (/ -1 re)) 2))))))))>
#<alt (/ -2 (* (log base) (log (pow re 2))))>
#<alt (- (* 2 (/ (pow im 2) (* (pow re 2) (* (log base) (pow (log (pow re 2)) 2))))) (* 2 (/ 1 (* (log base) (log (pow re 2))))))>
#<alt (- (* (pow im 2) (+ (* -1 (* (pow im 2) (+ (* 2 (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 3))))) (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 2))))))) (* 2 (/ 1 (* (pow re 2) (* (log base) (pow (log (pow re 2)) 2))))))) (* 2 (/ 1 (* (log base) (log (pow re 2))))))>
#<alt (- (* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (- (+ (* 2/3 (/ 1 (* (pow re 6) (* (log base) (pow (log (pow re 2)) 2))))) (/ 1 (* (pow re 6) (* (log base) (pow (log (pow re 2)) 3))))) (* -1 (/ (+ (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 2)))) (* 2 (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 3)))))) (* (pow re 2) (log (pow re 2))))))) (+ (* 2 (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 3))))) (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 2))))))) (* 2 (/ 1 (* (pow re 2) (* (log base) (pow (log (pow re 2)) 2))))))) (* 2 (/ 1 (* (log base) (log (pow re 2))))))>
#<alt (/ 1 (* (log base) (log (/ 1 im))))>
#<alt (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))) (/ 1 (* (log base) (log (/ 1 im)))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 2))))) (pow im 4))) (/ 1 (* (log base) (log (/ 1 im))))) (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/6 (/ (pow re 6) (* (log base) (pow (log (/ 1 im)) 2)))) (+ (* 1/8 (/ (pow re 6) (* (log base) (pow (log (/ 1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 2)))))) (log (/ 1 im)))))) (pow im 6))) (/ 1 (* (log base) (log (/ 1 im))))) (+ (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ 1 im)) 3))))) (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ 1 im)) 2))))))))>
#<alt (/ 1 (* (log base) (log (/ -1 im))))>
#<alt (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2))))) (pow im 4))) (/ 1 (* (log base) (log (/ -1 im))))) (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/6 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 2)))) (+ (* 1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))))) (log (/ -1 im)))))) (pow im 6))) (/ 1 (* (log base) (log (/ -1 im))))) (+ (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))))))>
#<alt (/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>

Calls

102 calls:

Time	Variable		Point	Expression
80.0ms	im	@	0	(/ (log im) (pow (E) (log (log base))))
40.0ms	base	@	inf	(/ (log im) (pow (E) (log (log base))))
34.0ms	im	@	-inf	(/ 1 (log im))
20.0ms	base	@	-inf	(/ (log im) (pow (E) (log (log base))))
13.0ms	base	@	0	(/ (log im) (pow (E) (log (log base))))

rewrite291.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2700×	`-lowering-.f32`
2700×	`-lowering-.f64`
2034×	`pow-lowering-pow.f64`
2034×	`pow-lowering-pow.f32`
1952×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	178
1	170	102
2	1031	88
3	4753	88
0	8259	88

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1373

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 #s(literal 2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (log.f64 base))) (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)))
(neg.f64 (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)))
(neg.f64 (.f64 (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base)))
(/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 2 binary64)) (log.f64 base))
(/.f64 (log.f64 base) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
(/.f64 #s(literal -1 binary64) (/.f64 (.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
(/.f64 (/.f64 (log.f64 base) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base))) #s(literal 1 binary64))
(/.f64 (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (/.f64 (log.f64 base) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)) #s(literal -1 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) #s(literal -2 binary64))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (log.f64 base))) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (/.f64 #s(literal 1 binary64) (log.f64 base))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal -2 binary64))
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(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (log.f64 base))) (/.f64 #s(literal 2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
(neg.f64 (/.f64 #s(literal 2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
(/.f64 (log.f64 base) (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 #s(literal 2 binary64) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(/.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base))))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base)))) #s(literal -2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)))
(/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(/.f64 #s(literal -2 binary64) (neg.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base)))))
(/.f64 #s(literal -2 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base))))))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)))
(/.f64 #s(literal -1 binary64) (/.f64 (log.f64 base) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
(/.f64 (/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base))))
(/.f64 (/.f64 #s(literal 2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (-.f64 #s(literal 0 binary64) (log.f64 base)))
(/.f64 (/.f64 (.f64 #s(literal 2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (/.f64 (.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) #s(literal -1/2 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (/.f64 #s(literal 2 binary64) (log.f64 base)) (.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 re re) (*.f64 im im))))))
(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (log.f64 base))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/.f64 (neg.f64 (/.f64 #s(literal -2 binary64) (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 re re) (*.f64 im im)))))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(/.f64 (/.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (-.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 2 binary64) (log.f64 base)) #s(literal -1 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(pow.f64 (/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) #s(literal 1 binary64))
(pow.f64 (/.f64 (log.f64 base) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (neg.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base)))) #s(literal -2 binary64)) #s(literal -1 binary64))
(.f64 (log.f64 base) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -2 binary64))))
(.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (-.f64 #s(literal 0 binary64) (log.f64 base)))))
(.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (-.f64 #s(literal 0 binary64) (log.f64 base))))
(.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 re re) (*.f64 im im))))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(.f64 #s(literal -2 binary64) (.f64 (/.f64 #s(literal -1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))))
(.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(.f64 (/.f64 #s(literal -2 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(.f64 (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 #s(literal -2 binary64) (log.f64 base)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))) #s(literal -2 binary64))
(.f64 (/.f64 #s(literal 2 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))

simplify493.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

4176×	`-lowering-.f32`
4176×	`-lowering-.f64`
2758×	`+-lowering-+.f64`
2758×	`+-lowering-+.f32`
2182×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	586	5631
1	1790	4960
2	6064	4860
0	8401	4860

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

Inputs
(/ (log im) (log base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(* -1 (/ (log (/ 1 re)) (log base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(* -1 (/ (log (/ -1 re)) (log base)))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow im 6)) (* 90 (pow im 6))) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))
(/ (log re) (log base))
(+ (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(+ (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))) (/ (log re) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(* -1 (/ (log (/ -1 im)) (log base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (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 (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))))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (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))))
(log im)
(log im)
(log im)
(log im)
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(* -1 (/ (log (/ 1 im)) (pow (log base) (log (E)))))
(* -1 (/ (log (/ 1 im)) (pow (log base) (log (E)))))
(* -1 (/ (log (/ 1 im)) (pow (log base) (log (E)))))
(* -1 (/ (log (/ 1 im)) (pow (log base) (log (E)))))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) (log (E))))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) (log (E))))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) (log (E))))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (log base) (log (E))))
(/ (log im) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (log im) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (log im) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (log im) (pow (* -1 (log (/ 1 base))) (log (E))))
(/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E))))
(pow (log base) (log (E)))
(pow (log base) (log (E)))
(pow (log base) (log (E)))
(pow (log base) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (* -1 (log (/ 1 base))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) (log (E)))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
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Outputs
(/ (log im) (log base))
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(+.f64 (.f64 (.f64 im im) (-.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (log.f64 base) (.f64 re re)) (pow.f64 (log.f64 (.f64 re re)) #s(literal 2 binary64)))) (.f64 (.f64 im im) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 2 binary64)))))))) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (*.f64 re re))))
(- (* (pow im 2) (+ (* (pow im 2) (- (* (pow im 2) (- (+ (* 2/3 (/ 1 (* (pow re 6) (* (log base) (pow (log (pow re 2)) 2))))) (/ 1 (* (pow re 6) (* (log base) (pow (log (pow re 2)) 3))))) (* -1 (/ (+ (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 2)))) (* 2 (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 3)))))) (* (pow re 2) (log (pow re 2))))))) (+ (* 2 (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 3))))) (/ 1 (* (pow re 4) (* (log base) (pow (log (pow re 2)) 2))))))) (* 2 (/ 1 (* (pow re 2) (* (log base) (pow (log (pow re 2)) 2))))))) (* 2 (/ 1 (* (log base) (log (pow re 2))))))
(+.f64 (.f64 (.f64 im im) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (log.f64 base) (.f64 re re)) (pow.f64 (log.f64 (.f64 re re)) #s(literal 2 binary64)))) (.f64 im (.f64 im (-.f64 (.f64 (.f64 im im) (+.f64 (+.f64 (/.f64 #s(literal 2/3 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 6 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 2 binary64)))) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (pow.f64 (log.f64 (.f64 re re)) #s(literal 3 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 2 binary64))))) (.f64 (.f64 re re) (log.f64 (.f64 re re)))))) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (.f64 re re)) #s(literal 2 binary64)))))))))) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (.f64 re re))))
(/ 1 (* (log base) (log (/ 1 im))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal 1 binary64) im)))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))) (/ 1 (* (log base) (log (/ 1 im)))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (.f64 im (.f64 im (log.f64 base)))) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im)))
(- (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 2))))) (pow im 4))) (/ 1 (* (log base) (log (/ 1 im))))) (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))))
(-.f64 (-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (.f64 im (.f64 im (log.f64 base)))) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 im) #s(literal 3 binary64))))) (/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64)))) (pow.f64 im #s(literal 4 binary64))))
(- (+ (* -1 (/ (+ (* -1/6 (/ (pow re 6) (* (log base) (pow (log (/ 1 im)) 2)))) (+ (* 1/8 (/ (pow re 6) (* (log base) (pow (log (/ 1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 2)))))) (log (/ 1 im)))))) (pow im 6))) (/ 1 (* (log base) (log (/ 1 im))))) (+ (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ 1 im)) 3))))) (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ 1 im)) 2))))))))
(-.f64 (-.f64 (-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (.f64 im (.f64 im (log.f64 base)))) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))) (+.f64 (/.f64 (/.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (pow.f64 im #s(literal 4 binary64))) (log.f64 base)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 im) #s(literal 3 binary64)))) (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (.f64 (log.f64 base) (pow.f64 im #s(literal 4 binary64)))) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64))))) (/.f64 (+.f64 (/.f64 (/.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal -1/6 binary64)) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64))) (-.f64 (/.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal 1/8 binary64)) (.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 im) #s(literal 3 binary64))))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (.f64 (log.f64 base) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 im) #s(literal 3 binary64))))) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal 1 binary64) im)) #s(literal 2 binary64))))) (log.f64 im)))) (pow.f64 im #s(literal 6 binary64))))
(/ 1 (* (log base) (log (/ -1 im))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))
(+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (.f64 im (.f64 im (log.f64 base)))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2))))) (pow im 4))) (/ 1 (* (log base) (log (/ -1 im))))) (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))))
(-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (.f64 im (.f64 im (log.f64 base)))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (pow.f64 im #s(literal 4 binary64))))
(- (+ (* -1 (/ (+ (* -1/6 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 2)))) (+ (* 1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))))) (log (/ -1 im)))))) (pow im 6))) (/ 1 (* (log base) (log (/ -1 im))))) (+ (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))))))
(-.f64 (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (.f64 im (.f64 im (log.f64 base)))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (+.f64 (/.f64 (/.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (pow.f64 im #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (.f64 (log.f64 base) (pow.f64 im #s(literal 4 binary64)))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 re re) (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))))) (log.f64 (/.f64 #s(literal -1 binary64) im))) (+.f64 (/.f64 (.f64 #s(literal -1/6 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (pow.f64 im #s(literal 6 binary64))))
(/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ -2 (* (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (/.f64 #s(literal -2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(/.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (log.f64 base))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(/.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (log.f64 base))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(/.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (log.f64 base))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ 2 (* (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))
(/.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (log.f64 base))) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
(/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(/.f64 #s(literal -2 binary64) (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(/.f64 #s(literal -2 binary64) (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(/.f64 #s(literal -2 binary64) (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
(/ -2 (* (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))
(/.f64 #s(literal -2 binary64) (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))

eval368.0ms (2.7%)

Compiler: Compiled 60151 to 6371 computations (89.4% saved)

prune420.0ms (3.1%)

Pruning

30 alts after pruning (24 fresh and 6 done)

	Pruned	Kept	Total
New	2966	11	2977
Fresh	6	13	19
Picked	2	3	5
Done	0	3	3
Total	2974	30	3004

Accuracy

100.0%

Counts

3004 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
	50.0%	(/.f64 (/.f64 (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 base))
	49.8%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (*.f64 im im))) (log.f64 base))) (log.f64 base))
✓	50.0%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	26.7%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 (.f64 (log.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal -1 binary64))))))
	98.8%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
	98.8%	(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
✓	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	45.3%	(/.f64 (log.f64 im) (pow.f64 (.f64 (E.f64) (.f64 (E.f64) (E.f64))) (.f64 #s(literal 1/9 binary64) (.f64 #s(literal 3 binary64) (log.f64 (log.f64 base))))))
✓	45.8%	(/.f64 (log.f64 im) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
▶	99.1%	(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
✓	99.1%	(/.f64 (log.f64 im) (log.f64 base))
	46.0%	(/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base))))
	50.0%	(/.f64 (log.f64 base) (neg.f64 (.f64 (log.f64 base) (/.f64 (log.f64 base) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64))))))
	50.0%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))))
▶	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
	50.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	98.9%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 im)))
✓	98.8%	(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
▶	98.8%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im))) (log.f64 base))
▶	50.0%	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
	98.7%	(.f64 (/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -6 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
	98.9%	(*.f64 (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
	98.8%	(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 im))
	45.8%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))))) (log.f64 im))
✓	98.9%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
▶	70.0%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (exp.f64 (log.f64 (log.f64 im))))
	98.8%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal -3 binary64))) (log.f64 im))
	98.8%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) (log.f64 base))
	54.5%	(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 im))) #s(literal -1 binary64)))

Compiler

Compiled 852 to 610 computations (28.4% saved)

simplify438.0ms (3.2%)

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	128	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
✓	cost-diff	13184	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im)))
✓	cost-diff	13184	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im))) (log.f64 base))
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	cost-diff	12800	(exp.f64 (log.f64 (log.f64 im)))
✓	cost-diff	12928	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (exp.f64 (log.f64 (log.f64 im))))
✓	cost-diff	0	(log.f64 im)
✓	cost-diff	0	(log.f64 base)
✓	cost-diff	0	(/.f64 (log.f64 base) (log.f64 im))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
✓	cost-diff	0	(log.f64 im)
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))
✓	cost-diff	256	(log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base)))
✓	cost-diff	256	(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))

Rules

3112×	`-lowering-.f32`
3112×	`-lowering-.f64`
2088×	`/-lowering-/.f32`
2088×	`/-lowering-/.f64`
1756×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	158
1	62	151
2	156	145
3	686	145
4	3477	145
5	6591	145
0	8281	145

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (log im) (log (/ 1 (/ 1 base))))
(log im)
im
(log (/ 1 (/ 1 base)))
(/ 1 (/ 1 base))
1
(/ 1 base)
base
(/ 1 (/ (log base) (log im)))
1
(/ (log base) (log im))
(log base)
base
(log im)
im
(* (/ 1 (log base)) (exp (log (log im))))
(/ 1 (log base))
1
(log base)
base
(exp (log (log im)))
(log (log im))
(log im)
im
(* (/ (/ 1 (log base)) (/ (log base) (log im))) (log base))
(/ (/ 1 (log base)) (/ (log base) (log im)))
(/ 1 (log base))
1
(log base)
base
(/ (log base) (log im))
(log im)
im
(* (/ (/ 1 (log base)) (* (/ 2 (log (+ (* re re) (* im im)))) (log base))) (log base))
(/ (/ 1 (log base)) (* (/ 2 (log (+ (* re re) (* im im)))) (log base)))
(/ 1 (log base))
1
(log base)
base
(* (/ 2 (log (+ (* re re) (* im im)))) (log base))
(/ 2 (log (+ (* re re) (* im im))))
2
(log (+ (* re re) (* im im)))
(+ (* re re) (* im im))
(* re re)
re
(* im im)
im

Outputs
(/ (log im) (log (/ 1 (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(log im)
(log.f64 im)
im
(log (/ 1 (/ 1 base)))
(log.f64 base)
(/ 1 (/ 1 base))
base
1
#s(literal 1 binary64)
(/ 1 base)
(/.f64 #s(literal 1 binary64) base)
base
(/ 1 (/ (log base) (log im)))
(/.f64 (log.f64 im) (log.f64 base))
1
#s(literal 1 binary64)
(/ (log base) (log im))
(/.f64 (log.f64 base) (log.f64 im))
(log base)
(log.f64 base)
base
(log im)
(log.f64 im)
im
(* (/ 1 (log base)) (exp (log (log im))))
(/.f64 (log.f64 im) (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
(exp (log (log im)))
(log.f64 im)
(log (log im))
(log.f64 (log.f64 im))
(log im)
(log.f64 im)
im
(* (/ (/ 1 (log base)) (/ (log base) (log im))) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(/ (/ 1 (log base)) (/ (log base) (log im)))
(/.f64 (log.f64 im) (*.f64 (log.f64 base) (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
(/ (log base) (log im))
(/.f64 (log.f64 base) (log.f64 im))
(log im)
(log.f64 im)
im
(* (/ (/ 1 (log base)) (* (/ 2 (log (+ (* re re) (* im im)))) (log base))) (log base))
(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (*.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (/ 1 (log base)) (* (/ 2 (log (+ (* re re) (* im im)))) (log base)))
(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (.f64 (log.f64 base) (.f64 (log.f64 base) #s(literal 2 binary64))))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
1
#s(literal 1 binary64)
(log base)
(log.f64 base)
base
(* (/ 2 (log (+ (* re re) (* im im)))) (log base))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
(/ 2 (log (+ (* re re) (* im im))))
(/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
2
#s(literal 2 binary64)
(log (+ (* re re) (* im im)))
(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
(+ (* re re) (* im im))
(+.f64 (.f64 re re) (.f64 im im))
(* re re)
(*.f64 re re)
re
(* im im)
(*.f64 im im)
im

localize189.0ms (1.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.6%	(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
✓	accuracy	55.7%	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.6%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im))) (log.f64 base))
✓	accuracy	99.5%	(/.f64 (log.f64 base) (log.f64 im))
✓	accuracy	99.9%	(log.f64 (log.f64 im))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (log.f64 base))
✓	accuracy	99.5%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (exp.f64 (log.f64 (log.f64 im))))
✓	accuracy	98.8%	(exp.f64 (log.f64 (log.f64 im)))
✓	accuracy	100.0%	(log.f64 im)
✓	accuracy	100.0%	(log.f64 base)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
✓	accuracy	99.5%	(/.f64 (log.f64 base) (log.f64 im))
✓	accuracy	100.0%	(log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base)))
✓	accuracy	100.0%	(log.f64 im)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))
✓	accuracy	99.6%	(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))

Results

109.0ms	183×	0	valid
32.0ms	73×	0	invalid

Compiler

Compiled 211 to 28 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-log: 22.0ms (40.5% of total)

ival-div: 16.0ms (29.5% of total)

ival-mult: 11.0ms (20.3% of total)

ival-exp: 4.0ms (7.4% of total)

ival-add: 1.0ms (1.8% of total)

const: 1.0ms (1.8% of total)

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

series91.0ms (0.7%)

Counts

17 → 360

Calls

Call 1

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

Outputs
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (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 base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt base>
#<alt (log im)>
#<alt (log im)>
#<alt (log im)>
#<alt (log im)>
#<alt (* -1 (log (/ 1 im)))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (log base) (log im))>
#<alt (/ (log base) (log im))>
#<alt (/ (log base) (log im))>
#<alt (/ (log base) (log im))>
#<alt (* -1 (/ (log (/ 1 base)) (log im)))>
#<alt (* -1 (/ (log (/ 1 base)) (log im)))>
#<alt (* -1 (/ (log (/ 1 base)) (log im)))>
#<alt (* -1 (/ (log (/ 1 base)) (log im)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log im))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log im))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log im))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log im))>
#<alt (/ (log base) (log im))>
#<alt (/ (log base) (log im))>
#<alt (/ (log base) (log im))>
#<alt (/ (log base) (log im))>
#<alt (* -1 (/ (log base) (log (/ 1 im))))>
#<alt (* -1 (/ (log base) (log (/ 1 im))))>
#<alt (* -1 (/ (log base) (log (/ 1 im))))>
#<alt (* -1 (/ (log base) (log (/ 1 im))))>
#<alt (/ (log base) (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (/ (log base) (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (/ (log base) (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (/ (log base) (+ (log -1) (* -1 (log (/ -1 im)))))>
#<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 im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (log im)>
#<alt (log im)>
#<alt (log im)>
#<alt (log im)>
#<alt (* -1 (log (/ 1 im)))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (* -1 (log (/ 1 im)))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<alt (+ (log -1) (* -1 (log (/ -1 im))))>
#<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 im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (* -1 (/ (log im) (log (/ 1 base))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (/ (log im) (log base))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log (/ 1 base)) 2))>
#<alt (/ (log im) (pow (log (/ 1 base)) 2))>
#<alt (/ (log im) (pow (log (/ 1 base)) 2))>
#<alt (/ (log im) (pow (log (/ 1 base)) 2))>
#<alt (/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (log im) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (/ (log im) (pow (log base) 2))>
#<alt (* -1 (/ (log (/ 1 im)) (pow (log base) 2)))>
#<alt (* -1 (/ (log (/ 1 im)) (pow (log base) 2)))>
#<alt (* -1 (/ (log (/ 1 im)) (pow (log base) 2)))>
#<alt (* -1 (/ (log (/ 1 im)) (pow (log base) 2)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (log base)))>
#<alt (* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (* -1/2 (/ (log (+ (pow im 2) (pow re 2))) (log (/ 1 base))))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (+ (log -1) (* -1 (log (/ -1 base))))))>
#<alt (* 1/2 (/ (log (pow im 2)) (log base)))>
#<alt (+ (* 1/2 (/ (log (pow im 2)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))>
#<alt (+ (* 1/2 (/ (log (pow im 2)) (log base))) (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))))>
#<alt (+ (* 1/2 (/ (log (pow im 2)) (log base))) (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))))>
#<alt (* -1 (/ (log (/ 1 re)) (log base)))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/6 (/ (pow im 6) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))>
#<alt (* -1 (/ (log (/ -1 re)) (log base)))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (+ (* 1/6 (/ (pow im 6) (* (pow re 6) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))))>
#<alt (* 1/2 (/ (log (pow re 2)) (log base)))>
#<alt (+ (* 1/2 (/ (log (pow re 2)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))>
#<alt (+ (* 1/2 (/ (log (pow re 2)) (log base))) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (log base)))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))))>
#<alt (+ (* 1/2 (/ (log (pow re 2)) (log base))) (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (log base)))) (* 1/4 (/ 1 (* (pow re 4) (log base)))))) (* 1/2 (/ 1 (* (pow re 2) (log base)))))))>
#<alt (* -1 (/ (log (/ 1 im)) (log base)))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))>
#<alt (* -1 (/ (log (/ -1 im)) (log base)))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (log base)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (log base)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log base) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log base) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log base) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log base) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log (/ 1 base)) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log (/ 1 base)) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log (/ 1 base)) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (log (/ 1 base)) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)))>
#<alt (* 1/2 (/ (log (+ (pow im 2) (pow re 2))) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)))>
#<alt (* 1/2 (/ (log (pow im 2)) (pow (log base) 2)))>
#<alt (+ (* 1/2 (/ (log (pow im 2)) (pow (log base) 2))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))>
#<alt (+ (* 1/2 (/ (log (pow im 2)) (pow (log base) 2))) (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (pow (log base) 2)))) (* 1/2 (/ 1 (* (pow im 2) (pow (log base) 2)))))))>
#<alt (+ (* 1/2 (/ (log (pow im 2)) (pow (log base) 2))) (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (pow (log base) 2)))) (* 1/4 (/ 1 (* (pow im 4) (pow (log base) 2)))))) (* 1/2 (/ 1 (* (pow im 2) (pow (log base) 2)))))))>
#<alt (* -1 (/ (log (/ 1 re)) (pow (log base) 2)))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (pow (log base) 2))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2)))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (pow (log base) 2))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (pow (log base) 2)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2))))))>
#<alt (+ (* -1 (/ (log (/ 1 re)) (pow (log base) 2))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (pow (log base) 2)))) (+ (* 1/6 (/ (pow im 6) (* (pow re 6) (pow (log base) 2)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2)))))))>
#<alt (* -1 (/ (log (/ -1 re)) (pow (log base) 2)))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (pow (log base) 2))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2)))))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (pow (log base) 2))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (pow (log base) 2)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2))))))>
#<alt (+ (* -1 (/ (log (/ -1 re)) (pow (log base) 2))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (pow (log base) 2)))) (+ (* 1/6 (/ (pow im 6) (* (pow re 6) (pow (log base) 2)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2)))))))>
#<alt (* 1/2 (/ (log (pow re 2)) (pow (log base) 2)))>
#<alt (+ (* 1/2 (/ (log (pow re 2)) (pow (log base) 2))) (* 1/2 (/ (pow im 2) (* (pow re 2) (pow (log base) 2)))))>
#<alt (+ (* 1/2 (/ (log (pow re 2)) (pow (log base) 2))) (* (pow im 2) (+ (* -1/4 (/ (pow im 2) (* (pow re 4) (pow (log base) 2)))) (* 1/2 (/ 1 (* (pow re 2) (pow (log base) 2)))))))>
#<alt (+ (* 1/2 (/ (log (pow re 2)) (pow (log base) 2))) (* (pow im 2) (+ (* (pow im 2) (- (* 1/6 (/ (pow im 2) (* (pow re 6) (pow (log base) 2)))) (* 1/4 (/ 1 (* (pow re 4) (pow (log base) 2)))))) (* 1/2 (/ 1 (* (pow re 2) (pow (log base) 2)))))))>
#<alt (* -1 (/ (log (/ 1 im)) (pow (log base) 2)))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (pow (log base) 2))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2))))))>
#<alt (+ (* -1 (/ (log (/ 1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))))>
#<alt (* -1 (/ (log (/ -1 im)) (pow (log base) 2)))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2))))))>
#<alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (+ (* 1/6 (/ (pow re 6) (* (pow im 6) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))))>
#<alt (log (log im))>
#<alt (log (log im))>
#<alt (log (log im))>
#<alt (log (log im))>
#<alt (log (* -1 (log (/ 1 im))))>
#<alt (log (* -1 (log (/ 1 im))))>
#<alt (log (* -1 (log (/ 1 im))))>
#<alt (log (* -1 (log (/ 1 im))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (log (+ (log -1) (* -1 (log (/ -1 im)))))>
#<alt (log (pow im 2))>
#<alt (+ (log (pow im 2)) (/ (pow re 2) (pow im 2)))>
#<alt (+ (log (pow im 2)) (* (pow re 2) (+ (* -1/2 (/ (pow re 2) (pow im 4))) (/ 1 (pow im 2)))))>
#<alt (+ (log (pow im 2)) (* (pow re 2) (+ (* (pow re 2) (- (* 1/3 (/ (pow re 2) (pow im 6))) (* 1/2 (/ 1 (pow im 4))))) (/ 1 (pow im 2)))))>
#<alt (* -2 (log (/ 1 re)))>
#<alt (+ (* -2 (log (/ 1 re))) (/ (pow im 2) (pow re 2)))>
#<alt (+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -2 (log (/ 1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))>
#<alt (* -2 (log (/ -1 re)))>
#<alt (+ (* -2 (log (/ -1 re))) (/ (pow im 2) (pow re 2)))>
#<alt (+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (/ (pow im 2) (pow re 2))))>
#<alt (+ (* -2 (log (/ -1 re))) (+ (* -1/2 (/ (pow im 4) (pow re 4))) (+ (* 1/3 (/ (pow im 6) (pow re 6))) (/ (pow im 2) (pow re 2)))))>
#<alt (log (pow re 2))>
#<alt (+ (log (pow re 2)) (/ (pow im 2) (pow re 2)))>
#<alt (+ (log (pow re 2)) (* (pow im 2) (+ (* -1/2 (/ (pow im 2) (pow re 4))) (/ 1 (pow re 2)))))>
#<alt (+ (log (pow re 2)) (* (pow im 2) (+ (* (pow im 2) (- (* 1/3 (/ (pow im 2) (pow re 6))) (* 1/2 (/ 1 (pow re 4))))) (/ 1 (pow re 2)))))>
#<alt (* -2 (log (/ 1 im)))>
#<alt (+ (* -2 (log (/ 1 im))) (/ (pow re 2) (pow im 2)))>
#<alt (+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -2 (log (/ 1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))>
#<alt (* -2 (log (/ -1 im)))>
#<alt (+ (* -2 (log (/ -1 im))) (/ (pow re 2) (pow im 2)))>
#<alt (+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (/ (pow re 2) (pow im 2))))>
#<alt (+ (* -2 (log (/ -1 im))) (+ (* -1/2 (/ (pow re 4) (pow im 4))) (+ (* 1/3 (/ (pow re 6) (pow im 6))) (/ (pow re 2) (pow im 2)))))>
#<alt (* 2 (/ (log base) (log (pow im 2))))>
#<alt (+ (* -2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* 2 (/ (log base) (log (pow im 2)))))>
#<alt (+ (* 2 (/ (log base) (log (pow im 2)))) (* (pow re 2) (+ (* -2 (* (pow re 2) (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2))))))) (* -2 (/ (log base) (* (pow im 2) (pow (log (pow im 2)) 2)))))))>
#<alt (+ (* 2 (/ (log base) (log (pow im 2)))) (* (pow re 2) (+ (* -2 (/ (log base) (* (pow im 2) (pow (log (pow im 2)) 2)))) (* (pow re 2) (+ (* -2 (* (pow re 2) (+ (* -1 (/ (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2))))) (* (pow im 2) (log (pow im 2))))) (+ (* 1/3 (/ (log base) (* (pow im 6) (pow (log (pow im 2)) 2)))) (* 1/2 (/ (log base) (* (pow im 6) (pow (log (pow im 2)) 3)))))))) (* -2 (+ (* -1 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 3)))) (* -1/2 (/ (log base) (* (pow im 4) (pow (log (pow im 2)) 2)))))))))))>
#<alt (* -1 (/ (log base) (log (/ 1 re))))>
#<alt (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3)))) (pow re 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow im 6) (log base)) (pow (log (/ 1 re)) 3))) (+ (* 1/12 (/ (* (pow im 6) (log base)) (pow (log (/ 1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ 1 re)) 3))))) (log (/ 1 re)))))) (pow re 6))) (+ (* -1 (/ (log base) (log (/ 1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ 1 re)) 2)))))))>
#<alt (* -1 (/ (log base) (log (/ -1 re))))>
#<alt (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3)))) (pow re 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow im 6) (log base)) (pow (log (/ -1 re)) 3))) (+ (* 1/12 (/ (* (pow im 6) (log base)) (pow (log (/ -1 re)) 2))) (* 1/2 (/ (* (pow im 2) (+ (* -1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 2))) (* 1/8 (/ (* (pow im 4) (log base)) (pow (log (/ -1 re)) 3))))) (log (/ -1 re)))))) (pow re 6))) (+ (* -1 (/ (log base) (log (/ -1 re)))) (* -1/2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (/ -1 re)) 2)))))))>
#<alt (* 2 (/ (log base) (log (pow re 2))))>
#<alt (+ (* -2 (/ (* (pow im 2) (log base)) (* (pow re 2) (pow (log (pow re 2)) 2)))) (* 2 (/ (log base) (log (pow re 2)))))>
#<alt (+ (* 2 (/ (log base) (log (pow re 2)))) (* (pow im 2) (+ (* -2 (* (pow im 2) (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2))))))) (* -2 (/ (log base) (* (pow re 2) (pow (log (pow re 2)) 2)))))))>
#<alt (+ (* 2 (/ (log base) (log (pow re 2)))) (* (pow im 2) (+ (* -2 (/ (log base) (* (pow re 2) (pow (log (pow re 2)) 2)))) (* (pow im 2) (+ (* -2 (* (pow im 2) (+ (* -1 (/ (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2))))) (* (pow re 2) (log (pow re 2))))) (+ (* 1/3 (/ (log base) (* (pow re 6) (pow (log (pow re 2)) 2)))) (* 1/2 (/ (log base) (* (pow re 6) (pow (log (pow re 2)) 3)))))))) (* -2 (+ (* -1 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 3)))) (* -1/2 (/ (log base) (* (pow re 4) (pow (log (pow re 2)) 2)))))))))))>
#<alt (* -1 (/ (log base) (log (/ 1 im))))>
#<alt (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3))))) (log (/ 1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2)))))))>
#<alt (* -1 (/ (log base) (log (/ -1 im))))>
#<alt (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))))>
#<alt (+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>
#<alt (* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))>

Calls

90 calls:

Time	Variable		Point	Expression
32.0ms	im	@	inf	(log (log im))
32.0ms	im	@	-inf	(log (log im))
14.0ms	im	@	0	(log (log im))
2.0ms	im	@	0	(* (/ 1 (log base)) (exp (log (log im))))
1.0ms	im	@	-inf	(/ (log base) (log im))

rewrite1.0s (7.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3614×	`/-lowering-/.f32`
3614×	`/-lowering-/.f64`
2752×	`-lowering-.f32`
2752×	`-lowering-.f64`
1208×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	99
1	124	90
2	612	86
3	3805	86
0	8535	86

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1571

Calls

Call 1

Inputs
(/ (log im) (log (/ 1 (/ 1 base))))
(log (/ 1 (/ 1 base)))
(/ 1 (/ 1 base))
(log im)
(/ 1 (/ (log base) (log im)))
(/ (log base) (log im))
(log base)
(* (/ 1 (log base)) (exp (log (log im))))
(exp (log (log im)))
(/ 1 (log base))
(* (/ (/ 1 (log base)) (/ (log base) (log im))) (log base))
(/ (/ 1 (log base)) (/ (log base) (log im)))
(* (/ (/ 1 (log base)) (* (/ 2 (log (+ (* re re) (* im im)))) (log base))) (log base))
(/ (/ 1 (log base)) (* (/ 2 (log (+ (* re re) (* im im)))) (log base)))
(log (log im))
(log (+ (* re re) (* im im)))
(* (/ 2 (log (+ (* re re) (* im im)))) (log base))

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

simplify405.0ms (3%)

Algorithm

1×	egg-herbie

Rules

4984×	`-lowering-.f32`
4984×	`-lowering-.f64`
2352×	`/-lowering-/.f32`
2352×	`/-lowering-/.f64`
2002×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	518	5168
1	1606	4578
2	5902	4464
0	8270	4464

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (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))))
base
base
base
base
base
base
base
base
base
base
base
base
(log im)
(log im)
(log im)
(log im)
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(* -1 (log (/ 1 im)))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(* -1 (/ (log (/ 1 im)) (log base)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/ (log base) (log im))
(/ (log base) (log im))
(/ (log base) (log im))
(/ (log base) (log im))
(* -1 (/ (log (/ 1 base)) (log im)))
(* -1 (/ (log (/ 1 base)) (log im)))
(* -1 (/ (log (/ 1 base)) (log im)))
(* -1 (/ (log (/ 1 base)) (log im)))
(/ (+ (log -1) (* -1 (log (/ -1 base)))) (log im))
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(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2))))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ 1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ 1 im)) 3))))) (log (/ 1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ 1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ 1 im)) 2)))))))
(* -1 (/ (log base) (log (/ -1 im))))
(+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))

Outputs
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log im) (log base))
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(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (log base))
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(/ (log im) (log base))
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base
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(/ (log im) (log base))
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(-.f64 (/.f64 (/.f64 (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 re re)) (.f64 im im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))))
(+.f64 (/.f64 (/.f64 (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 re re)) (.f64 im im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (-.f64 (/.f64 (.f64 #s(literal -2 binary64) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (*.f64 #s(literal 1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (pow.f64 im #s(literal 4 binary64))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im)))))
(+ (* -2 (/ (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3)))) (pow im 4))) (+ (* -2 (/ (+ (* -1/16 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/12 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 2))) (* 1/2 (/ (* (pow re 2) (+ (* -1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 2))) (* 1/8 (/ (* (pow re 4) (log base)) (pow (log (/ -1 im)) 3))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))
(+.f64 (-.f64 (/.f64 (/.f64 (.f64 (.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 re re)) (.f64 im im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im)))) (.f64 #s(literal -2 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64)))) (pow.f64 im #s(literal 4 binary64))) (/.f64 (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 (.f64 #s(literal 1/12 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) im))))) (pow.f64 im #s(literal 6 binary64))))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (log base) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* -2 (/ (log (/ 1 base)) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))
(* 2 (/ (+ (log -1) (* -1 (log (/ -1 base)))) (log (+ (pow im 2) (pow re 2)))))
(/.f64 (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64)) (log.f64 (+.f64 (.f64 im im) (*.f64 re re))))

eval523.0ms (3.8%)

Compiler: Compiled 52782 to 4764 computations (91% saved)

prune380.0ms (2.8%)

Pruning

30 alts after pruning (21 fresh and 9 done)

	Pruned	Kept	Total
New	2743	11	2754
Fresh	9	10	19
Picked	1	4	5
Done	1	5	6
Total	2754	30	2784

Accuracy

100.0%

Counts

2784 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
	98.8%	(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
	99.0%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
✓	50.0%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	98.8%	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
	98.8%	(/.f64 (neg.f64 (*.f64 (log.f64 im) (log.f64 base))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
✓	99.4%	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
✓	45.8%	(/.f64 (log.f64 im) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
✓	99.1%	(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
✓	99.1%	(/.f64 (log.f64 im) (log.f64 base))
	46.0%	(/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base))))
	50.0%	(/.f64 (log.f64 base) (neg.f64 (.f64 (log.f64 base) (/.f64 (log.f64 base) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64))))))
	98.7%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (*.f64 (log.f64 im) (log.f64 base))))
	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 im)) (log.f64 base)))
	98.7%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (log.f64 im) (log.f64 base)) (pow.f64 (log.f64 im) #s(literal 2 binary64))))
✓	98.9%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
	50.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
	98.9%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 im) (log.f64 base)))
✓	98.8%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im))) (log.f64 base))
	98.9%	(*.f64 (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
	98.8%	(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 im))
	45.8%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))))) (log.f64 im))
✓	98.9%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
✓	70.0%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (exp.f64 (log.f64 (log.f64 im))))
	98.8%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) (log.f64 base))
	54.5%	(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 im))) #s(literal -1 binary64)))
	54.5%	(exp.f64 (log.f64 (/.f64 (log.f64 im) (log.f64 base))))

Compiler

Compiled 1314 to 503 computations (61.7% saved)

regimes132.0ms (1%)

Counts

64 → 1

Calls

Call 1

Inputs
(/.f64 (log.f64 im) (log.f64 base))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
(/.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
(/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(exp.f64 (log.f64 (/.f64 (log.f64 im) (log.f64 base))))
(/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base))))
(/.f64 (log.f64 im) (pow.f64 (E.f64) (log.f64 (log.f64 base))))
(exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 im))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (exp.f64 (log.f64 (log.f64 im))))
(.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) (log.f64 base))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 im))
(*.f64 (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 im)))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 im) (log.f64 base)))
(/.f64 (*.f64 (log.f64 im) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (log.f64 im) (log.f64 base)) (pow.f64 (log.f64 im) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 im)) (log.f64 base)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (*.f64 (log.f64 im) (log.f64 base))))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 im))) (log.f64 base))
(/.f64 (neg.f64 (*.f64 (log.f64 im) (log.f64 base))) (/.f64 #s(literal -1 binary64) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(exp.f64 (log.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))))
(/.f64 (.f64 (log.f64 im) (log.f64 base)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (log.f64 im) (pow.f64 (.f64 (E.f64) (.f64 (E.f64) (E.f64))) (.f64 #s(literal 1/9 binary64) (.f64 #s(literal 3 binary64) (log.f64 (log.f64 base))))))
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (*.f64 im im))) (log.f64 base))) (log.f64 base))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 base))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base)))
(/.f64 (log.f64 base) (neg.f64 (.f64 (log.f64 base) (/.f64 (log.f64 base) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -1/2 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 (.f64 (log.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal -1 binary64))))))
(/.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 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)) (.f64 (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 base))
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 (/.f64 #s(literal -2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))) (log.f64 base))
(/.f64 (/.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 base))
(/.f64 (/.f64 (/.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) #s(literal -2 binary64)) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (log.f64 base))
(/.f64 (log.f64 (hypot.f64 re im)) (exp.f64 (log.f64 (log.f64 base))))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal -3 binary64))) (log.f64 im))
(/.f64 (log.f64 im) (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (log.f64 im) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log.f64 (log.f64 base))))) (log.f64 im))
(/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(.f64 (/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -6 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 base))
(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -2 binary64) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (pow.f64 (log.f64 base) #s(literal 2 binary64))))))
(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (log.f64 (hypot.f64 re im)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (log.f64 base))))))
(/.f64 (log.f64 (pow.f64 (exp.f64 (/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 base))) (log.f64 (/.f64 #s(literal 1 binary64) base)))) (log.f64 base))
(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (exp.f64 (log.f64 (log.f64 base)))) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))

Outputs
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Calls

5 calls:

51.0ms	base
21.0ms	im
18.0ms	(log.f64 base)
18.0ms	re
18.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))

Results

Accuracy	Segments	Branch
99.4%	1	`re`
99.4%	1	`im`
99.4%	1	`base`
99.4%	1	`(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))`
99.4%	1	`(log.f64 base)`

Compiler

Compiled 48 to 31 computations (35.4% saved)

regimes21.0ms (0.2%)

Counts

14 → 1

Calls

Call 1

Inputs
(/.f64 (log.f64 im) (log.f64 base))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 1 binary64) (log.f64 im)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (/.f64 #s(literal 1 binary64) (log.f64 base))))
(.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
(/.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 im))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
(/.f64 (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (/.f64 #s(literal 2 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) #s(literal 2 binary64))))

Outputs
(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))

Calls

4 calls:

6.0ms	im
5.0ms	re
5.0ms	(log.f64 base)
5.0ms	base

Results

Accuracy	Segments	Branch
99.1%	1	`re`
99.1%	1	`im`
99.1%	1	`base`
99.1%	1	`(log.f64 base)`

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes10.0ms (0.1%)

Accuracy

Total -0.4b remaining (-69.1%)

Threshold costs -0.4b (-69.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 (log.f64 im) (log.f64 base))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 im))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))

Outputs
(/.f64 (log.f64 im) (log.f64 base))

Calls

4 calls:

3.0ms	(log.f64 base)
2.0ms	base
2.0ms	re
2.0ms	im

Results

Accuracy	Segments	Branch
99.1%	1	`re`
99.1%	1	`im`
99.1%	1	`base`
99.1%	1	`(log.f64 base)`

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	17	21

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
(/.f64 (log.f64 im) (log.f64 base))

Outputs
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/.f64 (log.f64 im) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) base))))
(/.f64 (log.f64 im) (log.f64 base))

soundness1.1s (7.8%)

Rules

4436×	`-lowering-.f32`
4436×	`-lowering-.f64`
4332×	`-lowering-.f32`
4332×	`-lowering-.f64`
3660×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	362	4474
1	1118	3758
2	3856	3658
0	8092	3658
0	18	12
1	33	11
2	42	11
3	54	9
4	63	7
5	65	7
6	118	7
7	334	7
8	1447	7
9	2552	7
10	3732	7
11	3941	7
12	4230	7
13	4638	7
14	5161	7
15	6434	7
16	6861	7
17	7091	7
18	7262	7
19	7432	7
20	7626	7
0	8394	7
0	29	138
1	122	92
2	664	90
3	3439	90
0	8290	90

Stop Event

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

Compiler

Compiled 82 to 56 computations (31.7% saved)

preprocess35.0ms (0.3%)

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 230 to 148 computations (35.7% saved)

analyze239.0ms (1.8%)

sample2.0s (14.7%)

preprocess321.0ms (2.4%)

explain271.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify528.0ms (3.9%)

localize126.0ms (0.9%)

series92.0ms (0.7%)

rewrite321.0ms (2.4%)

simplify330.0ms (2.4%)

eval238.0ms (1.7%)

prune177.0ms (1.3%)

simplify226.0ms (1.7%)

localize209.0ms (1.5%)

series195.0ms (1.4%)

rewrite426.0ms (3.1%)

simplify477.0ms (3.5%)

eval444.0ms (3.3%)

prune380.0ms (2.8%)

simplify214.0ms (1.6%)

localize282.0ms (2.1%)

series213.0ms (1.6%)

rewrite291.0ms (2.1%)

simplify493.0ms (3.6%)

eval368.0ms (2.7%)

prune420.0ms (3.1%)

simplify438.0ms (3.2%)

localize189.0ms (1.4%)

series91.0ms (0.7%)

rewrite1.0s (7.6%)

simplify405.0ms (3%)

eval523.0ms (3.8%)

prune380.0ms (2.8%)

regimes132.0ms (1%)

regimes21.0ms (0.2%)

regimes10.0ms (0.1%)

simplify8.0ms (0.1%)

soundness1.1s (7.8%)

preprocess35.0ms (0.3%)

end0.0ms (0%)

Profiling