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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze234.0ms (2.1%)

Memory

8.0MiB live, 210.1MiB 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
9.4%	4.7%	45.2%	0.1%	0%	49.9%	0%	7
17.2%	8.6%	41.3%	0.1%	0%	49.9%	0%	8
27.3%	13.7%	36.3%	0.1%	0%	49.9%	0%	9
41%	20.5%	29.4%	0.1%	0%	49.9%	0%	10
48.6%	24.3%	25.6%	0.1%	0%	49.9%	0%	11
57.1%	28.5%	21.4%	0.1%	0%	49.9%	0%	12

Compiler

Compiled 30 to 17 computations (43.3% saved)

sample2.0s (17.7%)

Memory

-201.9MiB live, 2 560.6MiB allocated

Samples

1.3s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 983.0ms

ival-hypot: 311.0ms (31.6% of total)

ival-log: 246.0ms (25% of total)

ival-mult: 195.0ms (19.8% of total)

ival-add: 98.0ms (10% of total)

ival-atan2: 61.0ms (6.2% of total)

ival-div: 56.0ms (5.7% of total)

ival-true: 6.0ms (0.6% of total)

exact: 6.0ms (0.6% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain363.0ms (3.3%)

Memory

1.5MiB live, 390.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
126	-	2	(6.171118663840831e-160 1.61919720842612e-203 6.09669322802609e-106)	`(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	112	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	112
↳	`(*.f64 re re)`	overflow	58
↳	`(*.f64 im im)`	overflow	72
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`	uflow-rescue	12	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	underflow	12
↳	`(*.f64 re re)`	underflow	49
↳	`(*.f64 im im)`	underflow	55

Confusion

	Predicted +	Predicted -
+	124	2
-	0	130

Precision

1.0

Recall

0.9841269841269841

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	124	0	2
-	0	0	130

Precision?

1.0

Recall?

0.9841269841269841

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

131.0ms

512×

valid

Compiler

Compiled 270 to 58 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-log: 40.0ms (37% of total)

ival-hypot: 32.0ms (29.6% of total)

ival-mult: 15.0ms (13.9% of total)

ival-add: 13.0ms (12% of total)

ival-atan2: 4.0ms (3.7% of total)

ival-div: 3.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess214.0ms (1.9%)

Memory

9.3MiB live, 132.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 840×	`lower-*.f32`
6 832×	`lower-*.f64`
3 028×	`cube-prod`
2 360×	`lower-/.f32`
2 358×	`lower-/.f64`

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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.5%	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))

Status

Accuracy

Program

▶

52.5%

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

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify196.0ms (1.8%)

Memory

-19.3MiB live, 102.6MiB 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))))

Rules

6 840×	`lower-*.f32`
6 832×	`lower-*.f64`
3 028×	`cube-prod`
2 360×	`lower-/.f32`
2 358×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	113
0	34	99
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)

localize61.0ms (0.5%)

Memory

34.7MiB live, 71.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.33041000976844204	(/.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	0.36166000976844204	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
accuracy	0.532577539073768	(*.f64 (log.f64 base) (log.f64 base))
accuracy	28.971531710542997	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Samples

50.0ms

256×

valid

Compiler

Compiled 121 to 20 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-add: 18.0ms (46.5% of total)

ival-mult: 7.0ms (18.1% of total)

ival-log: 6.0ms (15.5% of total)

ival-hypot: 4.0ms (10.3% of total)

ival-div: 2.0ms (5.2% of total)

ival-atan2: 2.0ms (5.2% of total)

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

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

exact: 0.0ms (0% of total)

series228.0ms (2%)

Memory

17.2MiB live, 199.4MiB 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>) () ())) ())
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#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 (.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 (* (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
113.0ms	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)))
53.0ms	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)))
40.0ms	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)))
6.0ms	re	@	-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)))

simplify257.0ms (2.3%)

Memory

-4.2MiB live, 157.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 210×	`lower-fma.f64`
12 210×	`lower-fma.f32`
4 836×	`lower-*.f64`
4 836×	`lower-*.f32`
3 926×	`lower-+.f64`

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))
(/ (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)))))
(*.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)))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(* (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)))))
(*.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)))
(* -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 base) (log.f64 (hypot.f64 re im)))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(* -1 (* (log (sqrt (+ (pow im 2) (pow re 2)))) (log (/ 1 base))))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
(/ (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 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(* (log (sqrt (+ (pow im 2) (pow re 2)))) (+ (log -1) (* -1 (log (/ -1 base)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (log.f64 (hypot.f64 re im)))
(/ (log im) (log base))
(/.f64 (log.f64 im) (log.f64 base))
(+ (* 1/2 (/ (pow re 2) (* (pow im 2) (log base)))) (/ (log im) (log base)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (log.f64 base) im)) (/.f64 (.f64 re re) im) (/.f64 (log.f64 im) (log.f64 base)))
(+ (* (pow re 2) (+ (* -1/4 (/ (pow re 2) (* (pow im 4) (log base)))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) (.f64 (log.f64 base) im)) (/.f64 re im) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (log.f64 base)) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (/.f64 (log.f64 im) (log.f64 base))))
(+ (* (pow re 2) (+ (* (pow re 2) (- (* 1/6 (/ (pow re 2) (* (pow im 6) (log base)))) (* 1/4 (/ 1 (* (pow im 4) (log base)))))) (* 1/2 (/ 1 (* (pow im 2) (log base)))))) (/ (log im) (log base)))
(fma.f64 (pow.f64 re #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/6 binary64) re) (pow.f64 im #s(literal 6 binary64))) (/.f64 re (log.f64 base)) (/.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (log.f64 base))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (log.f64 base) im)) (/.f64 (*.f64 re re) im) (/.f64 (log.f64 im) (log.f64 base))))
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
(* (log base) (log im))
(*.f64 (log.f64 im) (log.f64 base))
(+ (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))) (* (log base) (log im)))
(fma.f64 (.f64 (/.f64 (log.f64 base) im) #s(literal 1/2 binary64)) (/.f64 (.f64 re re) im) (*.f64 (log.f64 im) (log.f64 base)))
(+ (* (log base) (log im)) (* (pow re 2) (+ (* -1/4 (/ (* (pow re 2) (log base)) (pow im 4))) (* 1/2 (/ (log base) (pow im 2))))))
(fma.f64 (fma.f64 (.f64 (.f64 (log.f64 base) re) re) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (.f64 (/.f64 (log.f64 base) im) (/.f64 #s(literal 1/2 binary64) im))) (.f64 re re) (*.f64 (log.f64 im) (log.f64 base)))
(+ (* (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))))))))
(fma.f64 (fma.f64 (/.f64 (log.f64 base) im) (/.f64 #s(literal 1/2 binary64) im) (.f64 (fma.f64 (.f64 (.f64 (log.f64 base) re) re) (/.f64 #s(literal 1/6 binary64) (pow.f64 im #s(literal 6 binary64))) (.f64 (log.f64 base) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))))) (.f64 re re))) (.f64 re re) (*.f64 (log.f64 im) (log.f64 base)))
im
(+ im (* 1/2 (/ (pow re 2) im)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) im) (*.f64 re re) im)
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) re) (/.f64 re (pow.f64 im #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) im)) (.f64 re re) 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)))))
(fma.f64 (pow.f64 re #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) re) (/.f64 re (pow.f64 im #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 im #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) im) (.f64 re re) im))
(* (log base) (log im))
(*.f64 (log.f64 im) (log.f64 base))
(+ (* 1/2 (/ (* (pow re 2) (log base)) (pow im 2))) (* (log base) (log im)))
(fma.f64 (.f64 (/.f64 (log.f64 base) im) #s(literal 1/2 binary64)) (/.f64 (.f64 re re) im) (*.f64 (log.f64 im) (log.f64 base)))
(+ (* (log base) (log im)) (* (pow re 2) (+ (* -1/4 (/ (* (pow re 2) (log base)) (pow im 4))) (* 1/2 (/ (log base) (pow im 2))))))
(fma.f64 (fma.f64 (.f64 (.f64 (log.f64 base) re) re) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (.f64 (/.f64 (log.f64 base) im) (/.f64 #s(literal 1/2 binary64) im))) (.f64 re re) (*.f64 (log.f64 im) (log.f64 base)))
(+ (* (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))))))))
(fma.f64 (fma.f64 (/.f64 (log.f64 base) im) (/.f64 #s(literal 1/2 binary64) im) (.f64 (fma.f64 (.f64 (.f64 (log.f64 base) re) re) (/.f64 #s(literal 1/6 binary64) (pow.f64 im #s(literal 6 binary64))) (.f64 (log.f64 base) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))))) (.f64 re re))) (.f64 re re) (*.f64 (log.f64 im) (log.f64 base)))
(* -1 (/ (log (/ 1 re)) (log base)))
(/.f64 (log.f64 re) (log.f64 base))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (log.f64 base) re)) (/.f64 (.f64 im im) re) (/.f64 (log.f64 re) (log.f64 base)))
(+ (* -1 (/ (log (/ 1 re)) (log base))) (+ (* -1/4 (/ (pow im 4) (* (pow re 4) (log base)))) (* 1/2 (/ (pow im 2) (* (pow re 2) (log base))))))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (log.f64 base) re)) (/.f64 im re) (fma.f64 (/.f64 (pow.f64 im #s(literal 4 binary64)) (log.f64 base)) (/.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (/.f64 (log.f64 re) (log.f64 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)))))))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) im) (.f64 (log.f64 base) re)) (/.f64 im re) (fma.f64 (/.f64 (*.f64 #s(literal 1/720 binary64) (pow.f64 im #s(literal 6 binary64))) (pow.f64 re #s(literal 6 binary64))) (/.f64 #s(literal 120 binary64) (log.f64 base)) (fma.f64 (/.f64 (pow.f64 im #s(literal 4 binary64)) (log.f64 base)) (/.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (/.f64 (log.f64 re) (log.f64 base)))))
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
(* -1 (* (log base) (log (/ 1 re))))
(*.f64 (log.f64 re) (log.f64 base))
(+ (* -1 (* (log base) (log (/ 1 re)))) (* 1/2 (/ (* (pow im 2) (log base)) (pow re 2))))
(fma.f64 (.f64 (/.f64 (log.f64 base) re) #s(literal 1/2 binary64)) (/.f64 (.f64 im im) re) (*.f64 (log.f64 re) (log.f64 base)))
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(fma.f64 (log.f64 re) (log.f64 base) (fma.f64 (.f64 (/.f64 (log.f64 base) re) #s(literal 1/2 binary64)) (/.f64 (.f64 im im) re) (.f64 (.f64 (pow.f64 im #s(literal 4 binary64)) (log.f64 base)) (/.f64 #s(literal -1/4 binary64) (pow.f64 re #s(literal 4 binary64))))))
(+ (* -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))))))
(fma.f64 (.f64 (/.f64 (log.f64 base) re) #s(literal 1/2 binary64)) (/.f64 (.f64 im im) re) (fma.f64 (.f64 #s(literal 1/720 binary64) (log.f64 base)) (.f64 (pow.f64 im #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 re #s(literal 6 binary64)))) (fma.f64 (.f64 (pow.f64 im #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (log.f64 base) (pow.f64 re #s(literal 4 binary64))) (.f64 (log.f64 re) (log.f64 base)))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(fma.f64 (.f64 (/.f64 (.f64 im im) re) #s(literal 1/2 binary64)) #s(literal 1 binary64) re)
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
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(* 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)))))))
(.f64 (fma.f64 (pow.f64 im #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 re #s(literal 6 binary64))) (fma.f64 (pow.f64 im #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) re) im) re) im #s(literal 1 binary64)))) re)
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(*.f64 (log.f64 re) (log.f64 base))
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(* -1 (/ (log (/ -1 re)) (log base)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) re)) (neg.f64 (log.f64 base)))
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(+ (* -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)))))))
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0
#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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(+ (* -1 (* (log base) (log (/ -1 im)))) (* 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) (*.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 #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))))))

rewrite276.0ms (2.5%)

Memory

-51.8MiB live, 177.1MiB allocated

Rules

5 018×	`lower-fma.f64`
5 018×	`lower-fma.f32`
3 884×	`lower-*.f32`
3 876×	`lower-*.f64`
2 884×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	75
0	34	61
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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eval428.0ms (3.8%)

Memory: 10.5MiB live, 311.0MiB allocated
Compiler: Compiled 54 027 to 3 323 computations (93.8% saved)

prune183.0ms (1.6%)

Memory

24.1MiB live, 139.6MiB allocated

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	1 630	26	1 656
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 631	26	1 657

Accuracy

100.0%

Counts

1 657 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	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)))))
	99.4%	(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))
	52.0%	(/.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 im im (.f64 re re)))))) (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))))
	99.2%	(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (log.f64 base))
	99.1%	(/.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 6 binary64)))
	99.1%	(/.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)))
	52.5%	(/.f64 (.f64 (.f64 (log.f64 base) #s(literal 1/2 binary64)) (log.f64 (fma.f64 im im (.f64 re re)))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
	98.9%	(/.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))))
	99.1%	(/.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)))
▶	99.2%	(/.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)))))
	98.8%	(.f64 (pow.f64 (log.f64 (hypot.f64 im re)) #s(literal 3 binary64)) (/.f64 (pow.f64 (log.f64 base) #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 4 binary64)) (.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))))
▶	99.2%	(.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))))
	99.0%	(.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))))
	99.2%	(*.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)))
	99.1%	(*.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 #s(literal -1 binary64) (log.f64 base)) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (neg.f64 (log.f64 base))))
	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 (hypot.f64 im re))) (log.f64 base))
	99.2%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (log.f64 (hypot.f64 im re)))
	98.8%	(.f64 (.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 6 binary64))) (pow.f64 (log.f64 base) #s(literal -4 binary64)))
	99.3%	(*.f64 (log.f64 (hypot.f64 im re)) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	92.3%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (log.f64 base) im)) (/.f64 (.f64 re re) im) (/.f64 (log.f64 im) (log.f64 base))))
▶	99.4%	#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)))
▶	98.9%	#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 824 to 628 computations (23.8% saved)

simplify151.0ms (1.4%)

Memory

18.1MiB live, 136.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal 4 binary64))
cost-diff	6720	(.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64)))
cost-diff	19264	(.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))))
cost-diff	0	(log.f64 base)
cost-diff	0	(/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))))
cost-diff	13824	(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
cost-diff	0	(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
cost-diff	12800	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
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)))

Rules

5 572×	`lower-*.f32`
5 564×	`lower-*.f64`
2 384×	`cube-prod`
2 324×	`lower-fma.f64`
2 324×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	238
0	61	197
1	88	193
2	140	178
3	299	172
4	424	172
5	1292	172
6	3013	172
7	3375	172
8	3640	172
9	3995	172
10	4588	172
11	5409	172
12	6982	172
13	7178	172
14	7245	172
15	7314	172
16	7392	172
0	8191	172

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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log.f64 base)
base
#s(literal -2 binary64)
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))))
#s(literal 1 binary64)
(/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))
(log.f64 base)
base
(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(.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))))
(pow.f64 (log.f64 base) #s(literal 4 binary64))
(log.f64 base)
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 (log.f64 base) (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 -6 binary64))
#s(literal -6 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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log.f64 base)
base
#s(literal -2 binary64)
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(*.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))))
(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
#s(literal 1 binary64)
(/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))
(/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(log.f64 base)
base
(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
(log.f64 (hypot.f64 im re))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(*.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(.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 (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 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -5 binary64)) (log.f64 (hypot.f64 im re)))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(*.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal -6 binary64))
#s(literal -6 binary64)

localize124.0ms (1.1%)

Memory

-13.6MiB live, 186.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.33822250976844204	(.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64)))
accuracy	0.36166000976844204	(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
accuracy	0.907295605643406	(pow.f64 (log.f64 base) #s(literal 4 binary64))
accuracy	1.2692947867559188	(pow.f64 (log.f64 base) #s(literal -6 binary64))
accuracy	0.28125	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))))
accuracy	0.3515625	(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
accuracy	0.36166000976844204	(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
accuracy	0.39357377930532605	(/.f64 (log.f64 base) (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))
accuracy	0	(log.f64 base)
accuracy	0.36166000976844204	(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
accuracy	0.4296875	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
accuracy	0.5384750976844203	(pow.f64 (log.f64 base) #s(literal -2 binary64))
accuracy	0	(log.f64 im)
accuracy	0	(log.f64 base)
accuracy	0.3096615642898099	#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	0.37109375	(/.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	0.375	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Samples

100.0ms

256×

valid

Compiler

Compiled 330 to 36 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 13.0ms (22.4% of total)

ival-log: 12.0ms (20.7% of total)

ival-div: 11.0ms (19% of total)

ival-pow: 9.0ms (15.5% of total)

ival-hypot: 8.0ms (13.8% of total)

ival-add: 2.0ms (3.4% of total)

ival-atan2: 2.0ms (3.4% of total)

exact: 1.0ms (1.7% of total)

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

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

series219.0ms (2%)

Memory

8.2MiB live, 471.3MiB allocated

Counts

18 → 492

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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) #<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 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) (patch (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) #<representation binary64>) () ())
#s(alt (.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)))) (patch (.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)))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (patch (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) #<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 (pow.f64 (log.f64 base) #s(literal -6 binary64)) (patch (pow.f64 (log.f64 base) #s(literal -6 binary64)) #<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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (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 -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (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 -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (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 -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow (log base) 2)) (taylor 0 base) (#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 (/ 1 (pow (log base) 2)) (taylor 0 base) (#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 (/ 1 (pow (log base) 2)) (taylor 0 base) (#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 (/ 1 (pow (log base) 2)) (taylor 0 base) (#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 (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (log (sqrt (+ (pow im 2) (pow re 2))))) (taylor 0 base) (#s(alt (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (log (sqrt (+ (pow im 2) (pow re 2)))) (taylor 0 base) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (log (sqrt (+ (pow im 2) (pow re 2)))) (taylor 0 base) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (log (sqrt (+ (pow im 2) (pow re 2)))) (taylor 0 base) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (log (sqrt (+ (pow im 2) (pow re 2)))) (taylor 0 base) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
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#s(alt (+ (log -1) (* -1 (log (/ -1 im)))) (taylor -inf im) (#s(alt (log.f64 im) (patch (log.f64 im) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 im)))) (taylor -inf im) (#s(alt (log.f64 im) (patch (log.f64 im) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log (/ -1 im)) (log base))) (taylor -inf im) (#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) #<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 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (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 -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (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 -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (log base) (log (/ -1 im)))) (taylor -inf im) (#s(alt (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (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 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (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 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (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 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ -1 im))) (taylor -inf im) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ -1 im))) (* 1/2 (/ (pow re 2) (pow im 2)))) (taylor -inf im) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))) (taylor -inf im) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))) (taylor -inf im) (#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log (/ -1 im)) (log base))) (taylor -inf im) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) #<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 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) #<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 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) #<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 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log base) (log (/ -1 im)))) (taylor -inf im) (#s(alt (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) (patch (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))) (taylor -inf im) (#s(alt (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) (patch (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))) (taylor -inf im) (#s(alt (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) (patch (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1 (/ (+ (* -1/8 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (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) (log base)) (* (pow im 4) (pow (log (/ -1 im)) 2)))) (+ (* 1/4 (/ (* (pow re 4) (log base)) (* (pow im 4) (pow (log (/ -1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2))))))) (taylor -inf im) (#s(alt (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) (patch (/.f64 (log.f64 base) (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log (/ -1 im)) (log base))) (taylor -inf im) (#s(alt (.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)))) (patch (.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)))) #<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 (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)))) (patch (.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)))) #<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 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64)))) (patch (.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)))) #<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 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64)))) (patch (.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)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (taylor -inf im) (#s(alt (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (patch (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5))))) (taylor -inf im) (#s(alt (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (patch (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5)))))) (taylor -inf im) (#s(alt (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (patch (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5))))))) (taylor -inf im) (#s(alt (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) (patch (.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (pow.f64 (log.f64 base) #s(literal -6 binary64))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
60.0ms	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) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (pow (log base) 4) (pow (log base) -6))
35.0ms	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) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (pow (log base) 4) (pow (log base) -6))
30.0ms	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) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (pow (log base) 4) (pow (log base) -6))
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) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (pow (log base) 4) (pow (log base) -6))
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) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (pow (log base) 4) (pow (log base) -6))

simplify189.0ms (1.7%)

Memory

-11.4MiB live, 291.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 194×	`lower-fma.f64`
9 194×	`lower-fma.f32`
6 176×	`lower-*.f64`
6 176×	`lower-*.f32`
3 926×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	704	10090
1	2024	9760
2	7057	9754
0	8528	8796

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 488

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))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (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)))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(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))
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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 (/ -1 im)))
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(* -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)))))
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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)))))))
(/ (+ (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))))
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(* -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))))))
(+ (* -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 (/ -1 im)))
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(* -1 (/ (log base) (log (/ -1 im))))
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(- (+ (* -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) (log base)) (* (pow im 2) (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 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (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) (log base)) (* (pow im 4) (pow (log (/ -1 im)) 2)))) (+ (* 1/4 (/ (* (pow re 4) (log base)) (* (pow im 4) (pow (log (/ -1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))
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(* -1 (/ (log (/ -1 im)) (pow (log base) 5)))
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Outputs
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(+ (* -1 (log (/ -1 im))) (* 1/2 (/ (pow re 2) (pow im 2))))
(fma.f64 (*.f64 (/.f64 re im) (/.f64 re im)) #s(literal 1/2 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) im))))
(+ (* -1 (log (/ -1 im))) (+ (* -1/4 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))
(fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (*.f64 (/.f64 re im) (/.f64 re im)) #s(literal 1/2 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)))))
(+ (* -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))))))
(-.f64 (fma.f64 (.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64)))) #s(literal 1/720 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 im im)) re) re (/.f64 (.f64 (pow.f64 re #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 im #s(literal 4 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(* -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 (neg.f64 (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im)))
(+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (/.f64 (log.f64 base) im) im) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (/.f64 (neg.f64 (log.f64 base)) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(- (+ (* -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) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 re im) (/.f64 re im))) (/.f64 (log.f64 base) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))) (-.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 #s(literal -1/4 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 im #s(literal 4 binary64)))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im)))))
(- (+ (* -1 (/ (log base) (log (/ -1 im)))) (* -1 (/ (+ (* -1/8 (/ (* (pow re 6) (log base)) (pow (log (/ -1 im)) 3))) (+ (* 1/720 (/ (* (log base) (+ (* 30 (pow re 6)) (* 90 (pow re 6)))) (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) (log base)) (* (pow im 4) (pow (log (/ -1 im)) 2)))) (+ (* 1/4 (/ (* (pow re 4) (log base)) (* (pow im 4) (pow (log (/ -1 im)) 3)))) (* 1/2 (/ (* (pow re 2) (log base)) (* (pow im 2) (pow (log (/ -1 im)) 2)))))))
(-.f64 (-.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 #s(literal -1/4 binary64) (log.f64 base)) (pow.f64 re #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64)))) (/.f64 (.f64 re re) (log.f64 (/.f64 #s(literal -1 binary64) im)))) #s(literal 1/2 binary64) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 6 binary64))) (/.f64 (log.f64 base) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/720 binary64) (log.f64 base)) (.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))))) (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 #s(literal 1/4 binary64) (pow.f64 re #s(literal 4 binary64))) (/.f64 (/.f64 (log.f64 base) (pow.f64 im #s(literal 4 binary64))) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 re re)) (/.f64 (/.f64 (/.f64 (log.f64 base) im) im) (pow.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) #s(literal 2 binary64))))))) (/.f64 (log.f64 base) (log.f64 (/.f64 #s(literal -1 binary64) im))))
(* -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 (/ -1 im)) (pow (log base) 5)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5))))))
(fma.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (*.f64 (/.f64 re im) (/.f64 re im)) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64))))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5)))))))
(-.f64 (fma.f64 (/.f64 #s(literal 1/720 binary64) (pow.f64 (log.f64 base) #s(literal 5 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 -1/4 binary64) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (*.f64 (/.f64 re im) (/.f64 re im))))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (pow.f64 (log.f64 base) #s(literal 5 binary64))))

rewrite578.0ms (5.2%)

Memory

6.7MiB live, 442.4MiB allocated

Rules

7 508×	`lower-fma.f64`
7 508×	`lower-fma.f32`
5 454×	`lower-*.f32`
5 446×	`lower-*.f64`
3 310×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	177
0	61	134
1	203	114
2	1119	111
0	8612	111

Stop Event

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

Counts

18 → 6 112

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

Outputs
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eval1.4s (12.3%)

Memory: 45.5MiB live, 2 544.4MiB allocated
Compiler: Compiled 190 745 to 8 896 computations (95.3% saved)

prune189.0ms (1.7%)

Memory

26.7MiB live, 578.6MiB allocated

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	7 313	21	7 334
Fresh	17	4	21
Picked	3	2	5
Done	0	0	0
Total	7 333	27	7 360

Accuracy

100.0%

Counts

7 360 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.7%	(pow.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
▶	99.4%	(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))
	99.2%	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 im re))))
	98.9%	(/.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 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 im re))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	52.5%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (.f64 (log.f64 (fma.f64 im im (.f64 re re))) #s(literal 1/2 binary64))))
	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))))
	99.2%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 im re))) (neg.f64 (log.f64 base))))
	99.1%	(.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -6 binary64)) (log.f64 (hypot.f64 im re))))
▶	98.9%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
▶	98.7%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	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 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
	99.3%	(*.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (neg.f64 (log.f64 (hypot.f64 im re))))
	99.2%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (log.f64 (hypot.f64 im re)))
	99.2%	(.f64 (.f64 (/.f64 (log.f64 (hypot.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
	52.6%	#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)))
✓	99.4%	#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)))
	52.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 im im (*.f64 re re)))))) (log.f64 base)))
▶	98.9%	#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 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))))
✓	98.9%	#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)))
	50.5%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base)))))
	50.9%	#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 -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (log.f64 im))))
	98.8%	#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)))
▶	98.9%	#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))))
	50.4%	#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 626 to 567 computations (9.4% saved)

simplify221.0ms (2%)

Memory

-66.7MiB live, 113.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal 4 binary64))
cost-diff	0	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
cost-diff	0	#s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base)))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
cost-diff	0	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
cost-diff	0	(log.f64 im)
cost-diff	0	(/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 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	(log.f64 base)
cost-diff	0	(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
cost-diff	0	(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))
cost-diff	13824	(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))

Rules

4 396×	`lower-*.f32`
4 386×	`lower-*.f64`
1 800×	`lower-fma.f64`
1 800×	`lower-fma.f32`
1 536×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	277
0	77	255
1	106	247
2	152	207
3	285	203
4	772	203
5	2915	203
6	5117	203
7	6800	203
8	7789	203
0	8311	203

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))
(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(log.f64 base)
base
(log.f64 (hypot.f64 im re))
(hypot.f64 im re)
im
re
#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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))))
(/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))
(log.f64 im)
im
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(log.f64 base)
base
#s(literal -1 binary64)
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log.f64 base)
base
#s(literal -2 binary64)
#s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base)))
(*.f64 (log.f64 im) (log.f64 base))
(log.f64 im)
im
(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
(pow.f64 (log.f64 base) #s(literal 4 binary64))
(log.f64 base)
base
#s(literal 4 binary64)
#s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
(log.f64 im)
im
(pow.f64 (log.f64 base) #s(literal 5 binary64))
#s(literal 5 binary64)

Outputs
(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))
(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
(log.f64 (hypot.f64 re im))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
(log.f64 base)
base
(log.f64 (hypot.f64 im re))
(log.f64 (hypot.f64 re im))
(hypot.f64 im re)
(hypot.f64 re im)
im
re
#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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #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 (log.f64 im) (log.f64 base)))
(/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))
(/.f64 (log.f64 im) (log.f64 base))
(log.f64 im)
im
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(log.f64 base)
#s(literal 1 binary64)
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(log.f64 base)
base
#s(literal -1 binary64)
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log.f64 base)
base
#s(literal -2 binary64)
#s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base)))
(*.f64 (log.f64 im) (log.f64 base))
(log.f64 im)
im
(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
(.f64 #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(pow.f64 (log.f64 base) #s(literal 4 binary64))
(log.f64 base)
base
#s(literal 4 binary64)
#s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
(log.f64 im)
im
(pow.f64 (log.f64 base) #s(literal 5 binary64))
#s(literal 5 binary64)

localize136.0ms (1.2%)

Memory

22.0MiB live, 218.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.31154252930532605	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
accuracy	0.38119125976844204	(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
accuracy	0.907295605643406	(pow.f64 (log.f64 base) #s(literal 4 binary64))
accuracy	1.0878132809682306	(pow.f64 (log.f64 base) #s(literal 5 binary64))
accuracy	0.31097454815907133	#s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base)))
accuracy	0.36947250976844204	(*.f64 (log.f64 im) (log.f64 base))
accuracy	0.4296875	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
accuracy	0.5384750976844203	(pow.f64 (log.f64 base) #s(literal -2 binary64))
accuracy	0.234375	(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
accuracy	0.28515625	(pow.f64 (log.f64 base) #s(literal -1 binary64))
accuracy	0.3096615642898099	#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 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))))
accuracy	0.37109375	(/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))
accuracy	0	(log.f64 base)
accuracy	0.28515625	(/.f64 #s(literal -1 binary64) (log.f64 base))
accuracy	0.3096615642898099	#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	0.34765625	(*.f64 (neg.f64 (log.f64 im)) (/.f64 #s(literal -1 binary64) (log.f64 base)))
accuracy	0	(log.f64 base)
accuracy	0.3515625	(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
accuracy	0.36166000976844204	(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
accuracy	0.375	(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))

Samples

107.0ms

256×

valid

Compiler

Compiled 281 to 44 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-pow: 25.0ms (29.1% of total)

ival-mult: 23.0ms (26.8% of total)

ival-log: 12.0ms (14% of total)

ival-div: 11.0ms (12.8% of total)

ival-hypot: 8.0ms (9.3% of total)

ival-add: 2.0ms (2.3% of total)

ival-atan2: 2.0ms (2.3% 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)

series164.0ms (1.5%)

Memory

-4.4MiB live, 350.3MiB allocated

Counts

22 → 528

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (patch (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base)) (patch (/.f64 (/.f64 (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base)) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (patch (.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) #<representation binary64>) () ())
#s(alt (log.f64 base) (patch (log.f64 base) #<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 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #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 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (patch (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (.f64 (log.f64 im) (log.f64 base)))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (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 #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (.f64 (log.f64 im) (log.f64 base))) (patch #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))) #<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 #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (patch #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) #<representation binary64>) () ())
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#s(alt (.f64 (log.f64 im) (log.f64 base)) (patch (.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())
#s(alt (pow.f64 (log.f64 base) #s(literal 5 binary64)) (patch (pow.f64 (log.f64 base) #s(literal 5 binary64)) #<representation binary64>) () ())
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Outputs
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#s(alt (log base) (taylor 0 base) (#s(alt (log.f64 base) (patch (log.f64 base) #<representation binary64>) () ())) ())
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#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>) () ())) ())
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#s(alt (log base) (taylor 0 base) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (log base) (taylor 0 base) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))) #<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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))) #<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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 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) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (patch (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (patch (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (patch (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (log im) (log base)) (taylor 0 base) (#s(alt (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (patch (/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
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#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)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))) (patch (.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (taylor -inf im) (#s(alt #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (patch #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5))))) (taylor -inf im) (#s(alt #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (patch #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5)))))) (taylor -inf im) (#s(alt #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (patch #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5))))))) (taylor -inf im) (#s(alt #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) (patch #s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))) (taylor -inf im) (#s(alt (.f64 (log.f64 im) (log.f64 base)) (patch (.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))) (taylor -inf im) (#s(alt (.f64 (log.f64 im) (log.f64 base)) (patch (.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))) (taylor -inf im) (#s(alt (.f64 (log.f64 im) (log.f64 base)) (patch (.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (* (log base) (+ (log -1) (* -1 (log (/ -1 im))))) (taylor -inf im) (#s(alt (.f64 (log.f64 im) (log.f64 base)) (patch (.f64 (log.f64 im) (log.f64 base)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5)) (taylor -inf im) (#s(alt (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5)) (taylor -inf im) (#s(alt (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5)) (taylor -inf im) (#s(alt (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5)) (taylor -inf im) (#s(alt (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (patch (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
27.0ms	base	@	-inf	((/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base) (* (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) (/ 1 (pow (log base) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (/ 1 (pow (log base) -1))) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/ -1 (log base)) (pow (log base) -1) (* (log im) (log base)) (pow (log base) 5) (/ (log im) (pow (log base) 5)))
27.0ms	base	@	inf	((/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base) (* (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) (/ 1 (pow (log base) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (/ 1 (pow (log base) -1))) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/ -1 (log base)) (pow (log base) -1) (* (log im) (log base)) (pow (log base) 5) (/ (log im) (pow (log base) 5)))
25.0ms	base	@	0	((/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base) (* (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) (/ 1 (pow (log base) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (/ 1 (pow (log base) -1))) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/ -1 (log base)) (pow (log base) -1) (* (log im) (log base)) (pow (log base) 5) (/ (log im) (pow (log base) 5)))
17.0ms	im	@	-inf	((/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base) (* (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) (/ 1 (pow (log base) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (/ 1 (pow (log base) -1))) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/ -1 (log base)) (pow (log base) -1) (* (log im) (log base)) (pow (log base) 5) (/ (log im) (pow (log base) 5)))
16.0ms	im	@	inf	((/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base) (* (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) (/ 1 (pow (log base) -1)) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (log im) (/ 1 (pow (log base) -1))) (* (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log base) (log (sqrt (+ (* im im) (* re re))))) (* (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6))) (pow (log base) 4) (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/ -1 (log base)) (pow (log base) -1) (* (log im) (log base)) (pow (log base) 5) (/ (log im) (pow (log base) 5)))

simplify225.0ms (2%)

Memory

-7.3MiB live, 332.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16 996×	`lower-fma.f64`
16 996×	`lower-fma.f32`
4 662×	`lower-*.f64`
4 662×	`lower-*.f32`
3 580×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	400	8476
1	1053	8178
2	2991	8174
3	7313	8174
0	8126	7364

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 528

Calls

Call 1

Inputs
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(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)))))
(log base)
(log base)
(log base)
(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))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (pow (log base) 2))
(/ 1 (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)))))
(/ (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) 4)
(pow (log base) 4)
(pow (log base) 4)
(pow (log base) 4)
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 5))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 5))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 5))
(/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log base) 5))
(/ -1 (log base))
(/ -1 (log base))
(/ -1 (log base))
(/ -1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(/ 1 (log base))
(* (log base) (log im))
(* (log base) (log im))
(* (log base) (log im))
(* (log base) (log im))
(pow (log base) 5)
(pow (log base) 5)
(pow (log base) 5)
(pow (log base) 5)
(/ (log im) (pow (log base) 5))
(/ (log im) (pow (log base) 5))
(/ (log im) (pow (log base) 5))
(/ (log im) (pow (log base) 5))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(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 (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* -1 (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 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (pow (log (/ 1 base)) 2))
(/ 1 (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 (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)) 4)
(pow (log (/ 1 base)) 4)
(pow (log (/ 1 base)) 4)
(pow (log (/ 1 base)) 4)
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log (/ 1 base)) 5)))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log (/ 1 base)) 5)))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log (/ 1 base)) 5)))
(* -1 (/ (log (sqrt (+ (pow im 2) (pow re 2)))) (pow (log (/ 1 base)) 5)))
(/ 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)))
(* -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 (pow (log (/ 1 base)) 5))
(* -1 (pow (log (/ 1 base)) 5))
(* -1 (pow (log (/ 1 base)) 5))
(* -1 (pow (log (/ 1 base)) 5))
(* -1 (/ (log im) (pow (log (/ 1 base)) 5)))
(* -1 (/ (log im) (pow (log (/ 1 base)) 5)))
(* -1 (/ (log im) (pow (log (/ 1 base)) 5)))
(* -1 (/ (log im) (pow (log (/ 1 base)) 5)))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 2))))
(log (sqrt (+ (pow im 2) (pow re 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 (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 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)))))
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Outputs
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(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))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 re (*.f64 im (log.f64 base))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (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 (.f64 re re) im)) (/.f64 (log.f64 base) 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 #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) (/.f64 (.f64 re re) im)) (/.f64 (log.f64 base) 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 #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))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 re re) im)) (/.f64 (log.f64 base) im) (.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)) (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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) (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))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 re (*.f64 im (log.f64 base))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))))
(* -1 (+ (log -1) (* -1 (log (/ -1 im)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 #s(literal -1 binary64)))
(* -1 (+ (log -1) (* -1 (log (/ -1 im)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 #s(literal -1 binary64)))
(* -1 (+ (log -1) (* -1 (log (/ -1 im)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 #s(literal -1 binary64)))
(* -1 (+ (log -1) (* -1 (log (/ -1 im)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (log.f64 #s(literal -1 binary64)))
(+ (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)))
(* -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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) (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))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 re (*.f64 im (log.f64 base))) (/.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)) (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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) (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))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 re (*.f64 im (log.f64 base))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (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 (.f64 re re) im)) (/.f64 (log.f64 base) 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 #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) (/.f64 (.f64 re re) im)) (/.f64 (log.f64 base) 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 #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))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 re re) im)) (/.f64 (log.f64 base) im) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) re) im) (/.f64 re (.f64 im (log.f64 base))) (/.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) (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))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 re (*.f64 im (log.f64 base))) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (log.f64 base))))))
(* -1 (/ (log (/ -1 im)) (pow (log base) 5)))
(/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5)))))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) (.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)) im)) (/.f64 re im) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5))))))
(fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) (.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)) im)) (/.f64 re im) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64))))))
(+ (* -1 (/ (log (/ -1 im)) (pow (log base) 5))) (+ (* -1/4 (/ (pow re 4) (* (pow im 4) (pow (log base) 5)))) (+ (* 1/720 (/ (+ (* 30 (pow re 6)) (* 90 (pow re 6))) (* (pow im 6) (pow (log base) 5)))) (* 1/2 (/ (pow re 2) (* (pow im 2) (pow (log base) 5)))))))
(fma.f64 (/.f64 (.f64 #s(literal 1/720 binary64) (pow.f64 re #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (/.f64 #s(literal 120 binary64) (pow.f64 im #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal 5 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 im #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) re) (*.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)) im)) (/.f64 re im) (/.f64 (log.f64 (/.f64 #s(literal -1 binary64) im)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 5 binary64)))))))
(* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (log.f64 base))
(* (log base) (+ (log -1) (* -1 (log (/ -1 im)))))
(*.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)))) (pow (log base) 5))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))
(/ (+ (log -1) (* -1 (log (/ -1 im)))) (pow (log base) 5))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) im))) (pow.f64 (log.f64 base) #s(literal 5 binary64)))

rewrite251.0ms (2.3%)

Memory

30.2MiB live, 346.5MiB allocated

Rules

5 504×	`lower-fma.f64`
5 504×	`lower-fma.f32`
5 006×	`lower-*.f32`
4 996×	`lower-*.f64`
2 940×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	239
0	77	208
1	239	192
2	1273	167
0	8412	167

Stop Event

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

Counts

22 → 1 341

Calls

Call 1

Inputs
(/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base))
(/.f64 (/.f64 (*.f64 (log.f64 base) (log.f64 (hypot.f64 im re))) (log.f64 base)) (log.f64 base))
(*.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
(log.f64 base)
(*.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)
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #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 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64)))))
(/.f64 (log.f64 im) (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1 binary64))))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
#s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base)))
(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
(pow.f64 (log.f64 base) #s(literal 4 binary64))
#s(approx (* (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64))))
(/.f64 #s(literal -1 binary64) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(*.f64 (log.f64 im) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal 5 binary64))
(/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))

Outputs
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eval371.0ms (3.3%)

Memory: -4.5MiB live, 632.5MiB allocated
Compiler: Compiled 42 388 to 4 325 computations (89.8% saved)

prune204.0ms (1.8%)

Memory

-7.7MiB live, 192.6MiB allocated

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	2 264	14	2 278
Fresh	11	9	20
Picked	2	3	5
Done	0	2	2
Total	2 277	28	2 305

Accuracy

100.0%

Counts

2 305 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(/.f64 (/.f64 #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))) (log.f64 base)) (log.f64 base))
▶	99.2%	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))
▶	99.2%	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im))) (log.f64 base))
	98.9%	(/.f64 #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 im re))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	52.5%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (.f64 (log.f64 (fma.f64 im im (.f64 re re))) #s(literal 1/2 binary64))))
▶	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))))
	99.2%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 im re))) (neg.f64 (log.f64 base))))
	98.8%	(.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal -1/2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	97.8%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) #s(literal -5 binary64)))))
✓	98.9%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
	98.8%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (*.f64 (pow.f64 (log.f64 base) #s(literal -5 binary64)) (log.f64 im))))
✓	98.7%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	99.2%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (log.f64 (hypot.f64 im re)))
▶	98.5%	(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 2 binary64))) #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	98.8%	#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)) (neg.f64 (pow.f64 (log.f64 im) #s(literal 2 binary64)))) (log.f64 im)))
	52.6%	#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)))
✓	99.4%	#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)))
	52.0%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 im im (*.f64 re re)))))) (log.f64 base)))
	50.9%	#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))))
	98.9%	#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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
✓	98.9%	#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)))
	50.5%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base)))))
	98.8%	#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) (/.f64 #s(literal -1 binary64) (log.f64 im))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
▶	98.8%	#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)))
✓	98.9%	#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))))
	47.3%	#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)) (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal -1 binary64)))))

Compiler

Compiled 611 to 569 computations (6.9% saved)

simplify129.0ms (1.2%)

Memory

22.9MiB live, 135.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1 binary64) (log.f64 base))
cost-diff	0	(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 2 binary64))) #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
cost-diff	320	(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 2 binary64)))
cost-diff	704	(pow.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 (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	(/.f64 (*.f64 #s(literal 1/2 binary64) re) im)
cost-diff	0	(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im))
cost-diff	0	#s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im)))
cost-diff	0	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im))) (log.f64 base))
cost-diff	0	#s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))
cost-diff	0	(log.f64 base)
cost-diff	0	(/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))))
cost-diff	0	(/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))
cost-diff	0	(log.f64 base)
cost-diff	0	(/.f64 #s(literal -1 binary64) (log.f64 base))
cost-diff	1408	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))

Rules

4 730×	`lower-*.f32`
4 718×	`lower-*.f64`
2 534×	`lower-fma.f32`
2 532×	`lower-fma.f64`
1 976×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	327
0	77	278
1	116	270
2	177	242
3	277	227
4	444	222
5	897	222
6	2600	222
7	4407	222
8	6134	222
9	6833	222
0	8026	222

Stop Event

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

Calls

Call 1

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

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

localize159.0ms (1.4%)

Memory

9.8MiB live, 240.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.31097454815907133	#s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base)))
accuracy	0.36947250976844204	(*.f64 (log.f64 im) (log.f64 base))
accuracy	0.4296875	(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 2 binary64))) #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
accuracy	0.48275375976844204	(pow.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 2 binary64))
accuracy	0.3096615642898099	#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	0.33888627930532605	(.f64 (.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (log.f64 base))
accuracy	0.35060502930532605	(*.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
accuracy	0.5384750976844203	(pow.f64 (log.f64 base) #s(literal -2 binary64))
accuracy	0	(log.f64 base)
accuracy	0.0078125	(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im))
accuracy	0.13069022087881652	#s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im)))
accuracy	0.375	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im))) (log.f64 base))
accuracy	0	(log.f64 base)
accuracy	0.28125	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))))
accuracy	0.308362990415605	#s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))
accuracy	0.39357377930532605	(/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im)))
accuracy	0	(log.f64 base)
accuracy	0.26953125	(/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im)))
accuracy	0.28515625	(/.f64 #s(literal -1 binary64) (log.f64 base))
accuracy	0.3203125	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 re im))))

Samples

131.0ms

256×

valid

Compiler

Compiled 301 to 45 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-div: 29.0ms (26.5% of total)

ival-add: 25.0ms (22.8% of total)

ival-mult: 19.0ms (17.4% of total)

ival-hypot: 15.0ms (13.7% of total)

ival-log: 12.0ms (11% of total)

ival-pow: 4.0ms (3.7% of total)

ival-atan2: 2.0ms (1.8% of total)

ival-pow2: 2.0ms (1.8% of total)

exact: 1.0ms (0.9% of total)

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

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

series267.0ms (2.4%)

Memory

-22.4MiB live, 432.7MiB allocated

Counts

21 → 540

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

Calls

9 calls:

Time	Variable		Point	Expression
52.0ms	base	@	0	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ -1 (log base)) (log base) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (/ (* 1/2 re) im) (* (* (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)) (log im) (pow (/ -1 (log base)) 2) (* 1 (pow (/ -1 (log base)) 2)) (* (* 1 (pow (/ -1 (log base)) 2)) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log im) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))))
40.0ms	base	@	inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ -1 (log base)) (log base) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (/ (* 1/2 re) im) (* (* (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)) (log im) (pow (/ -1 (log base)) 2) (* 1 (pow (/ -1 (log base)) 2)) (* (* 1 (pow (/ -1 (log base)) 2)) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log im) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))))
35.0ms	im	@	-inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ -1 (log base)) (log base) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (/ (* 1/2 re) im) (* (* (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)) (log im) (pow (/ -1 (log base)) 2) (* 1 (pow (/ -1 (log base)) 2)) (* (* 1 (pow (/ -1 (log base)) 2)) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log im) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))))
30.0ms	base	@	-inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ -1 (log base)) (log base) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (/ (* 1/2 re) im) (* (* (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)) (log im) (pow (/ -1 (log base)) 2) (* 1 (pow (/ -1 (log base)) 2)) (* (* 1 (pow (/ -1 (log base)) 2)) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log im) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))))
20.0ms	im	@	inf	((/ (/ -1 (log base)) (/ -1 (log (sqrt (+ (* re re) (* im im)))))) (/ -1 (log base)) (log base) (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/ 1 (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)))) (/ (log base) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base))) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (/ (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log base)) (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (/ (* 1/2 re) im) (* (* (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)) (log im) (pow (/ -1 (log base)) 2) (* 1 (pow (/ -1 (log base)) 2)) (* (* 1 (pow (/ -1 (log base)) 2)) (* (log base) (log (sqrt (+ (* im im) (* re re)))))) (pow (log base) -2) (* (log im) (log base)) (* (log base) (log (sqrt (+ (* im im) (* re re))))))

simplify300.0ms (2.7%)

Memory

-7.3MiB live, 362.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 992×	`lower-fma.f64`
7 992×	`lower-fma.f32`
6 292×	`lower-*.f64`
6 292×	`lower-*.f32`
3 160×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	751	10089
1	2190	9755
2	7845	9755
0	8039	8889

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 540

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

rewrite136.0ms (1.2%)

Memory

-21.6MiB live, 178.9MiB allocated

Rules

4 292×	`lower-fma.f32`
4 290×	`lower-fma.f64`
4 018×	`lower-*.f32`
4 006×	`lower-*.f64`
3 636×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	277
0	77	233
1	261	211
2	1619	169
0	8500	166

Stop Event

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

Counts

21 → 599

Calls

Call 1

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

Outputs
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eval357.0ms (3.2%)

Memory: 28.2MiB live, 345.2MiB allocated
Compiler: Compiled 25 788 to 2 890 computations (88.8% saved)

prune75.0ms (0.7%)

Memory

14.5MiB live, 130.6MiB allocated

Pruning

28 alts after pruning (20 fresh and 8 done)

	Pruned	Kept	Total
New	1 365	7	1 372
Fresh	5	13	18
Picked	2	3	5
Done	0	5	5
Total	1 372	28	1 400

Accuracy

100.0%

Counts

1 400 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.3%	(pow.f64 (pow.f64 (/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im)) (log.f64 base)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
	98.8%	(/.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(approx (/ -1 (log (sqrt (+ (* re re) (* im im))))) (/.f64 #s(literal -1 binary64) (log.f64 im))))
✓	99.2%	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (log.f64 im))) (log.f64 base))
	50.7%	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) #s(approx (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (/.f64 (fma.f64 (.f64 (log.f64 im) im) im (.f64 #s(literal 1/2 binary64) (.f64 re re))) (.f64 im im)))) (log.f64 base))
	53.9%	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) #s(approx (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (.f64 (+.f64 (/.f64 (/.f64 (log.f64 im) re) re) (/.f64 #s(literal 1/2 binary64) (.f64 im im))) (*.f64 re re)))) (log.f64 base))
	3.2%	(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) #s(approx (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 im im)) re) re))) (log.f64 base))
	98.9%	(/.f64 #s(approx (* (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 im re))) (/.f64 #s(literal -1 binary64) (log.f64 base))))
	52.5%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) (.f64 (log.f64 (fma.f64 im im (.f64 re re))) #s(literal 1/2 binary64))))
✓	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 base) #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im))))
	98.8%	(/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (log.f64 base)) (/.f64 #s(literal -1 binary64) #s(approx (/ ( (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (log.f64 im)))))
	98.8%	(.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal -1/2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
✓	98.9%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (/.f64 (log.f64 im) (pow.f64 (log.f64 base) #s(literal 5 binary64)))))
	98.8%	(.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(approx ( (* (log base) (log (sqrt (+ (* im im) (* re re))))) (pow (log base) -6)) (*.f64 (pow.f64 (log.f64 base) #s(literal -5 binary64)) (log.f64 im))))
✓	98.7%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(approx ( (log base) (log (sqrt (+ (* im im) (* re re))))) (*.f64 (log.f64 im) (log.f64 base))))
	99.2%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)) (log.f64 (hypot.f64 im re)))
	98.8%	#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)) (neg.f64 (pow.f64 (log.f64 im) #s(literal 2 binary64)))) (log.f64 im)))
	52.6%	#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)))
✓	99.4%	#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)))
	50.9%	#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))))
	98.9%	#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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (log.f64 base)))))
✓	98.9%	#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)))
	50.5%	#s(approx (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (log.f64 im) (exp.f64 (log.f64 (log.f64 base)))))
	98.6%	#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 (/.f64 #s(literal -1 binary64) (log.f64 base)) #s(literal 2 binary64))) (log.f64 base)))
✓	98.8%	#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)))
✓	98.9%	#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))))
	47.3%	#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)) (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal -1 binary64)))))

Compiler

Compiled 1 300 to 565 computations (56.5% saved)

regimes102.0ms (0.9%)

Memory

-32.1MiB live, 166.9MiB allocated

Counts

69 → 1

Calls

Call 1

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

20.0ms	(log.f64 base)
19.0ms	im
19.0ms	base
18.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
17.0ms	re

Results

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

Compiler

Compiled 33 to 31 computations (6.1% saved)

regimes26.0ms (0.2%)

Memory

9.1MiB live, 46.1MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

5 calls:

7.0ms	re
5.0ms	(log.f64 base)
4.0ms	im
4.0ms	base
4.0ms	(/.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
99.2%	1	`re`
99.2%	1	`im`
99.2%	1	`base`
99.2%	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))))`
99.2%	1	`(log.f64 base)`

Compiler

Compiled 33 to 31 computations (6.1% saved)

regimes21.0ms (0.2%)

Memory

0.4MiB live, 37.1MiB allocated

Counts

10 → 1

Calls

Call 1

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

Calls

5 calls:

6.0ms	re
4.0ms	(log.f64 base)
4.0ms	im
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))))
3.0ms	base

Results

Accuracy	Segments	Branch
98.9%	1	`re`
98.9%	1	`im`
98.9%	1	`base`
98.9%	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))))`
98.9%	1	`(log.f64 base)`

Compiler

Compiled 33 to 31 computations (6.1% saved)

regimes7.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs

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

Outputs

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

Calls

5 calls:

1.0ms	(/.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))))
1.0ms	im
1.0ms	(log.f64 base)
1.0ms	re
1.0ms	base

Results

Accuracy	Segments	Branch
3.2%	1	`re`
3.2%	1	`im`
3.2%	1	`base`
3.2%	1	`(log.f64 base)`
3.2%	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 33 to 31 computations (6.1% saved)

simplify23.0ms (0.2%)

Memory

10.0MiB live, 47.4MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	137
1	54	137

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)))
(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (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) (log.f64 base)))
(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) #s(approx (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 im 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 (hypot.f64 re im)) (log.f64 base)))
(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) re) im) (/.f64 re im) (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) (log.f64 base)))
(/.f64 #s(approx (/ (* (log base) (log (sqrt (+ (* im im) (* re re))))) (log base)) #s(approx (+ (* (/ (* 1/2 re) im) (/ re im)) (log im)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 im im)) re) re))) (log.f64 base))

soundness671.0ms (6%)

Memory

2.7MiB live, 538.0MiB allocated

Rules

16 996×	`lower-fma.f64`
16 996×	`lower-fma.f32`
12 210×	`lower-fma.f64`
12 210×	`lower-fma.f32`
7 992×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	299	2912
1	840	2860
2	2641	2828
3	6330	2818
0	8095	2516
0	751	10089
1	2190	9755
2	7845	9755
0	8039	8889
0	400	8476
1	1053	8178
2	2991	8174
3	7313	8174
0	8126	7364
0	18	75
0	34	61
1	99	55
2	688	55
3	6199	55
0	8222	35

Stop Event

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

Compiler

Compiled 139 to 99 computations (28.8% saved)

preprocess58.0ms (0.5%)

Memory

-2.2MiB live, 73.8MiB allocated

Remove

(sort re im)

(abs re)

(abs im)

Compiler

Compiled 190 to 134 computations (29.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze234.0ms (2.1%)

sample2.0s (17.7%)

explain363.0ms (3.3%)

preprocess214.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify196.0ms (1.8%)

localize61.0ms (0.5%)

series228.0ms (2%)

simplify257.0ms (2.3%)

rewrite276.0ms (2.5%)

eval428.0ms (3.8%)

prune183.0ms (1.6%)

simplify151.0ms (1.4%)

localize124.0ms (1.1%)

series219.0ms (2%)

simplify189.0ms (1.7%)

rewrite578.0ms (5.2%)

eval1.4s (12.3%)

prune189.0ms (1.7%)

simplify221.0ms (2%)

localize136.0ms (1.2%)

series164.0ms (1.5%)

simplify225.0ms (2%)

rewrite251.0ms (2.3%)

eval371.0ms (3.3%)

prune204.0ms (1.8%)

simplify129.0ms (1.2%)

localize159.0ms (1.4%)

series267.0ms (2.4%)

simplify300.0ms (2.7%)

rewrite136.0ms (1.2%)

eval357.0ms (3.2%)

prune75.0ms (0.7%)

regimes102.0ms (0.9%)

regimes26.0ms (0.2%)

regimes21.0ms (0.2%)

regimes7.0ms (0.1%)

simplify23.0ms (0.2%)

soundness671.0ms (6%)

preprocess58.0ms (0.5%)

end0.0ms (0%)

Profiling