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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze166.0ms (1.6%)

Memory

0.7MiB live, 157.1MiB allocated

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
34.4%	17.2%	32.8%	0.1%	0%	49.9%	0%	7
42.2%	21.1%	28.9%	0.1%	0%	49.9%	0%	8
46.1%	23%	26.9%	0.1%	0%	49.9%	0%	9
69.1%	34.5%	15.4%	0.1%	0%	49.9%	0%	10
72.1%	36%	13.9%	0.1%	0%	49.9%	0%	11
73.5%	36.7%	13.2%	0.1%	0%	49.9%	0%	12

Compiler

Compiled 30 to 17 computations (43.3% saved)

sample2.0s (19.9%)

Memory

38.1MiB live, 2 605.0MiB allocated

Samples

1.4s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-log: 377.0ms (33% of total)

ival-mult: 288.0ms (25.2% of total)

ival-hypot: 226.0ms (19.8% of total)

ival-add: 97.0ms (8.5% of total)

ival-atan2: 84.0ms (7.4% of total)

ival-div: 52.0ms (4.6% of total)

ival-true: 7.0ms (0.6% of total)

exact: 6.0ms (0.5% of total)

ival-assert: 4.0ms (0.4% of total)

Bogosity

explain502.0ms (5%)

Memory

-29.1MiB live, 352.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
132	-	1	(1.6883276826975982e-155 1.9433993967199346e-208 4.343389803482682e+298)	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	0	-	`(log.f64 base)`
0	-	0	-	`(*.f64 re re)`
0	-	0	-	`(atan2.f64 im re)`
0	-	0	-	`im`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	0	-	`re`
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	-	`(/.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	-	`#s(literal 0 binary64)`
0	-	0	-	`(*.f64 (atan2.f64 im re) #s(literal 0 binary64))`
0	-	0	-	`(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))`
0	-	0	-	`(*.f64 (log.f64 base) (log.f64 base))`
0	-	0	-	`(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))`
0	-	0	-	`(*.f64 im im)`
0	-	0	-	`base`
0	-	0	-	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	oflow-rescue	118	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	118
↳	`(*.f64 re re)`	overflow	68
↳	`(*.f64 im im)`	overflow	66
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	uflow-rescue	13	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	13
↳	`(*.f64 re re)`	underflow	62
↳	`(*.f64 im im)`	underflow	56

Confusion

	Predicted +	Predicted -
+	131	0
-	0	125

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	0	0	125

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	125
1	131

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

142.0ms

512×

valid

Compiler

Compiled 389 to 76 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-log: 46.0ms (38.6% of total)

ival-hypot: 42.0ms (35.3% of total)

ival-mult: 15.0ms (12.6% of total)

ival-add: 7.0ms (5.9% of total)

ival-atan2: 5.0ms (4.2% of total)

ival-div: 3.0ms (2.5% of total)

ival-true: 1.0ms (0.8% of total)

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

exact: 0.0ms (0% of total)

preprocess386.0ms (3.8%)

Memory

32.5MiB live, 255.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	189
1	144	171
2	238	171
3	459	125
4	851	113
5	1590	113
6	4794	113
7	7463	113
0	18	26
0	34	20
1	43	18
2	48	18
3	58	14
4	67	12
5	68	12
6	121	12
7	325	12
8	1198	12
9	1934	12
10	2395	12
11	2701	12
12	3169	12
13	3904	12
14	4909	12
15	6035	12
16	6376	12
17	6583	12
18	6778	12
19	6985	12
0	8478	7

Stop Event

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

Calls

Call 1

Inputs

(/.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))))

Outputs

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

Symmetry

(abs im)

(abs re)

(sort re im)

Compiler

Compiled 28 to 18 computations (35.7% saved)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune50.0ms (0.5%)

Memory

-35.7MiB live, 3.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.1%	(/.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))))

Status

Accuracy

Program

▶

50.1%

(/.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))))

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify210.0ms (2.1%)

Memory

3.9MiB live, 105.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	192	(+.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	320	(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
cost-diff	6784	(*.f64 (atan2.f64 im re) #s(literal 0 binary64))
cost-diff	13440	(/.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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	113
0	34	95
1	43	93
2	48	93
3	58	89
4	67	87
5	68	87
6	121	87
7	325	87
8	1198	87
9	1934	87
10	2395	87
11	2701	87
12	3169	87
13	3904	87
14	4909	87
15	6035	87
16	6376	87
17	6583	87
18	6778	87
19	6985	87
0	8478	61

Stop Event

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

Calls

Call 1

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

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

localize98.0ms (1%)

Memory

3.9MiB live, 80.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.31478500976844204	(/.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	0.4030075195368841	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
accuracy	0.537441259768442	(*.f64 (log.f64 base) (log.f64 base))
accuracy	30.481914682494956	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Samples

86.0ms

256×

valid

Compiler

Compiled 240 to 38 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-atan2: 28.0ms (37.7% of total)

ival-log: 28.0ms (37.7% of total)

ival-mult: 7.0ms (9.4% of total)

ival-hypot: 5.0ms (6.7% of total)

ival-add: 3.0ms (4% of total)

ival-div: 2.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series179.0ms (1.8%)

Memory

-1.8MiB live, 197.0MiB allocated

Counts

7 → 168

Calls

Call 1

Inputs
#s(alt (/.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)))) (patch (/.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)))) #<representation binary64>) () ())
#s(alt (.f64 (atan2.f64 im re) #s(literal 0 binary64)) (patch (.f64 (atan2.f64 im re) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (patch (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (+.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))) (patch (+.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))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())

Outputs
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.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)))) (patch (/.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.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)))) (patch (/.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.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)))) (patch (/.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)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.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)))) (patch (/.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)))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (+.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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (+.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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (+.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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (+.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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (pow (log base) 2) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (pow (log base) 2) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (pow (log base) 2) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (pow (log base) 2) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())) ())
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#s(alt (+ (* -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)))))) (taylor -inf im) (#s(alt (+.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))) (patch (+.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))) #<representation binary64>) () ())) ())
#s(alt (* -1 im) (taylor -inf im) (#s(alt (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))) (taylor -inf im) (#s(alt (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))) (taylor -inf im) (#s(alt (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))) (taylor -inf im) (#s(alt (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) (patch (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (log base) (log (/ -1 im)))) (taylor -inf im) (#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (log base) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2)))) (taylor -inf im) (#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))))) (taylor -inf im) (#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (+ (* -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)))))) (taylor -inf im) (#s(alt (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (patch (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
105.0ms	base	@	0	((/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (atan2 im re) 0) (* 0 0) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (sqrt (+ (* re re) (* im im))) (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
39.0ms	base	@	-inf	((/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (atan2 im re) 0) (* 0 0) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (sqrt (+ (* re re) (* im im))) (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
18.0ms	base	@	inf	((/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (atan2 im re) 0) (* 0 0) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (sqrt (+ (* re re) (* im im))) (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
2.0ms	re	@	0	((/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (atan2 im re) 0) (* 0 0) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (sqrt (+ (* re re) (* im im))) (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
2.0ms	im	@	0	((/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (atan2 im re) 0) (* 0 0) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (sqrt (+ (* re re) (* im im))) (* (log base) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))

simplify178.0ms (1.8%)

Memory

-2.3MiB live, 187.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	299	2912
1	840	2860
2	2641	2828
3	6330	2818
0	8095	2516

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 164

Calls

Call 1

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

Outputs
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
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(+ (* -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)))))
(fma.f64 (.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 (log.f64 base) im) #s(literal 1/2 binary64)) (/.f64 (.f64 re re) im) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))))
(+ (* -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))))))
(fma.f64 (.f64 (/.f64 (log.f64 base) im) #s(literal 1/2 binary64)) (/.f64 (.f64 re re) im) (fma.f64 (.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))))

rewrite213.0ms (2.1%)

Memory

15.4MiB live, 291.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	75
0	34	57
1	99	55
2	688	55
3	6199	55
0	8222	35

Stop Event

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

Counts

7 → 1 492

Calls

Call 1

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

Outputs
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eval275.0ms (2.7%)

Memory: 6.6MiB live, 521.2MiB allocated
Compiler: Compiled 54 027 to 3 323 computations (93.8% saved)

prune51.0ms (0.5%)

Memory

-5.4MiB live, 154.4MiB allocated

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	1 634	22	1 656
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 635	22	1 657

Accuracy

100.0%

Counts

1 657 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f64 (pow.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (hypot.f64 im re))) #s(literal 2 binary64)))
	99.2%	(/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (/.f64 (log.f64 base) (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
▶	99.1%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	99.3%	(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
	99.3%	(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (log.f64 base))
	99.2%	(/.f64 (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -4 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
	98.0%	(/.f64 #s(approx (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (.f64 (log.f64 im) (log.f64 base))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (hypot.f64 im re))) (log.f64 base)))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))))
	99.2%	(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
	99.1%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))))
	99.3%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
▶	99.2%	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))))
	99.2%	(.f64 (/.f64 (.f64 (neg.f64 (log.f64 base)) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	99.3%	(*.f64 (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
	99.2%	(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (hypot.f64 im re))) (log.f64 base))
	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (log.f64 (hypot.f64 im re)))
	99.2%	(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
▶	99.3%	(*.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
▶	99.6%	#s(approx (/ (+ (* (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)))
▶	98.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))

Compiler

Compiled 636 to 510 computations (19.8% saved)

simplify210.0ms (2.1%)

Memory

18.2MiB live, 207.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	256	(*.f64 (log.f64 base) (log.f64 base))
cost-diff	320	(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
cost-diff	7552	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))))
cost-diff	13184	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
cost-diff	0	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -4 binary64))
cost-diff	19264	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))))
cost-diff	0	(log.f64 (hypot.f64 im re))
cost-diff	0	(log.f64 base)
cost-diff	384	(/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
cost-diff	12800	(*.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
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	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 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	0	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
cost-diff	0	#s(approx (/ (+ (* (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)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	240
0	71	198
1	101	190
2	151	180
3	379	180
4	1017	180
5	2053	180
6	2764	180
7	3143	180
8	3710	180
9	4466	180
10	4781	180
11	4944	180
12	5542	180
13	5706	180
14	5888	180
15	6938	180
16	7402	180
17	7611	180
18	7751	180
19	7889	180
0	8012	180

Stop Event

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

Calls

Call 1

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

Outputs
#s(approx (/ (+ (* (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)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(log.f64 (hypot.f64 re im))
(log.f64 (hypot.f64 im re))
(hypot.f64 re im)
(hypot.f64 im re)
re
im
(log.f64 base)
base
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
(/.f64 (log.f64 im) (log.f64 base))
(log.f64 im)
im
(log.f64 base)
base
(*.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(log.f64 base)
base
(/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (hypot.f64 im re)))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -4 binary64))
(log.f64 base)
base
#s(literal -4 binary64)
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))
(pow.f64 (log.f64 base) #s(literal 3 binary64))
#s(literal 3 binary64)
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))))
(*.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
#s(literal 1 binary64)
(/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(log.f64 base)
base
#s(literal -1 binary64)
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(*.f64 (log.f64 base) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(literal 0 binary64)

localize131.0ms (1.3%)

Memory

-28.5MiB live, 229.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))))
accuracy	0.31478500976844204	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
accuracy	0.32421875	(/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))
accuracy	0.537441259768442	(*.f64 (log.f64 base) (log.f64 base))
accuracy	0.30078125	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))
accuracy	0.32421875	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))))
accuracy	0.6850740235163768	(pow.f64 (log.f64 base) #s(literal 3 binary64))
accuracy	0.903830383284567	(pow.f64 (log.f64 base) #s(literal -4 binary64))
accuracy	0	(log.f64 base)
accuracy	0.34603500976844204	(/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
accuracy	0.35775375976844204	(*.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
accuracy	0.537441259768442	(pow.f64 (log.f64 base) #s(literal 2 binary64))
accuracy	0	(log.f64 im)
accuracy	0	(log.f64 base)
accuracy	0.29296875	(/.f64 (log.f64 im) (log.f64 base))
accuracy	0.7899806417453918	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
accuracy	0	(log.f64 (hypot.f64 re im))
accuracy	0	(log.f64 base)
accuracy	0	#s(approx (/ (+ (* (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)))
accuracy	0.28515625	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Samples

92.0ms

256×

valid

Compiler

Compiled 532 to 71 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-log: 16.0ms (23.8% of total)

ival-div: 13.0ms (19.3% of total)

ival-pow: 11.0ms (16.3% of total)

ival-hypot: 10.0ms (14.9% of total)

ival-mult: 9.0ms (13.4% of total)

ival-add: 3.0ms (4.5% of total)

ival-atan2: 3.0ms (4.5% of total)

ival-pow2: 3.0ms (4.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series194.0ms (1.9%)

Memory

-2.4MiB live, 390.1MiB allocated

Counts

21 → 528

Calls

Call 1

Inputs
#s(alt #s(approx (/ (+ (* (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))) (patch #s(approx (/ (+ (* (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))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (patch (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) #<representation binary64>) () ())
#s(alt (log.f64 (hypot.f64 re im)) (patch (log.f64 (hypot.f64 re im)) #<representation binary64>) () ())
#s(alt (hypot.f64 re im) (patch (hypot.f64 re im) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 im) (log.f64 base)) (patch (/.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())
#s(alt (log.f64 im) (patch (log.f64 im) #<representation binary64>) () ())
#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (patch (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (patch (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (log.f64 (hypot.f64 im re)) (patch (log.f64 (hypot.f64 im re)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 base) #s(literal -4 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (patch (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 base) #s(literal 2 binary64)) (patch (pow.f64 (log.f64 base) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 base) #s(literal 3 binary64)) (patch (pow.f64 (log.f64 base) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) (patch (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())

Outputs
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (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))) (patch #s(approx (/ (+ (* (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))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (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))) (patch #s(approx (/ (+ (* (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))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (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))) (patch #s(approx (/ (+ (* (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))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (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))) (patch #s(approx (/ (+ (* (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))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (patch (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (patch (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (patch (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (patch (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (log.f64 base)) (patch (/.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (log.f64 base)) (patch (/.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (log.f64 base)) (patch (/.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (log.f64 base)) (patch (/.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (log base) (taylor 0 base) (#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())) ())
#s(alt (log base) (taylor 0 base) (#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())) ())
#s(alt (log base) (taylor 0 base) (#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())) ())
#s(alt (log base) (taylor 0 base) (#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (patch (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (patch (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (patch (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (patch (.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (patch (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (patch (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (patch (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2)) (taylor 0 base) (#s(alt (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (patch (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow (log base) 4)) (taylor 0 base) (#s(alt (pow.f64 (log.f64 base) #s(literal -4 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow (log base) 4)) (taylor 0 base) (#s(alt (pow.f64 (log.f64 base) #s(literal -4 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow (log base) 4)) (taylor 0 base) (#s(alt (pow.f64 (log.f64 base) #s(literal -4 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2)))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (pow (log base) 3)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2))))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (pow (log base) 3)) (pow im 4))) (+ (* 1/720 (/ (* (pow (log base) 3) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2)))))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log (/ -1 im)) (log base))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (log base) (log (/ -1 im)))) (taylor -inf im) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (log base) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2)))) (taylor -inf im) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))))) (taylor -inf im) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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)))))) (taylor -inf im) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (log base) (log (/ -1 im)))) (taylor -inf im) (#s(alt (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) (patch (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))) (taylor -inf im) (#s(alt (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) (patch (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3))))) (pow im 4))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))) (taylor -inf im) (#s(alt (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) (patch (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))))) (taylor -inf im) (#s(alt (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) (patch (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
49.0ms	base	@	0	((/ (+ (* (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)) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (log base)) (log im) (log base) (* (log base) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2))) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2)) (log (sqrt (+ (* im im) (* re re)))) (* (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (* 0 0) (* (log base) (log base)) (pow (log base) 2) (pow (log base) 3) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))))
27.0ms	base	@	-inf	((/ (+ (* (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)) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (log base)) (log im) (log base) (* (log base) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2))) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2)) (log (sqrt (+ (* im im) (* re re)))) (* (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (* 0 0) (* (log base) (log base)) (pow (log base) 2) (pow (log base) 3) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))))
25.0ms	im	@	0	((/ (+ (* (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)) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (log base)) (log im) (log base) (* (log base) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2))) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2)) (log (sqrt (+ (* im im) (* re re)))) (* (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (* 0 0) (* (log base) (log base)) (pow (log base) 2) (pow (log base) 3) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))))
24.0ms	base	@	inf	((/ (+ (* (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)) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (log base)) (log im) (log base) (* (log base) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2))) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2)) (log (sqrt (+ (* im im) (* re re)))) (* (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (* 0 0) (* (log base) (log base)) (pow (log base) 2) (pow (log base) 3) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))))
19.0ms	im	@	inf	((/ (+ (* (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)) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (log base)) (log im) (log base) (* (log base) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2))) (/ (log (sqrt (+ (* im im) (* re re)))) (pow (log base) 2)) (log (sqrt (+ (* im im) (* re re)))) (* (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -4) (* (pow (log base) 3) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (* 0 0) (* (log base) (log base)) (pow (log base) 2) (pow (log base) 3) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))))

simplify221.0ms (2.2%)

Memory

27.3MiB live, 219.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	787	11036
1	2262	10700
2	7794	10698
0	8016	9706

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 524

Calls

Call 1

Inputs
(/ (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))
(/ (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))
(/ (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))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(log base)
(log base)
(log base)
(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))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2))
(/ (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 (pow (log base) 4))
(/ 1 (pow (log base) 4))
(/ 1 (pow (log base) 4))
(/ 1 (pow (log base) 4))
(* (pow (log base) 3) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (pow (log base) 3) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (pow (log base) 3) (log (sqrt (+ (pow im 2) (pow re 2)))))
(* (pow (log base) 3) (log (sqrt (+ (pow im 2) (pow re 2)))))
(/ (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))
(* (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)))))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 3)
(pow (log base) 3)
(pow (log base) 3)
(pow (log base) 3)
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (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))))
(* -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))))
(* -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))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (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))))
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(- (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 3))))) (pow im 4))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))) (/ 1 (* (log base) (log (/ 1 im))))))
(- (* -1 (/ (+ (* -1/8 (/ (pow re 6) (* (log base) (pow (log (/ 1 im)) 3)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (log base) (pow (log (/ 1 im)) 2)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ 1 im)) 3)))))) (log (/ 1 im)))))) (pow im 6))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ 1 im)) 2))))) (+ (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ 1 im)) 3))))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ 1 im)) 2))))) (/ 1 (* (log base) (log (/ 1 im))))))))
(* -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)))))))
(* -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 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))))))))
(* -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 -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 -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(+ (log -1) (* -1 (log (/ -1 im))))
(* -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)) (pow (log base) 2)))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))
(+ (* -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))))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 2))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 2)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (pow (log base) 2)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 2)))))))
(* -1 (log (/ -1 im)))
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(+ (* -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)) (log base)))
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(+ (* -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))))))
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(+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (pow (log base) 3)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2)))))
(+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (pow (log base) 3)) (pow im 4))) (+ (* 1/720 (/ (* (pow (log base) 3) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2))))))
(* -1 (/ (log (/ -1 im)) (log base)))
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(+ (* -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 base) (log (/ -1 im))))
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(+ (* -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))))
(- (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))
(- (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3))))) (pow im 4))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))))
(- (* -1 (/ (+ (* -1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))))))

Outputs
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
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(/ (log im) (log base))
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(/ (log im) (log base))
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(/ (log im) (log base))
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(/ (log im) (log base))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 2))
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(* (pow (log base) 3) (log (sqrt (+ (pow im 2) (pow re 2)))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 re im)))
(* (pow (log base) 3) (log (sqrt (+ (pow im 2) (pow re 2)))))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
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(* (log base) (log (sqrt (+ (pow im 2) (pow re 2)))))
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(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
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(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
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(-.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (.f64 (/.f64 re im) (/.f64 re im)) (fma.f64 (/.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (.f64 (pow.f64 im #s(literal 4 binary64)) (log.f64 base))))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 base)))
(* -1 (* (pow (log base) 3) (log (/ -1 im))))
(*.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (pow.f64 (neg.f64 (log.f64 base)) #s(literal 3 binary64)))
(+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) im) im) (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (pow.f64 (neg.f64 (log.f64 base)) #s(literal 3 binary64))))
(+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (pow (log base) 3)) (pow im 4))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2)))))
(fma.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) im) im) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (pow.f64 (neg.f64 (log.f64 base)) #s(literal 3 binary64)))))
(+ (* -1 (* (pow (log base) 3) (log (/ -1 im)))) (+ (* -1/4 (/ (* (pow re 4) (pow (log base) 3)) (pow im 4))) (+ (* 1/720 (/ (* (pow (log base) 3) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (pow im 6))) (* 1/2 (/ (* (pow re 2) (pow (log base) 3)) (pow im 2))))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (pow.f64 (neg.f64 (log.f64 base)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/720 binary64) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) im) im) (.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 im #s(literal 4 binary64)))))))
(* -1 (/ (log (/ -1 im)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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)))))))
(-.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (.f64 (/.f64 re im) (/.f64 re im)) (fma.f64 (/.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (.f64 (pow.f64 im #s(literal 4 binary64)) (log.f64 base))))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 base)))
(* -1 (* (log base) (log (/ -1 im))))
(*.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (* (log base) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (log.f64 base) im) im) (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))
(+ (* -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)))))
(fma.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (log.f64 base) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (log.f64 base) im) im) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))))
(+ (* -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))))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)) (fma.f64 (.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (log.f64 base) im) im) (.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (log.f64 base) (pow.f64 im #s(literal 4 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)))))
(fma.f64 (/.f64 (.f64 (/.f64 re (.f64 im im)) (/.f64 re (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(- (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3))))) (pow im 4))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))))
(-.f64 (/.f64 (fma.f64 (/.f64 (/.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))) #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 im #s(literal 4 binary64)))) (fma.f64 (/.f64 (.f64 (/.f64 re (*.f64 im im)) (/.f64 re (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im)))))
(- (* -1 (/ (+ (* -1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))))))
(-.f64 (/.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (/.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))) #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (/.f64 (.f64 re re) (log.f64 (/.f64 #s(literal -1 binary64) im)))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal 1/720 binary64) (/.f64 (/.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) #s(literal -1/8 binary64)) (log.f64 base)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))))) (neg.f64 (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (/.f64 (/.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))) (fma.f64 (/.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (.f64 (pow.f64 im #s(literal 4 binary64)) (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) #s(literal 1/4 binary64) (fma.f64 (/.f64 (.f64 (/.f64 re (.f64 im im)) (/.f64 re (log.f64 base))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im)))))))

rewrite403.0ms (4%)

Memory

-6.1MiB live, 353.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	184
0	71	145
1	226	137
2	1260	127
0	8894	127

Stop Event

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

Counts

21 → 4 175

Calls

Call 1

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

Outputs
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eval847.0ms (8.4%)

Memory: 57.1MiB live, 1 769.2MiB allocated
Compiler: Compiled 134 872 to 8 004 computations (94.1% saved)

prune366.0ms (3.6%)

Memory

-10.6MiB live, 491.3MiB allocated

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	5 640	19	5 659
Fresh	16	1	17
Picked	3	2	5
Done	0	0	0
Total	5 659	22	5 681

Accuracy

100.0%

Counts

5 681 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	98.0%	(/.f64 #s(approx (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (.f64 (log.f64 im) (log.f64 base))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	99.2%	(.f64 (.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
	99.2%	(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	98.1%	(.f64 (log.f64 base) (/.f64 #s(approx (log (sqrt (+ ( im im) (* re re)))) (log.f64 im)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
▶	99.4%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)))
	50.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 im im (.f64 re re))) #s(literal 1/2 binary64)) (log.f64 base)))
✓	99.6%	#s(approx (/ (+ (* (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)))
	7.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (.f64 re #s(literal 1/2 binary64)) (.f64 (/.f64 im re) (/.f64 im re)) re))) (log.f64 base)))
▶	49.7%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))))
▶	49.6%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
	98.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (*.f64 (pow.f64 (log.f64 base) #s(literal -6 binary64)) (pow.f64 (log.f64 base) #s(literal 7 binary64)))))
✓	98.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
	49.4%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base)))))
	98.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (log.f64 im))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 im))))
	49.8%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -5/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (log.f64 im))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 im))))
	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)))
▶	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	48.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 im))) #s(literal -1 binary64))))

Compiler

Compiled 502 to 461 computations (8.2% saved)

simplify101.0ms (1%)

Memory

-6.1MiB live, 150.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))))
cost-diff	192	(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
cost-diff	320	(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
cost-diff	960	(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
cost-diff	0	(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))
cost-diff	0	(log.f64 im)
cost-diff	0	(/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))))
cost-diff	0	(log.f64 im)
cost-diff	0	(/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
cost-diff	7104	(pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))
cost-diff	0	(log.f64 im)
cost-diff	0	(neg.f64 (log.f64 im))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
cost-diff	448	(*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
cost-diff	0	(pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))
cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64)))

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	56	350
0	82	295
1	108	275
2	151	267
3	273	243
4	930	243
5	3002	240
6	5040	240
7	7939	240
0	8063	240

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
#s(literal -1 binary64)
(log.f64 base)
base
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(neg.f64 (log.f64 im))
(log.f64 im)
im
(/.f64 #s(literal -1 binary64) (log.f64 base))
#s(literal -1 binary64)
(log.f64 base)
base
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
(log.f64 im)
im
(pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))
(sqrt.f64 (log.f64 base))
(log.f64 base)
base
#s(literal 2 binary64)
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))))
(/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)))
(log.f64 im)
im
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(log.f64 base)
base
#s(literal -1/2 binary64)
#s(literal -2 binary64)
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))))
#s(literal 1 binary64)
#s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))
(/.f64 #s(literal 1 binary64) (log.f64 im))
(log.f64 im)
im
(log.f64 base)
base
(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 (log.f64 base) (log.f64 base))
(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)

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

localize147.0ms (1.5%)

Memory

18.5MiB live, 289.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.140625	(/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))))
accuracy	0.14128876953688405	(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))
accuracy	0.15810689406052583	#s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
accuracy	0.26400375976844204	(*.f64 (log.f64 base) (log.f64 base))
accuracy	0.04296875	(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
accuracy	0.1328125	(/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))))
accuracy	0.24609375	(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))
accuracy	0.0859375	(sqrt.f64 (log.f64 base))
accuracy	0.1328125	(/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
accuracy	0.270195019536884	(pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))
accuracy	0	(log.f64 base)
accuracy	0.1171875	(/.f64 #s(literal -1 binary64) (log.f64 base))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
accuracy	0.18359375	(*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
accuracy	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)))
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64)))
accuracy	0.125	(pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))
accuracy	0.1328125	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))

Samples

58.0ms	129×	0	valid
57.0ms	127×	0	invalid

Compiler

Compiled 567 to 80 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-log: 20.0ms (23.7% of total)

ival-div: 16.0ms (19% of total)

ival-pow: 15.0ms (17.8% of total)

ival-hypot: 12.0ms (14.2% of total)

ival-mult: 8.0ms (9.5% of total)

ival-sqrt: 4.0ms (4.7% of total)

ival-atan2: 3.0ms (3.6% of total)

ival-add: 2.0ms (2.4% of total)

ival-pow2: 2.0ms (2.4% of total)

exact: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

series250.0ms (2.5%)

Memory

-8.4MiB live, 311.4MiB allocated

Counts

25 → 552

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64)) (patch (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (patch (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (patch #s(approx (/ (+ ( (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) #<representation binary64>) () ())
#s(alt (neg.f64 (log.f64 im)) (patch (neg.f64 (log.f64 im)) #<representation binary64>) () ())
#s(alt (log.f64 im) (patch (log.f64 im) #<representation binary64>) () ())
#s(alt (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (patch (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (patch (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (patch (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (patch (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (log.f64 base)) (patch (/.f64 #s(literal -1 binary64) (log.f64 base)) #<representation binary64>) () ())
#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())
#s(alt (sqrt.f64 (log.f64 base)) (patch (sqrt.f64 (log.f64 base)) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 base) (log.f64 base)) (patch (.f64 (log.f64 base) (log.f64 base)) #<representation binary64>) () ())
#s(alt #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) (patch #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) #<representation binary64>) () ())

Outputs
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (patch (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (patch (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (patch (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (patch (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (patch #s(approx (/ (+ ( (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (patch #s(approx (/ (+ ( (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (patch #s(approx (/ (+ ( (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) (patch #s(approx (/ (+ ( (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))) #<representation binary64>) () ())) ())
#s(alt (log base) (taylor 0 base) (#s(alt (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (log base) (taylor 0 base) (#s(alt (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (* -1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))) (taylor -inf im) (#s(alt #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) (patch #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3))))) (pow im 4))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))) (taylor -inf im) (#s(alt #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) (patch #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ (* -1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im)))))))) (taylor -inf im) (#s(alt #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) (patch #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))) (taylor -inf im) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
86.0ms	base	@	0	((/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (log base)) (pow (log (sqrt (+ (* im im) (* re re)))) -1) (* (neg (log im)) (/ -1 (log base))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (neg (log im)) (log im) (pow (sqrt (log base)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (sqrt (log base)) 2)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (pow (pow (log base) -1/2) -2) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (* 0 0) (+ (* (log base) (log base)) (* 0 0)) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (/ -1 (log base)) (log base) (sqrt (log base)) (pow (log base) -1/2) (* (log base) (log base)) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (log im)) (log base)))
26.0ms	base	@	-inf	((/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (log base)) (pow (log (sqrt (+ (* im im) (* re re)))) -1) (* (neg (log im)) (/ -1 (log base))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (neg (log im)) (log im) (pow (sqrt (log base)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (sqrt (log base)) 2)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (pow (pow (log base) -1/2) -2) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (* 0 0) (+ (* (log base) (log base)) (* 0 0)) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (/ -1 (log base)) (log base) (sqrt (log base)) (pow (log base) -1/2) (* (log base) (log base)) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (log im)) (log base)))
26.0ms	base	@	inf	((/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (log base)) (pow (log (sqrt (+ (* im im) (* re re)))) -1) (* (neg (log im)) (/ -1 (log base))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (neg (log im)) (log im) (pow (sqrt (log base)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (sqrt (log base)) 2)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (pow (pow (log base) -1/2) -2) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (* 0 0) (+ (* (log base) (log base)) (* 0 0)) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (/ -1 (log base)) (log base) (sqrt (log base)) (pow (log base) -1/2) (* (log base) (log base)) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (log im)) (log base)))
17.0ms	im	@	inf	((/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (log base)) (pow (log (sqrt (+ (* im im) (* re re)))) -1) (* (neg (log im)) (/ -1 (log base))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (neg (log im)) (log im) (pow (sqrt (log base)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (sqrt (log base)) 2)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (pow (pow (log base) -1/2) -2) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (* 0 0) (+ (* (log base) (log base)) (* 0 0)) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (/ -1 (log base)) (log base) (sqrt (log base)) (pow (log base) -1/2) (* (log base) (log base)) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (log im)) (log base)))
17.0ms	im	@	-inf	((/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (/ 1 (pow (log (sqrt (+ (* im im) (* re re)))) -1)) (log base)) (pow (log (sqrt (+ (* im im) (* re re)))) -1) (* (neg (log im)) (/ -1 (log base))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (neg (log im)) (log im) (pow (sqrt (log base)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (sqrt (log base)) 2)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (pow (pow (log base) -1/2) -2) (/ (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (+ (* (log base) (log base)) (* 0 0))) (* 0 0) (+ (* (log base) (log base)) (* 0 0)) (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (/ -1 (log base)) (log base) (sqrt (log base)) (pow (log base) -1/2) (* (log base) (log base)) (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/ (/ 1 (log im)) (log base)))

simplify192.0ms (1.9%)

Memory

18.8MiB live, 287.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	772	10218
1	2186	9890
2	7632	9878
0	8077	9088

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 552

Calls

Call 1

Inputs
(/ (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))
(/ (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))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (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))
(log base)
(log base)
(log base)
(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))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (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))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(/ (log im) (log base))
(log base)
(log base)
(log base)
(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))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 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 base))
(/ -1 (log base))
(/ -1 (log base))
(/ -1 (log base))
(log base)
(log base)
(log base)
(log base)
(sqrt (log base))
(sqrt (log base))
(sqrt (log base))
(sqrt (log base))
(sqrt (/ 1 (log base)))
(sqrt (/ 1 (log base)))
(sqrt (/ 1 (log base)))
(sqrt (/ 1 (log base)))
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(pow (log base) 2)
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))))
(/ 1 (* (log base) (log im)))
(/ 1 (* (log base) (log im)))
(/ 1 (* (log base) (log im)))
(/ 1 (* (log base) (log im)))
(* -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))))
(* -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))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (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))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (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))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 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))))
(* -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))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (/ (log im) (log (/ 1 base))))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (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))))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 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))))
(/ 1 (log (/ 1 base)))
(/ 1 (log (/ 1 base)))
(/ 1 (log (/ 1 base)))
(/ 1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 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))))
(/ -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 (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 (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 -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 (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 -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (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 (sqrt (+ (pow im 2) (pow re 2)))) (+ (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 -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 (sqrt (+ (pow im 2) (pow re 2)))) (+ (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 -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(+ (log -1) (* -1 (log (/ -1 base))))
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Outputs
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 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))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(* -1 (/ (log (/ -1 im)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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)))))))
(-.f64 (fma.f64 (/.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (.f64 (/.f64 re im) (/.f64 re im)) (*.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))))) (/.f64 (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))
(/.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))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(* -1 (/ (log (/ -1 im)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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)))))))
(-.f64 (fma.f64 (/.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (.f64 (/.f64 re im) (/.f64 re im)) (*.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64)))))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 base)))
(* -1 (* (log base) (log (/ -1 im))))
(*.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (* (log base) (log (/ -1 im)))) (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (log.f64 base) im) im) (*.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))
(+ (* -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)))))
(fma.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (log.f64 base) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (log.f64 base) im) im) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))))
(+ (* -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))))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)) (fma.f64 (.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (log.f64 base) im) im) (.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (log.f64 base) (pow.f64 im #s(literal 4 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)))))
(fma.f64 (/.f64 (.f64 (/.f64 re (log.f64 base)) (/.f64 re (.f64 im im))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(- (* -1 (/ (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3))))) (pow im 4))) (+ (* 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 binary64) (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (log.f64 base)) (.f64 (/.f64 re im) (/.f64 re im))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (/.f64 (/.f64 (*.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 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 (/ (+ (* -1/8 (/ (pow re 6) (* (log base) (pow (log (/ -1 im)) 3)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 2)))) (* 1/4 (/ (pow re 4) (* (log base) (pow (log (/ -1 im)) 3)))))) (log (/ -1 im)))))) (pow im 6))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 2))))) (+ (* 1/4 (/ (pow re 4) (* (pow im 4) (* (log base) (pow (log (/ -1 im)) 3))))) (+ (* 1/2 (/ (pow re 2) (* (pow im 2) (* (log base) (pow (log (/ -1 im)) 2))))) (/ 1 (* (log base) (log (/ -1 im))))))))
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(/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(/ 1 (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))

rewrite344.0ms (3.4%)

Memory

-194.0MiB live, 221.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	306
0	82	236
1	257	202
2	1430	202
0	8958	202

Stop Event

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

Counts

25 → 925

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base))
(pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))
(*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(neg.f64 (log.f64 im))
(log.f64 im)
(pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
(/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))))
(/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64)))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(log.f64 base)
(sqrt.f64 (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(*.f64 (log.f64 base) (log.f64 base))
#s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))
(/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base))

Outputs
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eval454.0ms (4.5%)

Memory: 35.9MiB live, 493.0MiB allocated
Compiler: Compiled 38 062 to 4 391 computations (88.5% saved)

prune124.0ms (1.2%)

Memory

-35.4MiB live, 268.3MiB allocated

Pruning

24 alts after pruning (20 fresh and 4 done)

	Pruned	Kept	Total
New	1 900	12	1 912
Fresh	7	8	15
Picked	3	2	5
Done	0	2	2
Total	1 910	24	1 934

Accuracy

100.0%

Counts

1 934 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
	99.2%	(.f64 (.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
	99.2%	(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	98.1%	(.f64 (log.f64 base) (/.f64 #s(approx (log (sqrt (+ ( im im) (* re re)))) (log.f64 im)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	75.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (pow.f64 (pow.f64 (log.f64 (hypot.f64 re im)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (log.f64 base)))
	98.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (pow (log (sqrt (+ (* im im) (* re re)))) -1) (/.f64 #s(literal 1 binary64) (log.f64 im)))) (log.f64 base)))
▶	99.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))))
	50.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 re re (.f64 im im))) #s(literal 1/2 binary64)) (log.f64 base)))
✓	99.6%	#s(approx (/ (+ (* (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)))
	7.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (.f64 re #s(literal 1/2 binary64)) (.f64 (/.f64 im re) (/.f64 im re)) re))) (log.f64 base)))
	49.5%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal -4 binary64))))
▶	49.6%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))))
	49.6%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (log.f64 base))) #s(literal -2 binary64))))
✓	49.6%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
▶	49.7%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))))
✓	98.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
	99.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))) (/.f64 #s(literal -1 binary64) (log.f64 base)))))
	49.7%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (log.f64 base)) (/.f64 (log.f64 im) (sqrt.f64 (log.f64 base))))))
▶	98.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 im))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 im))))
▶	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)))
✓	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	74.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (exp.f64 (neg.f64 (.f64 (log.f64 (log.f64 im)) #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (log.f64 base))))

Compiler

Compiled 526 to 497 computations (5.5% saved)

simplify92.0ms (0.9%)

Memory

10.8MiB live, 88.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 im)
cost-diff	0	(/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))))
cost-diff	13632	(pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))
cost-diff	0	(log.f64 im)
cost-diff	0	(*.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)))
cost-diff	12800	(.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))
cost-diff	0	(pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))
cost-diff	0	(log.f64 im)
cost-diff	0	(/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64)))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))))
cost-diff	0	(log.f64 base)
cost-diff	0	(/.f64 (log.f64 base) (log.f64 im))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
cost-diff	0	(log.f64 base)
cost-diff	0	(/.f64 #s(literal -1 binary64) (log.f64 base))
cost-diff	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))))
cost-diff	1408	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	337
0	71	287
1	89	277
2	120	261
3	162	227
4	268	227
5	597	227
6	2635	227
7	4756	227
8	6665	227
9	7466	227
0	8012	227

Stop Event

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

Calls

Call 1

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

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

localize141.0ms (1.4%)

Memory

-6.5MiB live, 146.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
accuracy	0.1328125	(/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))))
accuracy	0.270195019536884	(pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)))
accuracy	0.1640625	(*.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
accuracy	0.171875	(.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))
accuracy	0.25427631837909404	(pow.f64 (log.f64 base) #s(literal -2 binary64))
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (log.f64 base))
accuracy	0.1328125	(/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64)))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))))
accuracy	0.24609375	(pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))
accuracy	0	(log.f64 base)
accuracy	0.09765625	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))
accuracy	0.15769677324952242	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
accuracy	0.174160009768442	(/.f64 (log.f64 base) (log.f64 im))
accuracy	0	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))))
accuracy	0.1171875	(/.f64 #s(literal -1 binary64) (log.f64 base))
accuracy	0.125	(/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))
accuracy	0.16634750976844204	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))

Samples

55.0ms	129×	0	valid
52.0ms	127×	0	invalid

Compiler

Compiled 533 to 73 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-pow: 20.0ms (24.2% of total)

ival-div: 14.0ms (17% of total)

ival-atan2: 14.0ms (17% of total)

ival-log: 14.0ms (17% of total)

ival-mult: 7.0ms (8.5% of total)

ival-hypot: 5.0ms (6.1% of total)

ival-pow2: 3.0ms (3.6% of total)

ival-add: 2.0ms (2.4% of total)

ival-sqrt: 2.0ms (2.4% of total)

exact: 1.0ms (1.2% of total)

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

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

series180.0ms (1.8%)

Memory

31.1MiB live, 223.9MiB allocated

Counts

21 → 480

Calls

Call 1

Inputs
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) (patch (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (log.f64 base)) (patch (/.f64 #s(literal -1 binary64) (log.f64 base)) #<representation binary64>) () ())
#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 base) (log.f64 im)) (patch (/.f64 (log.f64 base) (log.f64 im)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64)))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (log.f64 im) (patch (log.f64 im) #<representation binary64>) () ())
#s(alt (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64)) (patch (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)) (patch (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (patch (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)))) (patch #s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))) (patch (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (log.f64 base)) (patch (/.f64 #s(literal 1 binary64) (log.f64 base)) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 base) #s(literal -2 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) (patch (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) (patch (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) #<representation binary64>) () ())) ())
#s(alt (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base)) (taylor 0 base) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) (patch (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))) #<representation binary64>) () ())) ())
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Calls

9 calls:

Time	Variable		Point	Expression
36.0ms	im	@	-inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ -1 (log base)) (log base) (/ 1 (/ (log base) (log im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log base) (log im)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (log im) (pow (pow (log base) -1/2) -2) (* (* (log im) (pow (log base) -2)) (log base)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log im) (pow (log base) -2)) (pow (/ 1 (pow (log base) -1/2)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (/ 1 (pow (log base) -1/2)) 2)) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (log base)) (pow (log base) -2) (/ 1 (pow (log base) -1/2)))
30.0ms	base	@	-inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ -1 (log base)) (log base) (/ 1 (/ (log base) (log im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log base) (log im)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (log im) (pow (pow (log base) -1/2) -2) (* (* (log im) (pow (log base) -2)) (log base)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log im) (pow (log base) -2)) (pow (/ 1 (pow (log base) -1/2)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (/ 1 (pow (log base) -1/2)) 2)) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (log base)) (pow (log base) -2) (/ 1 (pow (log base) -1/2)))
26.0ms	base	@	0	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ -1 (log base)) (log base) (/ 1 (/ (log base) (log im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log base) (log im)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (log im) (pow (pow (log base) -1/2) -2) (* (* (log im) (pow (log base) -2)) (log base)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log im) (pow (log base) -2)) (pow (/ 1 (pow (log base) -1/2)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (/ 1 (pow (log base) -1/2)) 2)) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (log base)) (pow (log base) -2) (/ 1 (pow (log base) -1/2)))
24.0ms	base	@	inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ -1 (log base)) (log base) (/ 1 (/ (log base) (log im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log base) (log im)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (log im) (pow (pow (log base) -1/2) -2) (* (* (log im) (pow (log base) -2)) (log base)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log im) (pow (log base) -2)) (pow (/ 1 (pow (log base) -1/2)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (/ 1 (pow (log base) -1/2)) 2)) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (log base)) (pow (log base) -2) (/ 1 (pow (log base) -1/2)))
22.0ms	im	@	0	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ -1 (log base)) (log base) (/ 1 (/ (log base) (log im))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log base) (log im)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (pow (log base) -1/2) -2)) (log im) (pow (pow (log base) -1/2) -2) (* (* (log im) (pow (log base) -2)) (log base)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log im) (pow (log base) -2)) (pow (/ 1 (pow (log base) -1/2)) 2) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (pow (/ 1 (pow (log base) -1/2)) 2)) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (log base)) (pow (log base) -2) (/ 1 (pow (log base) -1/2)))

simplify189.0ms (1.9%)

Memory

-30.1MiB live, 327.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	404	7538
1	1060	7318
2	3651	7188
0	8139	6616

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

Inputs
(/ (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))
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(/ -1 (log base))
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(/ -1 (log base))
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(/ (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))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
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(/ (log im) (log base))
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(log base)
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(/ (log im) (log base))
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(/ (log im) (log base))
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(/ (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))
(/ (log im) (pow (log base) 2))
(/ (log im) (pow (log base) 2))
(/ (log im) (pow (log base) 2))
(/ (log im) (pow (log base) 2))
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(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
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(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(sqrt (log base))
(sqrt (log base))
(sqrt (log base))
(sqrt (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))))
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(+ (* -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 -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 (/ -1 im)))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log (/ -1 im)) 2)))) (/ 1 (log (/ -1 im))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow (log (/ -1 im)) 3))) (* 1/4 (/ (pow re 4) (pow (log (/ -1 im)) 2)))) (pow im 4))) (/ 1 (log (/ -1 im)))) (* -1/2 (/ (pow re 2) (* (pow im 2) (pow (log (/ -1 im)) 2)))))
(- (+ (* -1 (/ (+ (* -1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow (log (/ -1 im)) 2))) (+ (* 1/8 (/ (pow re 6) (pow (log (/ -1 im)) 3))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (pow (log (/ -1 im)) 3))) (* 1/4 (/ (pow re 4) (pow (log (/ -1 im)) 2))))) (log (/ -1 im)))))) (pow im 6))) (/ 1 (log (/ -1 im)))) (+ (* -1/2 (/ (pow re 2) (* (pow im 2) (pow (log (/ -1 im)) 2)))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log (/ -1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (pow im 4) (pow (log (/ -1 im)) 2)))))))

Outputs
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ -1 (log base))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(/ -1 (log base))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(/ -1 (log base))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(/ -1 (log base))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(/ (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))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log base) (log im))
(/.f64 (log.f64 base) (log.f64 im))
(/ (log base) (log im))
(/.f64 (log.f64 base) (log.f64 im))
(/ (log base) (log im))
(/.f64 (log.f64 base) (log.f64 im))
(/ (log base) (log im))
(/.f64 (log.f64 base) (log.f64 im))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (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))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(/ (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))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log im) (pow (log base) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (log im) (pow (log base) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (log im) (pow (log base) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (log im) (pow (log base) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(log base)
(log.f64 base)
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (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))
(/.f64 (log.f64 im) (log.f64 base))
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (pow (log base) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ 1 (pow (log base) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ 1 (pow (log base) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ 1 (pow (log base) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(sqrt (log base))
(sqrt.f64 (log.f64 base))
(sqrt (log base))
(sqrt.f64 (log.f64 base))
(sqrt (log base))
(sqrt.f64 (log.f64 base))
(sqrt (log base))
(sqrt.f64 (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ 1 (log (/ 1 base)))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(/ 1 (log (/ 1 base)))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(/ 1 (log (/ 1 base)))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(/ 1 (log (/ 1 base)))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (/ 1 base)) (log im)))
(/.f64 (log.f64 base) (log.f64 im))
(* -1 (/ (log (/ 1 base)) (log im)))
(/.f64 (log.f64 base) (log.f64 im))
(* -1 (/ (log (/ 1 base)) (log im)))
(/.f64 (log.f64 base) (log.f64 im))
(* -1 (/ (log (/ 1 base)) (log im)))
(/.f64 (log.f64 base) (log.f64 im))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/ (log im) (pow (log (/ 1 base)) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (log im) (pow (log (/ 1 base)) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (log im) (pow (log (/ 1 base)) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (log im) (pow (log (/ 1 base)) 2))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (log (/ 1 base)))
(log.f64 base)
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(* -1 (/ (log im) (log (/ 1 base))))
(/.f64 (log.f64 im) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/ 1 (pow (log (/ 1 base)) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ 1 (pow (log (/ 1 base)) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ 1 (pow (log (/ 1 base)) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ 1 (pow (log (/ 1 base)) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (log.f64 base))))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (log.f64 base))))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (log.f64 base))))
(* (sqrt (log (/ 1 base))) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (log.f64 base))))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 (hypot.f64 re im)) (-.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 re im)) (-.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 re im)) (-.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 re im)) (-.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 re im)) (-.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 re im)) (-.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 re im)) (-.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 re im)) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ -1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
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(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ -1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
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(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 im) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 im) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 im) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ (log im) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (log.f64 im) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
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(/.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))
(* -1 (/ (log (/ -1 im)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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)))))))
(fma.f64 (/.f64 #s(literal 1/720 binary64) (pow.f64 im #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 120 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (*.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))))
(/ (log base) (+ (log -1) (* -1 (log (/ -1 im)))))
(/.f64 (log.f64 base) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(/ (log base) (+ (log -1) (* -1 (log (/ -1 im)))))
(/.f64 (log.f64 base) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
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(/.f64 (log.f64 base) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(* -1 (/ (log (/ -1 im)) (log base)))
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(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
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(+ (* -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))))))
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(fma.f64 (/.f64 #s(literal 1/720 binary64) (pow.f64 im #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 120 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (*.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (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))
(/.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))
(/.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))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(+ (log -1) (* -1 (log (/ -1 im))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(+ (log -1) (* -1 (log (/ -1 im))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(+ (log -1) (* -1 (log (/ -1 im))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(/ (+ (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))
(/.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))
(* -1 (/ (log (/ -1 im)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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)))))))
(fma.f64 (/.f64 #s(literal 1/720 binary64) (pow.f64 im #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 120 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (*.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 2))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(* -1 (/ (log (/ -1 im)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base)))
(+ (* -1 (/ (log (/ -1 im)) (log base))) (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 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)))))))
(fma.f64 (/.f64 #s(literal 1/720 binary64) (pow.f64 im #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 120 binary64) (pow.f64 re #s(literal 6 binary64))) (log.f64 base)) (fma.f64 (/.f64 #s(literal -1/4 binary64) (log.f64 base)) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) (log.f64 base)) (*.f64 re re) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (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))
(/.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))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(/ 1 (log (/ -1 im)))
(/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log (/ -1 im)) 2)))) (/ 1 (log (/ -1 im))))
(fma.f64 (/.f64 (*.f64 (/.f64 re im) (/.f64 re im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (pow re 4) (pow (log (/ -1 im)) 3))) (* 1/4 (/ (pow re 4) (pow (log (/ -1 im)) 2)))) (pow im 4))) (/ 1 (log (/ -1 im)))) (* -1/2 (/ (pow re 2) (* (pow im 2) (pow (log (/ -1 im)) 2)))))
(-.f64 (fma.f64 (/.f64 (.f64 (/.f64 re im) (/.f64 re im)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)))) (/.f64 (.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))))) (pow.f64 im #s(literal 4 binary64))))
(- (+ (* -1 (/ (+ (* -1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow (log (/ -1 im)) 2))) (+ (* 1/8 (/ (pow re 6) (pow (log (/ -1 im)) 3))) (* 1/2 (/ (* (pow re 2) (+ (* -1/4 (/ (pow re 4) (pow (log (/ -1 im)) 3))) (* 1/4 (/ (pow re 4) (pow (log (/ -1 im)) 2))))) (log (/ -1 im)))))) (pow im 6))) (/ 1 (log (/ -1 im)))) (+ (* -1/2 (/ (pow re 2) (* (pow im 2) (pow (log (/ -1 im)) 2)))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log (/ -1 im)) 3)))) (* 1/4 (/ (pow re 4) (* (pow im 4) (pow (log (/ -1 im)) 2)))))))
(-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))) (/.f64 (fma.f64 (.f64 (.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))))) (/.f64 (.f64 re re) (log.f64 (/.f64 #s(literal -1 binary64) im)))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 #s(literal 120 binary64) (pow.f64 re #s(literal 6 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) #s(literal -1/720 binary64)))) (pow.f64 im #s(literal 6 binary64)))) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64)))) (/.f64 (/.f64 (.f64 #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)))))

rewrite167.0ms (1.7%)

Memory

43.7MiB live, 271.1MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	278
0	71	221
1	226	191
2	1300	162
0	8557	162

Stop Event

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

Counts

21 → 1 542

Calls

Call 1

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

Outputs
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eval442.0ms (4.4%)

Memory: 35.8MiB live, 718.9MiB allocated
Compiler: Compiled 45 315 to 6 083 computations (86.6% saved)

prune175.0ms (1.7%)

Memory

-44.3MiB live, 315.0MiB allocated

Pruning

26 alts after pruning (20 fresh and 6 done)

	Pruned	Kept	Total
New	2 380	10	2 390
Fresh	5	10	15
Picked	3	2	5
Done	0	4	4
Total	2 388	26	2 414

Accuracy

100.0%

Counts

2 414 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
	98.1%	(.f64 (log.f64 base) (/.f64 #s(approx (log (sqrt (+ ( im im) (* re re)))) (log.f64 im)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	47.9%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (pow.f64 (pow.f64 (/.f64 (log.f64 im) (log.f64 base)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
	75.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (pow.f64 (pow.f64 (log.f64 (hypot.f64 re im)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (log.f64 base)))
	98.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (pow (log (sqrt (+ (* im im) (* re re)))) -1) (/.f64 #s(literal 1 binary64) (log.f64 im)))) (log.f64 base)))
	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 im))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (log.f64 im) (log.f64 base))) (neg.f64 (log.f64 base))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	50.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 re re (.f64 im im))) #s(literal 1/2 binary64)) (log.f64 base)))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (*.f64 (log.f64 im) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓	99.6%	#s(approx (/ (+ (* (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)))
	7.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (.f64 re #s(literal 1/2 binary64)) (.f64 (/.f64 im re) (/.f64 im re)) re))) (log.f64 base)))
	49.5%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal -4 binary64))))
	49.6%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (log.f64 base))) #s(literal -2 binary64))))
✓	49.6%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
✓	98.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
✓	98.2%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 im)) (neg.f64 (log.f64 base)))))
	49.7%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (log.f64 im)))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 im) (log.f64 base))))
	98.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 im))))
	49.7%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (pow.f64 #s(approx (pow (log base) -1/2) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (log.f64 im)))
✓	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)))
	97.9%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (log.f64 base)))
✓	98.1%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	74.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (exp.f64 (neg.f64 (.f64 (log.f64 (log.f64 im)) #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (log.f64 base))))

Compiler

Compiled 1 146 to 541 computations (52.8% saved)

regimes115.0ms (1.1%)

Memory

10.6MiB live, 122.8MiB allocated

Counts

64 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 im im (.f64 re re))) #s(literal 1/2 binary64)) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 re re (.f64 im im))) #s(literal 1/2 binary64)) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 im)) (neg.f64 (log.f64 base)))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (pow (log (sqrt (+ (* im im) (* re re)))) -1) (/.f64 #s(literal 1 binary64) (log.f64 im)))) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (.f64 re #s(literal 1/2 binary64)) (.f64 (/.f64 im re) (/.f64 im re)) re))) (log.f64 base)))
#s(approx (/ (+ (* (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)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (sqrt.f64 (log.f64 base)) #s(literal 2 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal -2 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (log.f64 base))) #s(literal -2 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))) (/.f64 #s(literal -1 binary64) (log.f64 base)))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (log.f64 im)))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (log.f64 base)) (/.f64 (log.f64 im) (sqrt.f64 (log.f64 base))))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (pow.f64 #s(approx (pow (log base) -1/2) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (log.f64 im)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 im) (log.f64 base))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base)))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal -2 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal -4 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (pow.f64 (pow.f64 (/.f64 (log.f64 im) (log.f64 base)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 im))) #s(literal -1 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (*.f64 (log.f64 im) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (log.f64 base) (/.f64 #s(approx (log (sqrt (+ ( im im) (* re re)))) (log.f64 im)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) #s(literal 2 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal -1 binary64))) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (neg.f64 (exp.f64 (neg.f64 (.f64 (log.f64 (log.f64 im)) #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(/.f64 #s(approx (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (.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 #s(approx (/ 1 (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re)))))) (.f64 (log.f64 im) (log.f64 base))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 im)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (log.f64 im) (log.f64 base))) (neg.f64 (log.f64 base))))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (pow (log base) -1) (log (sqrt (+ (* im im) (* re re))))) (/.f64 (/.f64 #s(literal 1 binary64) (log.f64 im)) (log.f64 base)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal -5/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (log.f64 im))))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (log.f64 (hypot.f64 im re)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (hypot.f64 im re))) (log.f64 base))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (pow.f64 (pow.f64 (log.f64 (hypot.f64 re im)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (*.f64 (pow.f64 (log.f64 base) #s(literal -6 binary64)) (pow.f64 (log.f64 base) #s(literal 7 binary64)))))
(*.f64 (log.f64 base) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (hypot.f64 im re))) (log.f64 base)))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))))
(/.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 (.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))))
(*.f64 (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (log.f64 base))
(/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (/.f64 (log.f64 base) (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (log.f64 (hypot.f64 im re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))))
(/.f64 (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -4 binary64))) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(.f64 (/.f64 (.f64 (neg.f64 (log.f64 base)) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(/.f64 (pow.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (log.f64 (hypot.f64 im re))) #s(literal 2 binary64)))

Outputs
#s(approx (/ (+ (* (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)))

Calls

5 calls:

32.0ms	base
29.0ms	(log.f64 base)
20.0ms	im
16.0ms	re
15.0ms	(/.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
99.6%	1	`re`
99.6%	1	`im`
99.6%	1	`base`
99.6%	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))))`
99.6%	1	`(log.f64 base)`

Compiler

Compiled 33 to 31 computations (6.1% saved)

regimes44.0ms (0.4%)

Memory

-7.7MiB live, 29.0MiB allocated

Accuracy

Total -59.4b remaining (-5506.8%)

Threshold costs -59.4b (-5506.8%)

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 im im (.f64 re re))) #s(literal 1/2 binary64)) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (.f64 (log.f64 (fma.f64 re re (.f64 im im))) #s(literal 1/2 binary64)) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 im)) (neg.f64 (log.f64 base)))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 im))))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (pow (log (sqrt (+ (* im im) (* re re)))) -1) (/.f64 #s(literal 1 binary64) (log.f64 im)))) (log.f64 base)))
#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (fma.f64 (.f64 re #s(literal 1/2 binary64)) (.f64 (/.f64 im re) (/.f64 im re)) re))) (log.f64 base)))

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

Calls

5 calls:

30.0ms	base
3.0ms	im
3.0ms	re
3.0ms	(log.f64 base)
3.0ms	(/.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
98.3%	1	`re`
98.3%	1	`im`
98.3%	1	`base`
98.3%	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))))`
98.3%	1	`(log.f64 base)`

Compiler

Compiled 33 to 31 computations (6.1% saved)

simplify27.0ms (0.3%)

Memory

-7.7MiB live, 40.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	66

Stop Event

1×

saturated

Calls

Call 1

Inputs

#s(approx (/ (+ (* (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)))

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

Outputs

#s(approx (/ (+ (* (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)))

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

soundness165.0ms (1.6%)

Memory

-6.9MiB live, 105.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	299	2912
1	840	2860
2	2641	2828
3	6330	2818
0	8095	2516

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 26 to 24 computations (7.7% saved)

preprocess63.0ms (0.6%)

Memory

14.4MiB live, 100.8MiB allocated

Remove

(sort re im)

(abs re)

(abs im)

Compiler

Compiled 132 to 106 computations (19.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze166.0ms (1.6%)

sample2.0s (19.9%)

explain502.0ms (5%)

preprocess386.0ms (3.8%)

eval0.0ms (0%)

prune50.0ms (0.5%)

simplify210.0ms (2.1%)

localize98.0ms (1%)

series179.0ms (1.8%)

simplify178.0ms (1.8%)

rewrite213.0ms (2.1%)

eval275.0ms (2.7%)

prune51.0ms (0.5%)

simplify210.0ms (2.1%)

localize131.0ms (1.3%)

series194.0ms (1.9%)

simplify221.0ms (2.2%)

rewrite403.0ms (4%)

eval847.0ms (8.4%)

prune366.0ms (3.6%)

simplify101.0ms (1%)

localize147.0ms (1.5%)

series250.0ms (2.5%)

simplify192.0ms (1.9%)

rewrite344.0ms (3.4%)

eval454.0ms (4.5%)

prune124.0ms (1.2%)

simplify92.0ms (0.9%)

localize141.0ms (1.4%)

series180.0ms (1.8%)

simplify189.0ms (1.9%)

rewrite167.0ms (1.7%)

eval442.0ms (4.4%)

prune175.0ms (1.7%)

regimes115.0ms (1.1%)

regimes44.0ms (0.4%)

simplify27.0ms (0.3%)

soundness165.0ms (1.6%)

preprocess63.0ms (0.6%)

end0.0ms (0%)

Profiling