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

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze192.0ms (3%)

Memory

48.8MiB live, 374.8MiB allocated; 71ms collecting garbage

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)

sample2.2s (35.2%)

Memory

-53.8MiB live, 2 553.5MiB allocated; 450ms collecting garbage

Samples

1.6s

8 256×

valid

Precisions

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

ival-mult: 278.0ms (24.9% of total)

ival-log: 277.0ms (24.8% of total)

ival-hypot: 254.0ms (22.8% of total)

ival-sub: 112.0ms (10% of total)

ival-atan2: 86.0ms (7.7% of total)

ival-div: 48.0ms (4.3% of total)

ival-add: 43.0ms (3.9% of total)

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

exact: 6.0ms (0.5% of total)

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

adjust: 3.0ms (0.3% of total)

Bogosity

explain345.0ms (5.5%)

Memory

32.6MiB live, 311.4MiB allocated; 35ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
141	-	-	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	-	`(log.f64 base)`
0	-	-	`(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))`
0	-	-	`(*.f64 re re)`
0	-	-	`(atan2.f64 im re)`
0	-	-	`im`
0	-	-	`(*.f64 (atan2.f64 im re) (log.f64 base))`
0	-	-	`(+.f64 (.f64 re re) (.f64 im im))`
0	-	-	`re`
0	-	-	`(-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64)))`
0	-	-	`(+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))`
0	-	-	`(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))`
0	-	-	`#s(literal 0 binary64)`
0	-	-	`(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))`
0	-	-	`(*.f64 (log.f64 base) (log.f64 base))`
0	-	-	`(*.f64 im im)`
0	-	-	`base`
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	128	0
↳	`(+.f64 (.f64 re re) (.f64 im im))`	overflow	128
↳	`(*.f64 re re)`	overflow	64
↳	`(*.f64 im im)`	overflow	79

Confusion

	Predicted +	Predicted -
+	128	13
-	0	115

Precision

1.0

Recall

0.9078014184397163

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	13
-	0	0	115

Precision?

1.0

Recall?

0.9078014184397163

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

91.0ms

512×

valid

Compiler

Compiled 270 to 58 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-log: 30.0ms (43.4% of total)

ival-mult: 15.0ms (21.7% of total)

ival-hypot: 8.0ms (11.6% of total)

ival-add: 4.0ms (5.8% of total)

ival-atan2: 4.0ms (5.8% of total)

ival-div: 3.0ms (4.3% of total)

ival-sub: 2.0ms (2.9% of total)

ival-true: 1.0ms (1.4% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

preprocess166.0ms (2.6%)

Memory

-19.9MiB live, 129.6MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	139
1	207	121
2	627	78
3	1569	63
4	3269	63
5	6670	63
0	18	26
0	34	14
1	63	12
2	162	8
3	344	6
4	618	6
5	1493	6
6	5128	6
7	5816	6
8	6074	6
9	6092	6
10	6097	6
11	7853	6
0	8069	6

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Compiler

Compiled 28 to 18 computations (35.7% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.6%	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))

Status

Accuracy

Program

▶

44.6%

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

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify88.0ms (1.4%)

Memory

14.8MiB live, 101.7MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	2	(-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64)))
cost-diff	4	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
cost-diff	5	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
cost-diff	6	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	113
0	34	77
1	63	75
2	162	71
3	344	69
4	618	69
5	1493	69
6	5128	69
7	5816	69
8	6074	69
9	6092	69
10	6097	69
11	7853	69
0	8069	58

Stop Event

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

Calls

Call 1

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

localize98.0ms (1.6%)

Memory

-15.9MiB live, 126.3MiB allocated; 18ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.3359375	(*.f64 (atan2.f64 im re) (log.f64 base))
accuracy	0.34994125976844204	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
accuracy	0.5302925293053261	(*.f64 (log.f64 base) (log.f64 base))
accuracy	32.789994685290864	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Samples

47.0ms

256×

valid

Compiler

Compiled 121 to 20 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 20.0ms (54.9% of total)

ival-log: 5.0ms (13.7% of total)

ival-hypot: 4.0ms (11% of total)

ival-add: 2.0ms (5.5% of total)

ival-atan2: 2.0ms (5.5% of total)

ival-div: 1.0ms (2.7% of total)

ival-sub: 1.0ms (2.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series114.0ms (1.8%)

Memory

18.7MiB live, 209.1MiB allocated; 28ms collecting garbage

Counts

6 → 32

Calls

Call 1

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

Outputs
(/ (atan2 im re) (log base))
0
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) (atan2 im re))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(pow (log base) 2)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(pow (log (/ 1 base)) 2)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)

Calls

9 calls:

Time	Variable		Point	Expression
27.0ms	re	@	0	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (* (log base) (log base)) (* (atan2 im re) (log base)))
21.0ms	base	@	0	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (* (log base) (log base)) (* (atan2 im re) (log base)))
15.0ms	base	@	-inf	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (* (log base) (log base)) (* (atan2 im re) (log base)))
14.0ms	re	@	-inf	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (* (log base) (log base)) (* (atan2 im re) (log base)))
8.0ms	base	@	inf	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (* (log base) (log base)) (* (atan2 im re) (log base)))

simplify131.0ms (2.1%)

Memory

37.7MiB live, 222.0MiB allocated; 21ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	469
1	343	466
2	1279	462
3	5845	460
0	8117	428

Stop Event

1×	iter limit
1×	node limit

Counts

32 → 30

Calls

Call 1

Inputs
(/ (atan2 im re) (log base))
0
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) (atan2 im re))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(pow (log base) 2)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(pow (log (/ 1 base)) 2)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)

Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
0
#s(literal 0 binary64)
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 (/.f64 (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal -1/8 binary64) #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) (atan2 im re))
(*.f64 (log.f64 base) (atan2.f64 im re))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 (/.f64 im re) re) re)
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(.f64 (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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64))) re)
(* 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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64)))) re)
(* -1 re)
(neg.f64 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) re) (/.f64 (.f64 im im) re) #s(literal -1 binary64)) re)
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(.f64 (neg.f64 re) (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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64))))
(* -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))))))))
(.f64 (neg.f64 re) (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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64)))))
(+ re (* 1/2 (/ (pow im 2) re)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) re) (*.f64 im im) re)
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) re) re) (.f64 im im) #s(literal 1/2 binary64)) re) (.f64 im im) 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)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) im) (/.f64 im (pow.f64 re #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 3 binary64)))) (.f64 im im) (/.f64 #s(literal 1/2 binary64) re)) (*.f64 im im) re)
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64)) im)
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64))) im)
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(.f64 (fma.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 im #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64)))) im)
(* -1 im)
(neg.f64 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) im) (/.f64 (.f64 re re) im) #s(literal -1 binary64)) im)
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(.f64 (neg.f64 im) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(.f64 (neg.f64 im) (fma.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 im #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (atan2.f64 im re))
(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))

rewrite104.0ms (1.6%)

Memory

-0.8MiB live, 189.0MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	74
0	34	38
1	120	36
2	895	33
0	9566	28

Stop Event

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

Counts

6 → 328

Calls

Call 1

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

Outputs
(.f64 (.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (log.f64 base))) (neg.f64 (log.f64 base)))
(.f64 (.f64 (*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal -1 binary64)) (log.f64 base)) (log.f64 base))
(.f64 (.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (neg.f64 (log.f64 base)))
(.f64 (.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (log.f64 base))
(.f64 (.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (neg.f64 (log.f64 base))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(.f64 (.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(.f64 (/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (*.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (log.f64 base)) (*.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (fabs.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (fabs.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (.f64 (log.f64 base) (atan2.f64 im re))) (.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (/.f64 (log.f64 base) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (*.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (atan2.f64 im re) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3/2 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 3 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))) #s(literal -1 binary64))
(*.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))) #s(literal 1 binary64))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -1 binary64))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 3 binary64)) #s(literal 1 binary64) #s(literal 0 binary64)) (pow.f64 (*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64))) (pow.f64 (log.f64 base) #s(literal 10 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 12 binary64))) (*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (pow.f64 (log.f64 base) #s(literal 8 binary64))))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 10 binary64))) (pow.f64 (log.f64 base) #s(literal 12 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (log.f64 base)) (neg.f64 (log.f64 base)))
(/.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (log.f64 base)) (log.f64 base))
(/.f64 (pow.f64 (.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64)) (.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (pow.f64 (.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 2 binary64)))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))))
(/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64)) (.f64 (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))))
(fma.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (log.f64 base))) (neg.f64 (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal -1 binary64)) (log.f64 base)) (log.f64 base) #s(literal 0 binary64))
(fma.f64 (.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (neg.f64 (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (log.f64 base) #s(literal 0 binary64))
(fma.f64 (.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (neg.f64 (log.f64 base))) (pow.f64 (log.f64 base) #s(literal 3 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 3 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (atan2.f64 im re)) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (log.f64 base)) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (*.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (fabs.f64 (.f64 (log.f64 base) (atan2.f64 im re))) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (fabs.f64 (*.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (*.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (.f64 (log.f64 base) (atan2.f64 im re))) (*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base))) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 base) (.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (.f64 (pow.f64 (atan2.f64 im re) #s(literal 2 binary64)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
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eval50.0ms (0.8%)

Memory: -20.0MiB live, 118.2MiB allocated; 17ms collecting garbage
Compiler: Compiled 8 349 to 1 023 computations (87.7% saved)

prune18.0ms (0.3%)

Memory

8.8MiB live, 50.5MiB allocated; 6ms collecting garbage

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	286	13	299
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	13	300

Accuracy

100.0%

Counts

300 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	44.5%	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
▶	22.9%	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
▶	99.3%	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
	99.2%	(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 10 binary64))) (pow.f64 (log.f64 base) #s(literal 12 binary64)))
	99.2%	(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64))) (pow.f64 (log.f64 base) #s(literal 10 binary64)))
▶	99.3%	(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
	99.2%	(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
	99.3%	(/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
	99.3%	(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	82.1%	(.f64 (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 3 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
	99.1%	(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
▶	99.3%	(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
▶	99.6%	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))

Compiler

Compiled 494 to 358 computations (27.5% saved)

simplify96.0ms (1.5%)

Memory

0.7MiB live, 206.6MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	3	(exp.f64 (*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64)))
cost-diff	4	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
cost-diff	5	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
cost-diff	5	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
cost-diff	0	(log.f64 base)
cost-diff	0	(*.f64 (log.f64 base) (atan2.f64 im re))
cost-diff	0	(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
cost-diff	3	(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
cost-diff	0	(pow.f64 (log.f64 base) #s(literal 3 binary64))
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
cost-diff	0	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
cost-diff	0	(log.f64 base)
cost-diff	5	(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
cost-diff	0	(log.f64 base)
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(/.f64 (atan2.f64 im re) (log.f64 base))
cost-diff	0	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	302
0	84	232
1	145	230
2	310	221
3	887	219
4	3381	219
0	8926	208

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2.f64 im re)
im
re
(log.f64 base)
base
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(log.f64 base)
base
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 3 binary64))
(log.f64 base)
base
#s(literal 3 binary64)
(pow.f64 (log.f64 base) #s(literal 4 binary64))
#s(literal 4 binary64)
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(log.f64 base)
base
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 6 binary64))
#s(literal 6 binary64)
(pow.f64 (log.f64 base) #s(literal 8 binary64))
#s(literal 8 binary64)
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64)))
(*.f64 (atan2.f64 im re) (log.f64 base))
(atan2.f64 im re)
im
re
(log.f64 base)
base
(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
(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)
(*.f64 im im)
#s(literal 0 binary64)
(+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64)))
(*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))
(log.f64 (neg.f64 (log.f64 base)))
(neg.f64 (log.f64 base))
#s(literal 2 binary64)
(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))

Outputs
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2.f64 im re)
im
re
(log.f64 base)
base
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(log.f64 base)
base
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re))
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 3 binary64))
(log.f64 base)
base
#s(literal 3 binary64)
(pow.f64 (log.f64 base) #s(literal 4 binary64))
#s(literal 4 binary64)
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))
(*.f64 (log.f64 base) (atan2.f64 im re))
(log.f64 base)
base
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 6 binary64))
#s(literal 6 binary64)
(pow.f64 (log.f64 base) #s(literal 8 binary64))
#s(literal 8 binary64)
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 (log.f64 base) (atan2.f64 im re))
(atan2.f64 im re)
im
re
(log.f64 base)
base
(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
#s(literal 0 binary64)
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
(log.f64 (hypot.f64 re im))
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(hypot.f64 re im)
(+.f64 (.f64 re re) (.f64 im im))
(fma.f64 re re (*.f64 im im))
(*.f64 re re)
(*.f64 im im)
#s(literal 0 binary64)
(+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64)))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))
(log.f64 (neg.f64 (log.f64 base)))
(neg.f64 (log.f64 base))
#s(literal 2 binary64)
(*.f64 #s(literal 0 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)

localize238.0ms (3.8%)

Memory

4.9MiB live, 242.8MiB allocated; 13ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.171875	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
accuracy	0.1875	(*.f64 (atan2.f64 im re) (log.f64 base))
accuracy	0.8888069825458268	(exp.f64 (*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64)))
accuracy	16.930080235807523	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
accuracy	0.1875	(*.f64 (log.f64 base) (atan2.f64 im re))
accuracy	0.3128102777601868	(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
accuracy	0.6844493643975853	(pow.f64 (log.f64 base) #s(literal 6 binary64))
accuracy	0.8231506758459224	(pow.f64 (log.f64 base) #s(literal 8 binary64))
accuracy	0.16244125976844204	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
accuracy	0.19182889735365558	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
accuracy	0.41517270513728244	(pow.f64 (log.f64 base) #s(literal 3 binary64))
accuracy	0.535385351663913	(pow.f64 (log.f64 base) #s(literal 4 binary64))
accuracy	0.0	(log.f64 base)
accuracy	0.15625	(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
accuracy	0.18359375	(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
accuracy	0.297538769536884	(pow.f64 (log.f64 base) #s(literal 2 binary64))
accuracy	0.0	(atan2.f64 im re)
accuracy	0.0	(log.f64 base)
accuracy	0.0	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
accuracy	0.16015625	(/.f64 (atan2.f64 im re) (log.f64 base))

Samples

160.0ms	133×	0	valid
46.0ms	123×	0	invalid

Compiler

Compiled 305 to 44 computations (85.6% saved)

Precisions

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

ival-mult: 15.0ms (23.6% of total)

ival-pow: 13.0ms (20.5% of total)

ival-div: 8.0ms (12.6% of total)

ival-log: 7.0ms (11% of total)

ival-exp: 5.0ms (7.9% of total)

ival-hypot: 4.0ms (6.3% of total)

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

ival-atan2: 3.0ms (4.7% of total)

ival-pow2: 2.0ms (3.1% of total)

ival-sub: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

ival-neg: 1.0ms (1.6% of total)

adjust: 0.0ms (0% of total)

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

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

series207.0ms (3.3%)

Memory

-0.9MiB live, 302.0MiB allocated; 123ms collecting garbage

Counts

21 → 57

Calls

Call 1

Inputs
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2.f64 im re)
(log.f64 base)
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(pow.f64 (log.f64 base) #s(literal 3 binary64))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64)))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow.f64 (log.f64 base) #s(literal 4 binary64))
(pow.f64 (log.f64 base) #s(literal 8 binary64))
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(*.f64 (atan2.f64 im re) (log.f64 base))

Outputs
(/ (atan2 im re) (log base))
(atan2 im re)
(/ (atan2 im re) (pow (log base) 2))
(* (pow (log base) 3) (atan2 im re))
(* (pow (log base) 7) (atan2 im re))
(* (log base) (atan2 im re))
0
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(log base)
(pow (log base) 3)
(pow (log base) 2)
(pow (log base) 4)
(pow (log base) 8)
(pow (log base) 6)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (log (/ 1 base)))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(* -1 (* (pow (log (/ 1 base)) 3) (atan2 im re)))
(* -1 (pow (log (/ 1 base)) 3))
(* -1 (* (pow (log (/ 1 base)) 7) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 4)
(pow (log (/ 1 base)) 8)
(pow (log (/ 1 base)) 6)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 3) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 3)
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 7) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 4)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 8)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 6)

Calls

9 calls:

Time	Variable		Point	Expression
52.0ms	im	@	-inf	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (log base)) (atan2 im re) (log base) (* (log base) (/ (atan2 im re) (pow (log base) 2))) (/ (atan2 im re) (pow (log base) 2)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (log base) 4)) (* (atan2 im re) (pow (log base) 3)) (pow (log base) 3) (* (* (log base) (atan2 im re)) (pow (log base) 6)) (/ (* (* (log base) (atan2 im re)) (pow (log base) 6)) (pow (log base) 8)) (* (log base) (atan2 im re)) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (exp (* (log (neg (log base))) 2)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (exp (* (log (neg (log base))) 2)) (pow (log base) 2) (pow (log base) 4) (pow (log base) 8) (pow (log base) 6) (* (atan2 im re) (log base)))
43.0ms	base	@	0	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (log base)) (atan2 im re) (log base) (* (log base) (/ (atan2 im re) (pow (log base) 2))) (/ (atan2 im re) (pow (log base) 2)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (log base) 4)) (* (atan2 im re) (pow (log base) 3)) (pow (log base) 3) (* (* (log base) (atan2 im re)) (pow (log base) 6)) (/ (* (* (log base) (atan2 im re)) (pow (log base) 6)) (pow (log base) 8)) (* (log base) (atan2 im re)) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (exp (* (log (neg (log base))) 2)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (exp (* (log (neg (log base))) 2)) (pow (log base) 2) (pow (log base) 4) (pow (log base) 8) (pow (log base) 6) (* (atan2 im re) (log base)))
27.0ms	im	@	0	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (log base)) (atan2 im re) (log base) (* (log base) (/ (atan2 im re) (pow (log base) 2))) (/ (atan2 im re) (pow (log base) 2)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (log base) 4)) (* (atan2 im re) (pow (log base) 3)) (pow (log base) 3) (* (* (log base) (atan2 im re)) (pow (log base) 6)) (/ (* (* (log base) (atan2 im re)) (pow (log base) 6)) (pow (log base) 8)) (* (log base) (atan2 im re)) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (exp (* (log (neg (log base))) 2)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (exp (* (log (neg (log base))) 2)) (pow (log base) 2) (pow (log base) 4) (pow (log base) 8) (pow (log base) 6) (* (atan2 im re) (log base)))
21.0ms	base	@	inf	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (log base)) (atan2 im re) (log base) (* (log base) (/ (atan2 im re) (pow (log base) 2))) (/ (atan2 im re) (pow (log base) 2)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (log base) 4)) (* (atan2 im re) (pow (log base) 3)) (pow (log base) 3) (* (* (log base) (atan2 im re)) (pow (log base) 6)) (/ (* (* (log base) (atan2 im re)) (pow (log base) 6)) (pow (log base) 8)) (* (log base) (atan2 im re)) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (exp (* (log (neg (log base))) 2)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (exp (* (log (neg (log base))) 2)) (pow (log base) 2) (pow (log base) 4) (pow (log base) 8) (pow (log base) 6) (* (atan2 im re) (log base)))
18.0ms	base	@	-inf	((/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (log base)) (atan2 im re) (log base) (* (log base) (/ (atan2 im re) (pow (log base) 2))) (/ (atan2 im re) (pow (log base) 2)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (log base) 4)) (* (atan2 im re) (pow (log base) 3)) (pow (log base) 3) (* (* (log base) (atan2 im re)) (pow (log base) 6)) (/ (* (* (log base) (atan2 im re)) (pow (log base) 6)) (pow (log base) 8)) (* (log base) (atan2 im re)) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (exp (* (log (neg (log base))) 2)) (* 0 0))) (* (log (sqrt (+ (* re re) (* im im)))) 0) (sqrt (+ (* re re) (* im im))) (exp (* (log (neg (log base))) 2)) (pow (log base) 2) (pow (log base) 4) (pow (log base) 8) (pow (log base) 6) (* (atan2 im re) (log base)))

simplify187.0ms (3%)

Memory

15.9MiB live, 219.4MiB allocated; 100ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	651
1	395	640
2	1386	636
3	6308	634
0	8339	602

Stop Event

1×	iter limit
1×	node limit

Counts

57 → 55

Calls

Call 1

Inputs
(/ (atan2 im re) (log base))
(atan2 im re)
(/ (atan2 im re) (pow (log base) 2))
(* (pow (log base) 3) (atan2 im re))
(* (pow (log base) 7) (atan2 im re))
(* (log base) (atan2 im re))
0
im
(+ im (* 1/2 (/ (pow re 2) im)))
(+ im (* (pow re 2) (+ (* -1/8 (/ (pow re 2) (pow im 3))) (* 1/2 (/ 1 im)))))
(+ im (* (pow re 2) (+ (* (pow re 2) (- (* 1/16 (/ (pow re 2) (pow im 5))) (* 1/8 (/ 1 (pow im 3))))) (* 1/2 (/ 1 im)))))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (+ (* 1/16 (/ (pow im 6) (pow re 6))) (* 1/2 (/ (pow im 2) (pow re 2))))))))
(+ re (* 1/2 (/ (pow im 2) re)))
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(+ re (* (pow im 2) (+ (* (pow im 2) (- (* 1/16 (/ (pow im 2) (pow re 5))) (* 1/8 (/ 1 (pow re 3))))) (* 1/2 (/ 1 re)))))
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(log base)
(pow (log base) 3)
(pow (log base) 2)
(pow (log base) 4)
(pow (log base) 8)
(pow (log base) 6)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(* -1 (log (/ 1 base)))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(* -1 (* (pow (log (/ 1 base)) 3) (atan2 im re)))
(* -1 (pow (log (/ 1 base)) 3))
(* -1 (* (pow (log (/ 1 base)) 7) (atan2 im re)))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(pow (log (/ 1 base)) 2)
(pow (log (/ 1 base)) 4)
(pow (log (/ 1 base)) 8)
(pow (log (/ 1 base)) 6)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 3) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 3)
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 7) (atan2 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 4)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 8)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 6)

Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
(/ (atan2 im re) (pow (log base) 2))
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(* (pow (log base) 3) (atan2 im re))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re))
(* (pow (log base) 7) (atan2 im re))
(*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))
(* (log base) (atan2 im re))
(*.f64 (log.f64 base) (atan2.f64 im re))
0
#s(literal 0 binary64)
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 (/.f64 (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal -1/8 binary64) #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))
re
(* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) re) im) (/.f64 (/.f64 im re) re) re)
(* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2))))))
(.f64 (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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64))) re)
(* 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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64)))) re)
(* -1 re)
(neg.f64 re)
(* -1 (* re (+ 1 (* 1/2 (/ (pow im 2) (pow re 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) re) (/.f64 (.f64 im im) re) #s(literal -1 binary64)) re)
(* -1 (* re (+ 1 (+ (* -1/8 (/ (pow im 4) (pow re 4))) (* 1/2 (/ (pow im 2) (pow re 2)))))))
(.f64 (neg.f64 re) (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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64))))
(* -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))))))))
(.f64 (neg.f64 re) (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 #s(literal 1/2 binary64) (/.f64 im re)) (/.f64 im re) #s(literal 1 binary64)))))
(+ re (* 1/2 (/ (pow im 2) re)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) re) (*.f64 im im) re)
(+ re (* (pow im 2) (+ (* -1/8 (/ (pow im 2) (pow re 3))) (* 1/2 (/ 1 re)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) re) re) (.f64 im im) #s(literal 1/2 binary64)) re) (.f64 im im) 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)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) im) (/.f64 im (pow.f64 re #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 re #s(literal 3 binary64)))) (.f64 im im) (/.f64 #s(literal 1/2 binary64) re)) (*.f64 im im) re)
(* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64)) im)
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64))) im)
(* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(.f64 (fma.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 im #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64)))) im)
(* -1 im)
(neg.f64 im)
(* -1 (* im (+ 1 (* 1/2 (/ (pow re 2) (pow im 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) im) (/.f64 (.f64 re re) im) #s(literal -1 binary64)) im)
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (* 1/2 (/ (pow re 2) (pow im 2)))))))
(.f64 (neg.f64 im) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* im (+ 1 (+ (* -1/8 (/ (pow re 4) (pow im 4))) (+ (* 1/16 (/ (pow re 6) (pow im 6))) (* 1/2 (/ (pow re 2) (pow im 2))))))))
(.f64 (neg.f64 im) (fma.f64 (pow.f64 re #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 im #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 re re) im) im) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(log base)
(log.f64 base)
(pow (log base) 3)
(pow.f64 (log.f64 base) #s(literal 3 binary64))
(pow (log base) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log base) 4)
(pow.f64 (log.f64 base) #s(literal 4 binary64))
(pow (log base) 8)
(pow.f64 (log.f64 base) #s(literal 8 binary64))
(pow (log base) 6)
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(* -1 (log (/ 1 base)))
(log.f64 base)
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(* -1 (* (pow (log (/ 1 base)) 3) (atan2 im re)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re))
(* -1 (pow (log (/ 1 base)) 3))
(pow.f64 (log.f64 base) #s(literal 3 binary64))
(* -1 (* (pow (log (/ 1 base)) 7) (atan2 im re)))
(*.f64 (neg.f64 (pow.f64 (neg.f64 (log.f64 base)) #s(literal 7 binary64))) (atan2.f64 im re))
(* -1 (* (log (/ 1 base)) (atan2 im re)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(pow (log (/ 1 base)) 2)
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow (log (/ 1 base)) 4)
(pow.f64 (neg.f64 (log.f64 base)) #s(literal 4 binary64))
(pow (log (/ 1 base)) 8)
(pow.f64 (neg.f64 (log.f64 base)) #s(literal 8 binary64))
(pow (log (/ 1 base)) 6)
(pow.f64 (neg.f64 (log.f64 base)) #s(literal 6 binary64))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/.f64 (atan2.f64 im re) (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)))) 3) (atan2 im re))
(*.f64 (pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 3 binary64)) (atan2.f64 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 3)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 3 binary64))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 7) (atan2 im re))
(*.f64 (pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 7 binary64)) (atan2.f64 im re))
(* (+ (log -1) (* -1 (log (/ -1 base)))) (atan2 im re))
(*.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) (atan2.f64 im re))
(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)))) 4)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 4 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 8)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 8 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 6)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 6 binary64))

rewrite91.0ms (1.4%)

Memory

-7.8MiB live, 92.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	197
0	84	147
1	249	130
0	1505	125

Stop Event

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

Counts

21 → 738

Calls

Call 1

Inputs
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2.f64 im re)
(log.f64 base)
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(pow.f64 (log.f64 base) #s(literal 3 binary64))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) #s(literal 0 binary64))
(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64)))
(pow.f64 (log.f64 base) #s(literal 2 binary64))
(pow.f64 (log.f64 base) #s(literal 4 binary64))
(pow.f64 (log.f64 base) #s(literal 8 binary64))
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(*.f64 (atan2.f64 im re) (log.f64 base))

Outputs
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (neg.f64 (neg.f64 (atan2.f64 im re))) (neg.f64 (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(neg.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (log.f64 base)))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(atan2.f64 im re)
(*.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(pow.f64 (log.f64 base) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
(log.f64 base)
(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (/.f64 (log.f64 base) (fabs.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (fabs.f64 (log.f64 base))))
(*.f64 (/.f64 (atan2.f64 im re) (fabs.f64 (log.f64 base))) (/.f64 (log.f64 base) (fabs.f64 (log.f64 base))))
(*.f64 (/.f64 (log.f64 base) (neg.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(*.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))) (/.f64 (log.f64 base) (neg.f64 (log.f64 base))))
(*.f64 (/.f64 (log.f64 base) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))
(.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 base)))
(.f64 (log.f64 base) (/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64))))
(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(/.f64 (/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (log.f64 base)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (fabs.f64 (log.f64 base))) (fabs.f64 (log.f64 base)))
(/.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (neg.f64 (log.f64 base))) (neg.f64 (log.f64 base)))
(/.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (log.f64 base)) (log.f64 base))
(/.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (log.f64 base)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (*.f64 (log.f64 base) (neg.f64 (atan2.f64 im re))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re)) (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))) #s(literal 0 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re)))
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re)) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re)) (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re)) (+.f64 #s(literal 0 binary64) (.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re)) #s(literal 0 binary64)))))
(/.f64 (neg.f64 (.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64))) (.f64 (log.f64 base) (atan2.f64 im re)))) (neg.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (neg.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (log.f64 base) (atan2.f64 im re)))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) #s(literal 0 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (neg.f64 (*.f64 (log.f64 base) (atan2.f64 im re))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)))
(/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64)) (.f64 (+.f64 (pow.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal 0 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64))) (.f64 (log.f64 base) (atan2.f64 im re))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64))))
(/.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (log.f64 base)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(neg.f64 (/.f64 (.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64))) (.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 8 binary64))))
(neg.f64 (/.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(neg.f64 (/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (log.f64 base)) (atan2.f64 im re)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))))
(neg.f64 (/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(neg.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
(fma.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 base) (fabs.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (fabs.f64 (log.f64 base))) #s(literal 0 binary64))
(fma.f64 (/.f64 (atan2.f64 im re) (fabs.f64 (log.f64 base))) (/.f64 (log.f64 base) (fabs.f64 (log.f64 base))) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 base) (neg.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))) #s(literal 0 binary64))
(fma.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))) (/.f64 (log.f64 base) (neg.f64 (log.f64 base))) #s(literal 0 binary64))
(fma.f64 (/.f64 (log.f64 base) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re) #s(literal 0 binary64))
(fma.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64))) #s(literal 0 binary64))
(fma.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base) #s(literal 0 binary64))
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(fma.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 base)) #s(literal 0 binary64))
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(fma.f64 (log.f64 base) (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))) #s(literal 0 binary64))
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(fma.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -1 binary64)) #s(literal 0 binary64))
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(log.f64 (pow.f64 base (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64)))))
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(fma.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal 0 binary64))
(fma.f64 (log.f64 base) (*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) #s(literal 0 binary64))
(exp.f64 (fma.f64 (log.f64 (log.f64 base)) #s(literal 3 binary64) (*.f64 (log.f64 (log.f64 base)) #s(literal 3 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (log.f64 base)) #s(literal 3 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (log.f64 base)) #s(literal 2 binary64)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 6 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (log.f64 base)) #s(literal 6 binary64))) (sinh.f64 (.f64 (log.f64 (log.f64 base)) #s(literal 6 binary64))))
(+.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(*.f64 (log.f64 base) (atan2.f64 im re))
(*.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (+.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal 0 binary64)))
(/.f64 (neg.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (neg.f64 (.f64 (log.f64 base) (atan2.f64 im re))))
(/.f64 (neg.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64))) (neg.f64 (+.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re)))
(/.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (log.f64 base) (atan2.f64 im re) #s(literal 0 binary64))
(fma.f64 (atan2.f64 im re) (log.f64 base) #s(literal 0 binary64))
(-.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (.f64 (neg.f64 (neg.f64 (log.f64 (hypot.f64 re im)))) #s(literal 0 binary64)))
(-.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (/.f64 #s(literal 0 binary64) (.f64 (log.f64 base) (atan2.f64 im re))))
(-.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (/.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64)) #s(literal 0 binary64))))
(-.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 0 binary64))
(+.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 (log.f64 base) (atan2.f64 im re)))
(log.f64 (pow.f64 base (atan2.f64 im re)))

eval73.0ms (1.2%)

Memory: 30.0MiB live, 156.3MiB allocated; 21ms collecting garbage
Compiler: Compiled 13 300 to 1 934 computations (85.5% saved)

prune58.0ms (0.9%)

Memory

-27.3MiB live, 69.9MiB allocated; 23ms collecting garbage

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	538	9	547
Fresh	6	2	8
Picked	2	3	5
Done	0	0	0
Total	546	14	560

Accuracy

100.0%

Counts

560 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
▶	99.0%	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 2 binary64)))
✓	99.3%	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
	99.3%	(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
	99.2%	(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 10 binary64))) (pow.f64 (log.f64 base) #s(literal 12 binary64)))
	99.3%	(/.f64 #s(approx (* (* (log base) (atan2 im re)) (pow (log base) 6)) (*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
▶	99.3%	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
▶	99.4%	(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))
	99.4%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re)))
	99.3%	(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓	99.3%	(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
▶	99.3%	(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
✓	99.6%	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
▶	47.2%	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))))

Compiler

Compiled 421 to 318 computations (24.5% saved)

simplify128.0ms (2%)

Memory

-5.2MiB live, 229.7MiB allocated; 37ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
cost-diff	2	(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 2 binary64))
cost-diff	7	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 2 binary64)))
cost-diff	0	(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal 3 binary64))
cost-diff	7	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
cost-diff	0	(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))))
cost-diff	2	(*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))
cost-diff	2	(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
cost-diff	0	(log.f64 base)
cost-diff	5	(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -1 binary64))
cost-diff	2	(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	209
0	63	169
1	120	165
2	317	150
3	2084	150
0	9327	150

Stop Event

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

Calls

Call 1

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

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

localize167.0ms (2.6%)

Memory

33.2MiB live, 269.8MiB allocated; 76ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
accuracy	0.232753759768442	(pow.f64 (log.f64 base) #s(literal 2 binary64))
accuracy	0.27085878907376804	(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 2 binary64))
accuracy	0.3777314453688405	(pow.f64 (log.f64 base) #s(literal 3 binary64))
accuracy	0.11556625976844202	(/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
accuracy	0.125	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
accuracy	0.3777314453688405	(pow.f64 (log.f64 base) #s(literal 3 binary64))
accuracy	0.43964404305326066	(pow.f64 (log.f64 base) #s(literal 4 binary64))
accuracy	0.0	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))))
accuracy	0.01953125	(log.f64 (log.f64 base))
accuracy	0.1171875	(/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64))))
accuracy	0.5336368160625061	(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))
accuracy	0.0	(log.f64 base)
accuracy	0.13671875	(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
accuracy	0.1640625	(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
accuracy	0.26761630861065205	(pow.f64 (log.f64 base) #s(literal -2 binary64))
accuracy	0.0	(atan2.f64 im re)
accuracy	0.0	(log.f64 base)
accuracy	0.13671875	(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))
accuracy	0.16796875	(pow.f64 (log.f64 base) #s(literal -1 binary64))

Samples

86.0ms	133×	0	invalid
44.0ms	123×	0	valid

Compiler

Compiled 202 to 40 computations (80.2% saved)

Precisions

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

ival-log: 54.0ms (49.3% of total)

ival-pow: 14.0ms (12.8% of total)

ival-mult: 13.0ms (11.9% of total)

ival-hypot: 11.0ms (10% of total)

ival-div: 5.0ms (4.6% of total)

ival-pow2: 4.0ms (3.6% of total)

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

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

ival-add: 1.0ms (0.9% of total)

ival-sub: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

adjust: 0.0ms (0% of total)

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

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

series201.0ms (3.2%)

Memory

-17.7MiB live, 352.8MiB allocated; 52ms collecting garbage

Counts

20 → 34

Calls

Call 1

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

Outputs
(/ (atan2 im re) (log base))
(atan2 im re)
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 4))
(* (pow (log base) 3) (atan2 im re))
(/ 1 (log base))
(log base)
(log (log base))
(pow (log base) 3)
(pow (log base) 4)
(/ 1 (pow (log base) 2))
(pow (log base) 2)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(log (* -1 (log (/ 1 base))))
(* -1 (pow (log (/ 1 base)) 3))
(/ (atan2 im re) (pow (log (/ 1 base)) 4))
(pow (log (/ 1 base)) 4)
(* -1 (* (pow (log (/ 1 base)) 3) (atan2 im re)))
(/ 1 (pow (log (/ 1 base)) 2))
(pow (log (/ 1 base)) 2)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 3)
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 4))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 4)
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 3) (atan2 im re))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)

Calls

9 calls:

Time	Variable		Point	Expression
64.0ms	base	@	inf	((* (pow (log base) -1) (atan2 im re)) (pow (log base) -1) (log base) (atan2 im re) (* (log base) (* (atan2 im re) (pow (log base) -2))) (* (atan2 im re) (pow (log base) -2)) (exp (* (log (log base)) 1)) (* (log (log base)) 1) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (exp (* (log (log base)) 1))) (* (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4))) (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (pow (log base) 2) 2)) (pow (pow (log base) 2) 2) (* (atan2 im re) (pow (log base) 3)) (pow (log base) -2) (log (log base)) (pow (log base) 4) (pow (log base) 2))
48.0ms	base	@	0	((* (pow (log base) -1) (atan2 im re)) (pow (log base) -1) (log base) (atan2 im re) (* (log base) (* (atan2 im re) (pow (log base) -2))) (* (atan2 im re) (pow (log base) -2)) (exp (* (log (log base)) 1)) (* (log (log base)) 1) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (exp (* (log (log base)) 1))) (* (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4))) (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (pow (log base) 2) 2)) (pow (pow (log base) 2) 2) (* (atan2 im re) (pow (log base) 3)) (pow (log base) -2) (log (log base)) (pow (log base) 4) (pow (log base) 2))
25.0ms	base	@	-inf	((* (pow (log base) -1) (atan2 im re)) (pow (log base) -1) (log base) (atan2 im re) (* (log base) (* (atan2 im re) (pow (log base) -2))) (* (atan2 im re) (pow (log base) -2)) (exp (* (log (log base)) 1)) (* (log (log base)) 1) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (exp (* (log (log base)) 1))) (* (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4))) (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (pow (log base) 2) 2)) (pow (pow (log base) 2) 2) (* (atan2 im re) (pow (log base) 3)) (pow (log base) -2) (log (log base)) (pow (log base) 4) (pow (log base) 2))
15.0ms	re	@	0	((* (pow (log base) -1) (atan2 im re)) (pow (log base) -1) (log base) (atan2 im re) (* (log base) (* (atan2 im re) (pow (log base) -2))) (* (atan2 im re) (pow (log base) -2)) (exp (* (log (log base)) 1)) (* (log (log base)) 1) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (exp (* (log (log base)) 1))) (* (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4))) (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (pow (log base) 2) 2)) (pow (pow (log base) 2) 2) (* (atan2 im re) (pow (log base) 3)) (pow (log base) -2) (log (log base)) (pow (log base) 4) (pow (log base) 2))
11.0ms	re	@	-inf	((* (pow (log base) -1) (atan2 im re)) (pow (log base) -1) (log base) (atan2 im re) (* (log base) (* (atan2 im re) (pow (log base) -2))) (* (atan2 im re) (pow (log base) -2)) (exp (* (log (log base)) 1)) (* (log (log base)) 1) (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/ (atan2 im re) (exp (* (log (log base)) 1))) (* (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4))) (pow (log base) 3) (/ (atan2 im re) (pow (log base) 4)) (/ (* (atan2 im re) (pow (log base) 3)) (pow (pow (log base) 2) 2)) (pow (pow (log base) 2) 2) (* (atan2 im re) (pow (log base) 3)) (pow (log base) -2) (log (log base)) (pow (log base) 4) (pow (log base) 2))

simplify97.0ms (1.5%)

Memory

24.9MiB live, 114.9MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	242
1	84	231
2	182	231
3	675	231
4	2375	231
5	6713	231
0	8190	231

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 34

Calls

Call 1

Inputs
(/ (atan2 im re) (log base))
(atan2 im re)
(/ (atan2 im re) (pow (log base) 2))
(/ (atan2 im re) (pow (log base) 4))
(* (pow (log base) 3) (atan2 im re))
(/ 1 (log base))
(log base)
(log (log base))
(pow (log base) 3)
(pow (log base) 4)
(/ 1 (pow (log base) 2))
(pow (log base) 2)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(/ (atan2 im re) (pow (log (/ 1 base)) 2))
(log (* -1 (log (/ 1 base))))
(* -1 (pow (log (/ 1 base)) 3))
(/ (atan2 im re) (pow (log (/ 1 base)) 4))
(pow (log (/ 1 base)) 4)
(* -1 (* (pow (log (/ 1 base)) 3) (atan2 im re)))
(/ 1 (pow (log (/ 1 base)) 2))
(pow (log (/ 1 base)) 2)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(log (+ (log -1) (* -1 (log (/ -1 base)))))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 3)
(/ (atan2 im re) (pow (+ (log -1) (* -1 (log (/ -1 base)))) 4))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 4)
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 3) (atan2 im re))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 2)

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

rewrite65.0ms (1%)

Memory

2.2MiB live, 92.6MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	163
0	63	126
1	212	120
0	1255	120

Stop Event

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

Counts

20 → 348

Calls

Call 1

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

Outputs
(.f64 (.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3/2 binary64))) (pow.f64 (log.f64 base) #s(literal 3/2 binary64)))
(.f64 (.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (log.f64 base))
(.f64 (.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(*.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 3 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))
(.f64 (log.f64 base) (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(/.f64 (/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (atan2.f64 im re)) (log.f64 base))
(/.f64 (*.f64 (atan2.f64 im re) #s(literal 1 binary64)) (log.f64 base))
(/.f64 (neg.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64)))) (neg.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(/.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(neg.f64 (/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (log.f64 base) #s(literal 3/2 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(*.f64 (log.f64 base) (/.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(/.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(/.f64 #s(literal -1 binary64) (neg.f64 (log.f64 base)))
(exp.f64 (-.f64 (.f64 #s(literal 3 binary64) (log.f64 (log.f64 base))) (.f64 #s(literal 4 binary64) (log.f64 (log.f64 base)))))
(exp.f64 (-.f64 (.f64 #s(literal 3 binary64) (log.f64 (log.f64 base))) (.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -1 binary64))) (sinh.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (log.f64 base) #s(literal 1/2 binary64)) (pow.f64 (log.f64 base) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (log.f64 base)))
(pow.f64 (log.f64 base) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (log.f64 base))) (cosh.f64 (log.f64 (log.f64 base)))) (.f64 (sinh.f64 (log.f64 (log.f64 base))) (sinh.f64 (log.f64 (log.f64 base))))) (-.f64 (cosh.f64 (log.f64 (log.f64 base))) (sinh.f64 (log.f64 (log.f64 base)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (log.f64 base))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (log.f64 base))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (log.f64 base))) (cosh.f64 (log.f64 (log.f64 base))) (-.f64 (.f64 (sinh.f64 (log.f64 (log.f64 base))) (sinh.f64 (log.f64 (log.f64 base)))) (.f64 (cosh.f64 (log.f64 (log.f64 base))) (sinh.f64 (log.f64 (log.f64 base)))))))
(exp.f64 (log.f64 (log.f64 base)))
(+.f64 (sinh.f64 (log.f64 (log.f64 base))) (cosh.f64 (log.f64 (log.f64 base))))
(+.f64 (cosh.f64 (log.f64 (log.f64 base))) (sinh.f64 (log.f64 (log.f64 base))))
(log.f64 base)
(atan2.f64 im re)
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -1 binary64))) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(.f64 (.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal -2 binary64))) (atan2.f64 im re))
(.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
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eval70.0ms (1.1%)

Memory: 8.6MiB live, 168.7MiB allocated; 40ms collecting garbage
Compiler: Compiled 8 469 to 1 081 computations (87.2% saved)

prune16.0ms (0.2%)

Memory

6.9MiB live, 53.2MiB allocated; 3ms collecting garbage

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	396	6	402
Fresh	3	3	6
Picked	2	3	5
Done	0	3	3
Total	401	15	416

Accuracy

100.0%

Counts

416 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
✓	99.0%	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 2 binary64)))
✓	99.3%	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
▶	99.3%	(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
	99.3%	(/.f64 #s(approx (* (* (log base) (atan2 im re)) (pow (log base) 6)) (*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
▶	47.6%	(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
✓	99.3%	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
▶	47.6%	(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
	99.4%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
▶	99.4%	(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
▶	99.4%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
✓	99.3%	(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓	99.3%	(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
	47.2%	(.f64 (exp.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -1 binary64))) (atan2.f64 im re))
✓	99.6%	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))

Compiler

Compiled 338 to 268 computations (20.7% saved)

simplify50.0ms (0.8%)

Memory

-15.9MiB live, 86.7MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (log.f64 base) #s(literal 6 binary64))
cost-diff	0	(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re))
cost-diff	0	(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
cost-diff	3	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base))
cost-diff	0	(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
cost-diff	7	(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -2 binary64))
cost-diff	0	(atan2.f64 im re)
cost-diff	2	(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
cost-diff	3	(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base))
cost-diff	0	(log.f64 base)
cost-diff	0	(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
cost-diff	2	(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
cost-diff	2	(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
cost-diff	0	(atan2.f64 im re)
cost-diff	0	(log.f64 base)
cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 base))
cost-diff	2	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	169
0	43	154
1	66	146
2	98	140
3	190	140
4	293	140
5	422	140
6	604	140
7	812	140
8	1015	140
9	1398	140
10	1584	140
11	1736	140
12	1736	140
13	1736	140
0	1736	140

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(/.f64 #s(literal 1 binary64) (log.f64 base))
#s(literal 1 binary64)
(log.f64 base)
base
(atan2.f64 im re)
im
re
(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(log.f64 base)
base
#s(literal -1/2 binary64)
#s(literal 2 binary64)
(atan2.f64 im re)
im
re
(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
(atan2.f64 im re)
im
re
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log.f64 base)
base
#s(literal -2 binary64)
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(log.f64 base)
base
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))
(atan2.f64 im re)
im
re
(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base))
(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re))
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(log.f64 base)
base
#s(literal 6 binary64)
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 8 binary64))
#s(literal 8 binary64)

Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -1 binary64))
#s(literal 1 binary64)
(log.f64 base)
base
(atan2.f64 im re)
im
re
(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(log.f64 base)
base
#s(literal -1/2 binary64)
#s(literal 2 binary64)
(atan2.f64 im re)
im
re
(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2.f64 im re)
im
re
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -1 binary64))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(log.f64 base)
base
#s(literal -2 binary64)
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(log.f64 base)
base
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))
(atan2.f64 im re)
im
re
(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base))
(*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))
(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re))
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(log.f64 base)
base
#s(literal 6 binary64)
(atan2.f64 im re)
im
re
(pow.f64 (log.f64 base) #s(literal 8 binary64))
#s(literal 8 binary64)

localize151.0ms (2.4%)

Memory

27.3MiB live, 294.4MiB allocated; 43ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.15462875976844204	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base))
accuracy	0.158535009768442	(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
accuracy	0.5749079586096439	(pow.f64 (log.f64 base) #s(literal 6 binary64))
accuracy	0.7051121389161987	(pow.f64 (log.f64 base) #s(literal 8 binary64))
accuracy	0.0	(log.f64 base)
accuracy	0.078125	(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
accuracy	0.1328125	(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))
accuracy	0.15625	(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
accuracy	0.0	(log.f64 base)
accuracy	0.13671875	(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
accuracy	0.1484375	(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base))
accuracy	0.26761630861065205	(pow.f64 (log.f64 base) #s(literal -2 binary64))
accuracy	0.0	(log.f64 base)
accuracy	0.078125	(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
accuracy	0.13671875	(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
accuracy	0.236660009768442	(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
accuracy	0.0	(atan2.f64 im re)
accuracy	0.0	(log.f64 base)
accuracy	0.13671875	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
accuracy	0.16796875	(/.f64 #s(literal 1 binary64) (log.f64 base))

Samples

57.0ms	123×	0	valid
43.0ms	133×	0	invalid

Compiler

Compiled 171 to 28 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 24.0ms (49% of total)

ival-pow: 13.0ms (26.5% of total)

ival-div: 3.0ms (6.1% of total)

ival-log: 3.0ms (6.1% of total)

ival-pow2: 3.0ms (6.1% of total)

ival-atan2: 2.0ms (4.1% of total)

exact: 1.0ms (2% of total)

adjust: 0.0ms (0% of total)

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

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

series144.0ms (2.3%)

Memory

-57.1MiB live, 199.7MiB allocated; 60ms collecting garbage

Counts

17 → 31

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(log.f64 base)
(atan2.f64 im re)
(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base))
(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base))
(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re))
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(pow.f64 (log.f64 base) #s(literal 8 binary64))

Outputs
(/ (atan2 im re) (log base))
(atan2 im re)
(* (sqrt (/ 1 (log base))) (atan2 im re))
(* (pow (log base) 7) (atan2 im re))
(* (pow (log base) 6) (atan2 im re))
(/ 1 (log base))
(log base)
(sqrt (/ 1 (log base)))
(/ 1 (pow (log base) 2))
(pow (log base) 6)
(pow (log base) 8)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(/ 1 (pow (log (/ 1 base)) 2))
(* (sqrt (/ 1 (log (/ 1 base)))) (* (sqrt -1) (atan2 im re)))
(* -1 (* (pow (log (/ 1 base)) 7) (atan2 im re)))
(* (pow (log (/ 1 base)) 6) (atan2 im re))
(pow (log (/ 1 base)) 6)
(pow (log (/ 1 base)) 8)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(sqrt (/ 1 (+ (log -1) (* -1 (log (/ -1 base))))))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* (sqrt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))) (atan2 im re))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 7) (atan2 im re))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 6) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 6)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 8)

Calls

9 calls:

Time	Variable		Point	Expression
43.0ms	base	@	-inf	((* (/ 1 (log base)) (atan2 im re)) (/ 1 (log base)) (log base) (atan2 im re) (* (pow (pow (log base) -1/2) 2) (atan2 im re)) (pow (pow (log base) -1/2) 2) (pow (log base) -1/2) (* (pow (log base) -2) (log base)) (* (atan2 im re) (* (pow (log base) -2) (log base))) (pow (log base) -2) (* (pow (log base) -1/2) (* (pow (log base) -1/2) (atan2 im re))) (* (pow (log base) -1/2) (atan2 im re)) (* (* (pow (log base) 6) (atan2 im re)) (log base)) (/ (* (* (pow (log base) 6) (atan2 im re)) (log base)) (pow (log base) 8)) (* (pow (log base) 6) (atan2 im re)) (pow (log base) 6) (pow (log base) 8))
22.0ms	base	@	0	((* (/ 1 (log base)) (atan2 im re)) (/ 1 (log base)) (log base) (atan2 im re) (* (pow (pow (log base) -1/2) 2) (atan2 im re)) (pow (pow (log base) -1/2) 2) (pow (log base) -1/2) (* (pow (log base) -2) (log base)) (* (atan2 im re) (* (pow (log base) -2) (log base))) (pow (log base) -2) (* (pow (log base) -1/2) (* (pow (log base) -1/2) (atan2 im re))) (* (pow (log base) -1/2) (atan2 im re)) (* (* (pow (log base) 6) (atan2 im re)) (log base)) (/ (* (* (pow (log base) 6) (atan2 im re)) (log base)) (pow (log base) 8)) (* (pow (log base) 6) (atan2 im re)) (pow (log base) 6) (pow (log base) 8))
19.0ms	re	@	0	((* (/ 1 (log base)) (atan2 im re)) (/ 1 (log base)) (log base) (atan2 im re) (* (pow (pow (log base) -1/2) 2) (atan2 im re)) (pow (pow (log base) -1/2) 2) (pow (log base) -1/2) (* (pow (log base) -2) (log base)) (* (atan2 im re) (* (pow (log base) -2) (log base))) (pow (log base) -2) (* (pow (log base) -1/2) (* (pow (log base) -1/2) (atan2 im re))) (* (pow (log base) -1/2) (atan2 im re)) (* (* (pow (log base) 6) (atan2 im re)) (log base)) (/ (* (* (pow (log base) 6) (atan2 im re)) (log base)) (pow (log base) 8)) (* (pow (log base) 6) (atan2 im re)) (pow (log base) 6) (pow (log base) 8))
12.0ms	re	@	-inf	((* (/ 1 (log base)) (atan2 im re)) (/ 1 (log base)) (log base) (atan2 im re) (* (pow (pow (log base) -1/2) 2) (atan2 im re)) (pow (pow (log base) -1/2) 2) (pow (log base) -1/2) (* (pow (log base) -2) (log base)) (* (atan2 im re) (* (pow (log base) -2) (log base))) (pow (log base) -2) (* (pow (log base) -1/2) (* (pow (log base) -1/2) (atan2 im re))) (* (pow (log base) -1/2) (atan2 im re)) (* (* (pow (log base) 6) (atan2 im re)) (log base)) (/ (* (* (pow (log base) 6) (atan2 im re)) (log base)) (pow (log base) 8)) (* (pow (log base) 6) (atan2 im re)) (pow (log base) 6) (pow (log base) 8))
11.0ms	base	@	inf	((* (/ 1 (log base)) (atan2 im re)) (/ 1 (log base)) (log base) (atan2 im re) (* (pow (pow (log base) -1/2) 2) (atan2 im re)) (pow (pow (log base) -1/2) 2) (pow (log base) -1/2) (* (pow (log base) -2) (log base)) (* (atan2 im re) (* (pow (log base) -2) (log base))) (pow (log base) -2) (* (pow (log base) -1/2) (* (pow (log base) -1/2) (atan2 im re))) (* (pow (log base) -1/2) (atan2 im re)) (* (* (pow (log base) 6) (atan2 im re)) (log base)) (/ (* (* (pow (log base) 6) (atan2 im re)) (log base)) (pow (log base) 8)) (* (pow (log base) 6) (atan2 im re)) (pow (log base) 6) (pow (log base) 8))

simplify151.0ms (2.4%)

Memory

15.8MiB live, 104.7MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	244
1	93	234
2	152	232
3	282	232
4	593	232
5	1652	232
6	2635	232
7	3502	232
8	3882	232
9	3883	232
10	3883	232
11	3883	232
12	3931	232
13	4012	232
14	4024	232
15	4052	232
16	4089	232
17	4090	232
0	4090	232

Stop Event

1×	iter limit
1×	saturated

Counts

31 → 31

Calls

Call 1

Inputs
(/ (atan2 im re) (log base))
(atan2 im re)
(* (sqrt (/ 1 (log base))) (atan2 im re))
(* (pow (log base) 7) (atan2 im re))
(* (pow (log base) 6) (atan2 im re))
(/ 1 (log base))
(log base)
(sqrt (/ 1 (log base)))
(/ 1 (pow (log base) 2))
(pow (log base) 6)
(pow (log base) 8)
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/ -1 (log (/ 1 base)))
(* -1 (log (/ 1 base)))
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(/ 1 (pow (log (/ 1 base)) 2))
(* (sqrt (/ 1 (log (/ 1 base)))) (* (sqrt -1) (atan2 im re)))
(* -1 (* (pow (log (/ 1 base)) 7) (atan2 im re)))
(* (pow (log (/ 1 base)) 6) (atan2 im re))
(pow (log (/ 1 base)) 6)
(pow (log (/ 1 base)) 8)
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(+ (log -1) (* -1 (log (/ -1 base))))
(sqrt (/ 1 (+ (log -1) (* -1 (log (/ -1 base))))))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(* (sqrt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))) (atan2 im re))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 7) (atan2 im re))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 6) (atan2 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 6)
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 8)

Outputs
(/ (atan2 im re) (log base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(atan2 im re)
(atan2.f64 im re)
(* (sqrt (/ 1 (log base))) (atan2 im re))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base))) (atan2.f64 im re))
(* (pow (log base) 7) (atan2 im re))
(*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))
(* (pow (log base) 6) (atan2 im re))
(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re))
(/ 1 (log base))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(log base)
(log.f64 base)
(sqrt (/ 1 (log base)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))
(/ 1 (pow (log base) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(pow (log base) 6)
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(pow (log base) 8)
(pow.f64 (log.f64 base) #s(literal 8 binary64))
(* -1 (/ (atan2 im re) (log (/ 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/ -1 (log (/ 1 base)))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(* -1 (log (/ 1 base)))
(log.f64 base)
(* (sqrt (/ 1 (log (/ 1 base)))) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (log.f64 base))))
(/ 1 (pow (log (/ 1 base)) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(* (sqrt (/ 1 (log (/ 1 base)))) (* (sqrt -1) (atan2 im re)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)))) (atan2.f64 im re))
(* -1 (* (pow (log (/ 1 base)) 7) (atan2 im re)))
(*.f64 (neg.f64 (pow.f64 (neg.f64 (log.f64 base)) #s(literal 7 binary64))) (atan2.f64 im re))
(* (pow (log (/ 1 base)) 6) (atan2 im re))
(*.f64 (pow.f64 (neg.f64 (log.f64 base)) #s(literal 6 binary64)) (atan2.f64 im re))
(pow (log (/ 1 base)) 6)
(pow.f64 (neg.f64 (log.f64 base)) #s(literal 6 binary64))
(pow (log (/ 1 base)) 8)
(pow.f64 (neg.f64 (log.f64 base)) #s(literal 8 binary64))
(/ (atan2 im re) (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))))
(/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))
(/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64))))
(+ (log -1) (* -1 (log (/ -1 base))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base)))
(sqrt (/ 1 (+ (log -1) (* -1 (log (/ -1 base))))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64)))))
(/ 1 (pow (+ (log -1) (* -1 (log (/ -1 base)))) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 2 binary64)))
(* (sqrt (/ 1 (+ (log -1) (* -1 (log (/ -1 base)))))) (atan2 im re))
(*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) base)) (log.f64 #s(literal -1 binary64))))) (atan2.f64 im re))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 7) (atan2 im re))
(*.f64 (pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 7 binary64)) (atan2.f64 im re))
(* (pow (+ (log -1) (* -1 (log (/ -1 base)))) 6) (atan2 im re))
(*.f64 (pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 6 binary64)) (atan2.f64 im re))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 6)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 6 binary64))
(pow (+ (log -1) (* -1 (log (/ -1 base)))) 8)
(pow.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) base))) #s(literal 8 binary64))

rewrite103.0ms (1.6%)

Memory

26.7MiB live, 128.1MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	123
0	43	108
1	106	100
2	371	94
0	2788	94

Stop Event

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

Counts

17 → 802

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(/.f64 #s(literal 1 binary64) (log.f64 base))
(log.f64 base)
(atan2.f64 im re)
(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
(pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (log.f64 base) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base))
(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
(pow.f64 (log.f64 base) #s(literal -2 binary64))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base))
(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re))
(pow.f64 (log.f64 base) #s(literal 6 binary64))
(pow.f64 (log.f64 base) #s(literal 8 binary64))

Outputs
(.f64 (.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -1/8 binary64))) (pow.f64 (log.f64 base) #s(literal -1/8 binary64)))
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -3/2 binary64))) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -4 binary64))) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -1 binary64))) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (pow.f64 (log.f64 base) #s(literal -3/2 binary64)))
(.f64 (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -3 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64))))
(.f64 (.f64 (atan2.f64 im re) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))
(.f64 (.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/4 binary64))) (*.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (atan2.f64 im re)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(.f64 (.f64 #s(literal 1 binary64) (log.f64 base)) (*.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal -3/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (pow.f64 (log.f64 base) #s(literal -3 binary64)) (.f64 (log.f64 base) (*.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -3/4 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -4 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (*.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/8 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/8 binary64)) (*.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (atan2.f64 im re))))
(.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64))) (.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64))) (*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))))
(.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (.f64 (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)) (log.f64 base))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) #s(literal 1 binary64))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (atan2.f64 im re)))
(*.f64 #s(literal -1 binary64) (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
(.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base))))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -3/2 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -1 binary64)))
(.f64 (log.f64 base) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (atan2.f64 im re)))
(*.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (atan2.f64 im re) (log.f64 base))) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (atan2.f64 im re) (log.f64 base)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (.f64 (atan2.f64 im re) (log.f64 base))) (neg.f64 (log.f64 base)))
(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (.f64 (atan2.f64 im re) (log.f64 base))) (log.f64 base))
(/.f64 (.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 #s(literal -1 binary64) (log.f64 base))) (neg.f64 (log.f64 base)))
(/.f64 (.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -1 binary64))) (log.f64 base))
(/.f64 (neg.f64 (neg.f64 (atan2.f64 im re))) (log.f64 base))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(/.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(neg.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (log.f64 base)))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(neg.f64 (*.f64 (atan2.f64 im re) (/.f64 #s(literal -1 binary64) (log.f64 base))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (log.f64 base)) (atan2.f64 im re)))
(fma.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))))
(fma.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (atan2.f64 im re) (*.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (atan2.f64 im re)))
(fma.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (*.f64 (atan2.f64 im re) (log.f64 base))))
(fma.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64))))))
(fma.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (.f64 (*.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))))
(fma.f64 (atan2.f64 im re) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (*.f64 (atan2.f64 im re) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64))))))
(+.f64 (.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (.f64 (atan2.f64 im re) (log.f64 base))) (.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)))) (.f64 (atan2.f64 im re) (log.f64 base))))
(+.f64 (.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))) (.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re))))
(+.f64 (.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (atan2.f64 im re)) (.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)))) (atan2.f64 im re)))
(+.f64 (.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64))))) (.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64))))))
(+.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))) (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))))
(+.f64 (.f64 (atan2.f64 im re) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64))))) (.f64 (atan2.f64 im re) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64))))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64))) (*.f64 (atan2.f64 im re) (log.f64 base))))
(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64)) (pow.f64 (log.f64 base) #s(literal -1/8 binary64))) (pow.f64 (log.f64 base) #s(literal -1/8 binary64)))
(.f64 (.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal -3/2 binary64))) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(.f64 (.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (pow.f64 (log.f64 base) #s(literal -3/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -3/4 binary64))) (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/4 binary64))) (pow.f64 (log.f64 base) #s(literal -3/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (log.f64 base) #s(literal -1/2 binary64))) (pow.f64 (log.f64 base) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(.f64 (.f64 (log.f64 base) #s(literal 1 binary64)) (pow.f64 (log.f64 base) #s(literal -2 binary64)))
(.f64 (.f64 (log.f64 base) (/.f64 #s(literal -1 binary64) (log.f64 base))) (/.f64 #s(literal -1 binary64) (log.f64 base)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))) (neg.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (log.f64 base) #s(literal -3/4 binary64))) (pow.f64 (log.f64 base) #s(literal -1/4 binary64)))
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(fabs.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(exp.f64 (fma.f64 #s(literal 4 binary64) (log.f64 (log.f64 base)) (*.f64 #s(literal 4 binary64) (log.f64 (log.f64 base)))))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 (log.f64 base))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64))))
(+.f64 (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))) (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))) (sinh.f64 (log.f64 (pow.f64 (log.f64 base) #s(literal 8 binary64)))))

eval77.0ms (1.2%)

Memory: 6.5MiB live, 135.6MiB allocated; 27ms collecting garbage
Compiler: Compiled 10 753 to 1 573 computations (85.4% saved)

prune26.0ms (0.4%)

Memory

-1.7MiB live, 54.8MiB allocated; 13ms collecting garbage

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	569	8	577
Fresh	2	2	4
Picked	4	1	5
Done	2	4	6
Total	577	15	592

Accuracy

100.0%

Counts

592 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.5%	(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal 4 binary64)) (atan2.f64 im re))
✓	99.3%	(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
	99.2%	(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base))))
	47.7%	(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) (atan2.f64 im re)))
	99.4%	(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
	99.3%	(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)))
	47.6%	(*.f64 (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal 2 binary64)) (atan2.f64 im re))
	99.4%	(.f64 (atan2.f64 im re) (.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal -1/2 binary64)) (log.f64 base)))
✓	99.4%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
	99.3%	(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal -3 binary64))) (atan2.f64 im re))
	52.2%	(*.f64 (sqrt.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64))) (atan2.f64 im re))
✓	99.3%	(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
✓	99.3%	(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
	47.2%	(.f64 (exp.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -1 binary64))) (atan2.f64 im re))
✓	99.6%	#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))

Compiler

Compiled 809 to 327 computations (59.6% saved)

regimes91.0ms (1.4%)

Memory

3.2MiB live, 92.8MiB allocated; 12ms collecting garbage

Accuracy

Total -63.7b remaining (-22976.1%)

Threshold costs -63.7b (-22976.1%)

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (log.f64 base)))
(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)) (atan2.f64 im re))
(*.f64 (pow.f64 (log.f64 base) #s(literal -1 binary64)) (atan2.f64 im re))
(*.f64 (sqrt.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64))) (atan2.f64 im re))
(*.f64 (pow.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) #s(literal 2 binary64)) (atan2.f64 im re))
(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (atan2.f64 im re))
(*.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal -1/4 binary64)) #s(literal 4 binary64)) (atan2.f64 im re))
(.f64 (exp.f64 (.f64 (log.f64 (log.f64 base)) #s(literal -1 binary64))) (atan2.f64 im re))
(.f64 (log.f64 base) (.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal -2 binary64))))
(.f64 (atan2.f64 im re) (.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (log.f64 base)))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal -2 binary64)) (.f64 (atan2.f64 im re) (log.f64 base)))
#s(approx (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))) (/.f64 (atan2.f64 im re) (exp.f64 (*.f64 (log.f64 (log.f64 base)) #s(literal 1 binary64)))))
(*.f64 (log.f64 base) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(*.f64 (atan2.f64 im re) (/.f64 (log.f64 base) (pow.f64 (log.f64 base) #s(literal 2 binary64))))
(/.f64 (*.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 2 binary64)))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 #s(approx (pow (log base) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (log.f64 base)))) (atan2.f64 im re)))
(.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (pow.f64 (log.f64 base) #s(literal -3 binary64))) (atan2.f64 im re))
(.f64 (atan2.f64 im re) (.f64 (pow.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) #s(literal -1/2 binary64)) (log.f64 base)))
(.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (atan2.f64 im re)))
(.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -1/2 binary64)) (atan2.f64 im re)))
(*.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 4 binary64))))
(/.f64 #s(approx (* (* (log base) (atan2 im re)) (pow (log base) 6)) (*.f64 (pow.f64 (log.f64 base) #s(literal 7 binary64)) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (pow.f64 (log.f64 base) #s(literal -4 binary64)) (*.f64 (atan2.f64 im re) (log.f64 base))))
(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) #s(literal 3 binary64))) (pow.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 4 binary64))) (pow.f64 (log.f64 base) #s(literal 6 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 6 binary64))) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 8 binary64))) (pow.f64 (log.f64 base) #s(literal 10 binary64)))
(/.f64 (.f64 (.f64 (log.f64 base) (atan2.f64 im re)) (pow.f64 (log.f64 base) #s(literal 10 binary64))) (pow.f64 (log.f64 base) #s(literal 12 binary64)))
(/.f64 (.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 6 binary64)) (atan2.f64 im re)) (log.f64 base)) (pow.f64 (log.f64 base) #s(literal 8 binary64)))
(/.f64 (.f64 (pow.f64 (log.f64 base) #s(literal 2 binary64)) (.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (log.f64 base) #s(literal 4 binary64)))
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (exp.f64 (.f64 (log.f64 (neg.f64 (log.f64 base))) #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (/.f64 (pow.f64 (log.f64 base) #s(literal 4 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (/.f64 (pow.f64 (atan2.f64 im re) #s(literal 3 binary64)) (pow.f64 (.f64 (log.f64 base) (atan2.f64 im re)) #s(literal 2 binary64))) (/.f64 (pow.f64 (log.f64 base) #s(literal 3 binary64)) (pow.f64 (log.f64 base) #s(literal 2 binary64))))

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

Calls

5 calls:

45.0ms	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
18.0ms	base
9.0ms	im
9.0ms	re
9.0ms	(log.f64 base)

Results

Accuracy	Segments	Branch
99.6%	1	`(log.f64 base)`
99.6%	1	`(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) #s(literal 0 binary64))) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 #s(literal 0 binary64) #s(literal 0 binary64))))`
99.6%	1	`re`
99.6%	1	`im`
99.6%	1	`base`

Compiler

Compiled 33 to 31 computations (6.1% saved)

simplify64.0ms (1%)

Memory

-4.7MiB live, 88.9MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	21
1	49	19
2	150	15
3	345	13
4	650	13
5	1578	13
6	3340	13
7	4381	13
8	6087	13

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations100.0ms (1.6%)

Memory

-17.8MiB live, 116.4MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	469
1	343	466
2	1279	462
3	5845	460
0	8117	428

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 35 to 22 computations (37.1% saved)

preprocess134.0ms (2.1%)

Memory: -19.7MiB live, 101.6MiB allocated; 126ms collecting garbage
Compiler: Compiled 126 to 80 computations (36.5% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze192.0ms (3%)

sample2.2s (35.2%)

explain345.0ms (5.5%)

preprocess166.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify88.0ms (1.4%)

localize98.0ms (1.6%)

series114.0ms (1.8%)

simplify131.0ms (2.1%)

rewrite104.0ms (1.6%)

eval50.0ms (0.8%)

prune18.0ms (0.3%)

simplify96.0ms (1.5%)

localize238.0ms (3.8%)

series207.0ms (3.3%)

simplify187.0ms (3%)

rewrite91.0ms (1.4%)

eval73.0ms (1.2%)

prune58.0ms (0.9%)

simplify128.0ms (2%)

localize167.0ms (2.6%)

series201.0ms (3.2%)

simplify97.0ms (1.5%)

rewrite65.0ms (1%)

eval70.0ms (1.1%)

prune16.0ms (0.2%)

simplify50.0ms (0.8%)

localize151.0ms (2.4%)

series144.0ms (2.3%)

simplify151.0ms (2.4%)

rewrite103.0ms (1.6%)

eval77.0ms (1.2%)

prune26.0ms (0.4%)

regimes91.0ms (1.4%)

simplify64.0ms (1%)

derivations100.0ms (1.6%)

preprocess134.0ms (2.1%)

end0.0ms (0%)

Profiling