Metrics for 2atan (example 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	8.1%	91.9%	0%	0%	0%	0
0%	0%	8.1%	91.9%	0%	0%	0%	1
50%	4.1%	4.1%	91.9%	0%	0%	0%	2
75%	6.1%	2%	91.9%	0%	0%	0%	3
87.5%	7.1%	1%	91.9%	0%	0%	0%	4
93.8%	7.6%	0.5%	91.9%	0%	0%	0%	5
96.9%	7.9%	0.3%	91.9%	0%	0%	0%	6
98.4%	8%	0.1%	91.9%	0%	0%	0%	7
99.2%	8%	0.1%	91.9%	0%	0%	0%	8
99.6%	8.1%	0%	91.9%	0%	0%	0%	9
99.8%	8.1%	0%	91.9%	0%	0%	0%	10
99.9%	8.1%	0%	91.9%	0%	0%	0%	11
100%	8.1%	0%	91.9%	0%	0%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample2.3s (39.8%)

Memory

-29.9MiB live, 2 019.5MiB allocated

Samples

1.2s	7 491×	1	valid
551.0ms	387×	0	valid
73.0ms	378×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

const: 671.0ms (42.5% of total)

ival-atan: 359.0ms (22.8% of total)

adjust: 249.0ms (15.8% of total)

ival-add: 122.0ms (7.7% of total)

ival-sub: 101.0ms (6.4% of total)

ival->: 33.0ms (2.1% of total)

ival-<: 19.0ms (1.2% of total)

ival-and: 12.0ms (0.8% of total)

exact: 8.0ms (0.5% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain157.0ms (2.8%)

Memory

-8.7MiB live, 184.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
0	-	-	`N`
0	-	-	`(+.f64 N #s(literal 1 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(atan.f64 N)`
0	-	-	`(atan.f64 (+.f64 N #s(literal 1 binary64)))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`	cancellation	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

63.0ms	470×	1	valid
5.0ms	26×	2	valid
1.0ms	16×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-atan: 20.0ms (45.4% of total)

adjust: 13.0ms (29.5% of total)

ival-add: 5.0ms (11.4% of total)

ival-sub: 5.0ms (11.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess19.0ms (0.3%)

Memory

-23.0MiB live, 21.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	11	19
0	6	7
0	10	7
1	13	7
0	13	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.3%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(atan.f64 N)
cost-diff	0	(+.f64 N #s(literal 1 binary64))
cost-diff	0	(atan.f64 (+.f64 N #s(literal 1 binary64)))
cost-diff	0	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
0	13	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
N
#s(literal 1 binary64)
(atan.f64 N)

Outputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(atan.f64 (+.f64 #s(literal 1 binary64) N))
(+.f64 N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) N)
N
#s(literal 1 binary64)
(atan.f64 N)

localize42.0ms (0.7%)

Memory

14.4MiB live, 60.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 N #s(literal 1 binary64))
accuracy	0.0	(atan.f64 (+.f64 N #s(literal 1 binary64)))
accuracy	0.0	(atan.f64 N)
accuracy	59.343564891670006	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Samples

28.0ms	235×	1	valid
2.0ms	13×	2	valid
0.0ms	8×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-atan: 9.0ms (41% of total)

adjust: 6.0ms (27.4% of total)

ival-add: 3.0ms (13.7% of total)

ival-sub: 3.0ms (13.7% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Counts

4 → 9

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
(atan.f64 N)

Outputs
(- (atan (+ 1 N)) (atan N))
(atan (+ 1 N))
1
(+ 1 N)
(atan N)
N
(* N (+ 1 (/ 1 N)))
(- (atan (- 1 (* -1 N))) (atan N))
(atan (- 1 (* -1 N)))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) (atan N))
0.0ms	N	@	-inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) (atan N))
0.0ms	N	@	0	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) (atan N))

simplify6.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	29	32
2	42	32
3	79	32
4	128	32
5	206	32
6	222	32
7	224	32
0	224	32

Stop Event

1×	iter limit
1×	saturated

Counts

9 → 8

Calls

Call 1

Inputs
(- (atan (+ 1 N)) (atan N))
(atan (+ 1 N))
1
(+ 1 N)
(atan N)
N
(* N (+ 1 (/ 1 N)))
(- (atan (- 1 (* -1 N))) (atan N))
(atan (- 1 (* -1 N)))

Outputs
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(atan N)
(atan.f64 N)
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(- (atan (- 1 (* -1 N))) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(atan (- 1 (* -1 N)))
(atan.f64 (-.f64 N #s(literal -1 binary64)))

rewrite173.0ms (3.1%)

Memory

-4.6MiB live, 182.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	43	16
2	266	16
3	2561	16
0	9660	16

Stop Event

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

Counts

4 → 118

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
(atan.f64 N)

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64))) (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (*.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N))))
(.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N)) #s(literal 3 binary64)) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N)) (-.f64 (.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N)) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (pow.f64 (atan.f64 N) #s(literal 2 binary64))) (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (pow.f64 (atan.f64 N) #s(literal 2 binary64)))) (-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N)))
(*.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (pow.f64 (atan.f64 N) #s(literal 2 binary64))) (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64)))) (fma.f64 (atan.f64 N) (-.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))))
(*.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (/.f64 (-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))))
(*.f64 (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))) (/.f64 (-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (*.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (neg.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64))))) (pow.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (*.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (neg.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64))))) (pow.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (*.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (pow.f64 (atan.f64 N) #s(literal 2 binary64)))) (pow.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (*.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (pow.f64 (atan.f64 N) #s(literal 2 binary64)))) (pow.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))) (neg.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)))) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64))) (-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (atan.f64 N) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan.f64 N) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) (/.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (atan.f64 N) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 N) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan.f64 N) #s(literal 3 binary64)) (fma.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (atan.f64 N) (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64))))))))
(/.f64 (-.f64 (.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N)))) (.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) (pow.f64 (atan.f64 N) #s(literal 2 binary64)))) (pow.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)))
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(+.f64 #s(literal 1 binary64) N)
(+.f64 N #s(literal 1 binary64))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (atan.f64 N)))) (sqrt.f64 (neg.f64 (neg.f64 (atan.f64 N)))))
(*.f64 (sqrt.f64 (neg.f64 (atan.f64 N))) (sqrt.f64 (neg.f64 (atan.f64 N))))
(*.f64 (sqrt.f64 (atan.f64 N)) (sqrt.f64 (atan.f64 N)))
(pow.f64 (neg.f64 (atan.f64 N)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (atan.f64 N) #s(literal 1 binary64))
(atan.f64 N)
(sqrt.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (atan.f64 N))))
(fabs.f64 (neg.f64 (atan.f64 N)))
(fabs.f64 (atan.f64 N))
(+.f64 (cosh.f64 (log.f64 (atan.f64 N))) (sinh.f64 (log.f64 (atan.f64 N))))
(exp.f64 (/.f64 (log.f64 (pow.f64 (atan.f64 N) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (atan.f64 N)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (atan.f64 N)))

eval35.0ms (0.6%)

Memory: -8.3MiB live, 50.8MiB allocated
Compiler: Compiled 3 055 to 504 computations (83.5% saved)

prune2.0ms (0%)

Memory

9.6MiB live, 9.6MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	1	124

Accuracy

99.6%

Counts

124 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify25.0ms (0.4%)

Memory

-25.7MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 #s(literal 1 binary64) N)
cost-diff	0	(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

New

Metric

Score

Program

cost-diff

(+.f64 #s(literal 1 binary64) N)

cost-diff

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

cost-diff

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	19
0	9	19
1	14	19
2	27	19
3	70	19
4	172	19
5	275	19
6	415	19
7	512	19
8	603	19
9	678	19
10	687	19
0	687	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) N)
N

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
(fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) N)
(+.f64 N #s(literal 1 binary64))
N

localize17.0ms (0.3%)

Memory

33.3MiB live, 33.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(+.f64 #s(literal 1 binary64) N)
accuracy	0.0078125	(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

New

Metric

Score

Program

accuracy

0.0

(+.f64 #s(literal 1 binary64) N)

accuracy

0.0078125

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

accuracy

0.2578125

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Samples

12.0ms

256×

valid

Compiler

Compiled 23 to 8 computations (65.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 3.0ms (47.8% of total)

ival-atan2: 2.0ms (31.9% of total)

ival-mult: 2.0ms (31.9% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

3 → 11

Calls

Call 1

Inputs

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

(+.f64 #s(literal 1 binary64) N)

Outputs
(atan2 1 (+ 1 (* N (+ 1 N))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
N
(* N (+ 1 (/ 1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	((atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ 1 N))
0.0ms	N	@	inf	((atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ 1 N))
0.0ms	N	@	0	((atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ 1 N))

simplify146.0ms (2.6%)

Memory

-60.1MiB live, 111.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	61
1	71	57
2	192	57
3	676	57
4	3357	57
0	8117	51

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 10

Calls

Call 1

Inputs
(atan2 1 (+ 1 (* N (+ 1 N))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
N
(* N (+ 1 (/ 1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))

Outputs
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))

rewrite159.0ms (2.8%)

Memory

14.8MiB live, 144.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	9	17
1	38	17
2	261	17
3	2707	17
0	8997	17

Stop Event

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

Counts

3 → 248

Calls

Call 1

Inputs

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

(+.f64 #s(literal 1 binary64) N)

Outputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) (fma.f64 N N N) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 4 binary64)) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (fma.f64 N N N))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #s(literal 3 binary64)) (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (pow.f64 (fma.f64 N N N) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)))) (fma.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) (fma.f64 N N N) #s(literal 1 binary64)))
(*.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) (/.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(*.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -2 binary64)))) (neg.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)))) (neg.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64))))) (neg.f64 (neg.f64 (neg.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) (.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 N N))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 N N (*.f64 (fma.f64 N N #s(literal 1 binary64)) N)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) (-.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 N N N) N)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)))))
(/.f64 (-.f64 (neg.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 N N)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N)))
(/.f64 (-.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))) (pow.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 N N (*.f64 (fma.f64 N N #s(literal 1 binary64)) N))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
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(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (-.f64 (.f64 N N) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal -1 binary64) (.f64 N N))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -1 binary64) N #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 N N)) (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 N N)) (+.f64 #s(literal -1 binary64) (.f64 N N))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(fma.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)))) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) N) (/.f64 (.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) (/.f64 (*.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (/.f64 (pow.f64 N #s(literal 3/2 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 N N) (/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64))) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 N (/.f64 (*.f64 N N) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 N #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) N #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 N N) (-.f64 N #s(literal 1 binary64))) (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N))))
(-.f64 #s(literal 1 binary64) (neg.f64 N))
(-.f64 #s(literal 1 binary64) N)
(+.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))) (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (pow.f64 (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(+.f64 N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 N))
(+.f64 #s(literal 1 binary64) N)

eval35.0ms (0.6%)

Memory: 31.5MiB live, 31.5MiB allocated
Compiler: Compiled 6 027 to 955 computations (84.2% saved)

prune59.0ms (1%)

Memory

-10.6MiB live, 49.0MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	240	15	255
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	240	16	256

Accuracy

99.8%

Counts

256 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
	46.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) N #s(literal 1 binary64)))
▶	94.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
	70.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #s(literal 1 binary64)))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	94.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N)) (sqrt.f64 N) #s(literal 1 binary64)))
	47.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))))) (fabs.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
	94.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fabs.f64 (/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) #s(literal 1 binary64)))
▶	93.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
	77.0%	(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
	14.4%	(atan2.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))))
▶	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
▶	97.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	7.7%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
	94.7%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
▶	6.2%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 536 to 315 computations (41.2% saved)

simplify136.0ms (2.4%)

Memory

-18.9MiB live, 169.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(log1p.f64 N)
cost-diff	0	(exp.f64 (log1p.f64 N))
cost-diff	0	(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
cost-diff	0	(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
cost-diff	1	(fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))
cost-diff	1	(fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
cost-diff	0	(fma.f64 N N N)
cost-diff	0	#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
cost-diff	0	#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 N N #s(literal 1 binary64))
cost-diff	0	(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	164
0	45	160
1	86	160
2	208	156
3	671	156
4	2271	154
0	8547	154

Stop Event

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

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
#s(literal 1 binary64)
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 N N #s(literal 1 binary64))
N
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
(fma.f64 N N N)
N
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
#s(literal -1 binary64)
(pow.f64 N #s(literal 3 binary64))
N
#s(literal 3 binary64)
(fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))
(fma.f64 N N N)
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(log1p.f64 N)
N

Outputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(fma.f64 N N #s(literal 1 binary64))
N
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
(fma.f64 N N N)
N
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal -1 binary64) (fma.f64 N N N)))))
#s(literal 1 binary64)
(fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal -1 binary64) (fma.f64 N N N))))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
#s(literal -1 binary64)
(pow.f64 N #s(literal 3 binary64))
N
#s(literal 3 binary64)
(fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))
(-.f64 #s(literal -1 binary64) (fma.f64 N N N))
(fma.f64 N N N)
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(+.f64 N #s(literal 1 binary64))
(log1p.f64 N)
N

localize92.0ms (1.6%)

Memory

26.1MiB live, 71.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(log1p.f64 N)
accuracy	0.0078125	(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
accuracy	4.384033882380809	(exp.f64 (log1p.f64 N))
accuracy	0.0	(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
accuracy	0.00390625	(fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
accuracy	0.23828125	(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
accuracy	0.26953125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
accuracy	0.0	(fma.f64 N N N)
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
accuracy	1.2878078304564844	#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
accuracy	60.061477829729206	#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 N N #s(literal 1 binary64))
accuracy	0.0390625	(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Samples

76.0ms

256×

valid

Compiler

Compiled 177 to 28 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-atan2: 33.0ms (52.5% of total)

ival-add: 9.0ms (14.3% of total)

ival-mult: 8.0ms (12.7% of total)

ival-exp: 3.0ms (4.8% of total)

ival-log1p: 3.0ms (4.8% of total)

ival-pow: 3.0ms (4.8% of total)

ival-div: 2.0ms (3.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series17.0ms (0.3%)

Memory

-30.6MiB live, 12.8MiB allocated

Counts

17 → 53

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 N N #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
(fma.f64 N N N)
(fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(log1p.f64 N)
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))

Outputs
(atan2 1 (+ 1 (+ N (pow N 2))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (pow N 2))
(atan2 1 (+ 1 (* N (+ 1 N))))
N
(* N (+ 1 N))
(+ 1 (* N (+ 1 (* -1 N))))
(+ 1 (* N (+ 1 (* N (- (* 2 (pow N 2)) 1)))))
-1
(- (* -1 N) 1)
(- (* N (- (* -1 N) 1)) 1)
(atan2 1 (+ 1 (* -1 (/ (* N (+ 1 (pow N 3))) (- (* -1 (+ N (pow N 2))) 1)))))
(+ 1 (* -1 N))
(+ 1 (* N (- (* 2 (pow N 2)) 1)))
(+ 1 (* N (- (* (pow N 2) (+ 2 (* -2 N))) 1)))
(* N (+ 1 (* -1/2 N)))
(* N (+ 1 (* N (- (* 1/3 N) 1/2))))
(* N (+ 1 (* N (- (* N (+ 1/3 (* -1/4 N))) 1/2))))
(- (* -1 (pow N 3)) 1)
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (- 1 (/ 1 N)))
(* (pow N 2) (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)))
(* (pow N 2) (- (+ 1 (+ (/ 1 (pow N 2)) (* 2 (/ 1 (pow N 3))))) (/ 1 N)))
(* -1 (pow N 2))
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(* (pow N 2) (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1))
(* N (- 1 (/ 1 N)))
(* N (- (+ 1 (/ 2 (pow N 3))) (/ 1 N)))
(* N (- (+ 1 (/ 2 (pow N 3))) (+ (/ 1 N) (* 2 (/ 1 (pow N 4))))))
(* N (+ 1 (/ 1 N)))
(* -1 (log (/ 1 N)))
(+ (* -1 (log (/ 1 N))) (/ 1 N))
(- (+ (* -1 (log (/ 1 N))) (/ 1 N)) (/ 1/2 (pow N 2)))
(- (+ (* -1 (log (/ 1 N))) (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3))))) (/ 1/2 (pow N 2)))
(* -1 (pow N 3))
(* -1 (* (pow N 3) (+ 1 (/ 1 (pow N 3)))))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(* (pow N 2) (+ 1 (* -1 (/ (- 1 (/ 1 N)) N))))
(* (pow N 2) (+ 1 (* -1 (/ (+ 1 (* -1 (/ (+ 1 (* 2 (/ 1 N))) N))) N))))
(atan2 1 (+ 1 (/ (* N (- (* -1 (pow N 3)) 1)) (- (* -1 (- (pow N 2) (* -1 N))) 1))))
(* -1 (* N (- (/ 1 N) 1)))
(* -1 (* N (- (* -1 (/ (- (* 2 (/ 1 (pow N 2))) 1) N)) 1)))
(* -1 (* N (- (* -1 (/ (- (* 2 (/ 1 (pow N 2))) (+ 1 (/ 2 (pow N 3)))) N)) 1)))
(+ (log -1) (* -1 (log (/ -1 N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (/ 1 N)))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* 1/2 (/ 1 N)) 1) N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 N)) 1/2) N)) 1) N))))

Calls

3 calls:

Time

Variable

Point

Expression

12.0ms

((atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ (* N N) N) (+ (* (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) N) 1) (+ (* -1 (+ (* N N) N)) -1) (atan2 1 (+ (* (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) N) 1)) (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) (atan2 1 (+ (* (exp (log (+ 1 N))) N) 1)) (+ (* (exp (log (+ 1 N))) N) 1) (exp (log (+ 1 N))) (log (+ 1 N)) (- -1 (pow N 3)))

2.0ms

inf

((atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ (* N N) N) (+ (* (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) N) 1) (+ (* -1 (+ (* N N) N)) -1) (atan2 1 (+ (* (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) N) 1)) (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) (atan2 1 (+ (* (exp (log (+ 1 N))) N) 1)) (+ (* (exp (log (+ 1 N))) N) 1) (exp (log (+ 1 N))) (log (+ 1 N)) (- -1 (pow N 3)))

2.0ms

-inf

((atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ (* N N) N) (+ (* (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) N) 1) (+ (* -1 (+ (* N N) N)) -1) (atan2 1 (+ (* (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) N) 1)) (/ (- -1 (pow N 3)) (+ (* -1 (+ (* N N) N)) -1)) (atan2 1 (+ (* (exp (log (+ 1 N))) N) 1)) (+ (* (exp (log (+ 1 N))) N) 1) (exp (log (+ 1 N))) (log (+ 1 N)) (- -1 (pow N 3)))

simplify214.0ms (3.8%)

Memory

23.0MiB live, 249.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	178	535
1	542	509
2	1597	477
3	6437	463
0	8481	441

Stop Event

1×	iter limit
1×	node limit

Counts

53 → 52

Calls

Call 1

Inputs
(atan2 1 (+ 1 (+ N (pow N 2))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (pow N 2))
(atan2 1 (+ 1 (* N (+ 1 N))))
N
(* N (+ 1 N))
(+ 1 (* N (+ 1 (* -1 N))))
(+ 1 (* N (+ 1 (* N (- (* 2 (pow N 2)) 1)))))
-1
(- (* -1 N) 1)
(- (* N (- (* -1 N) 1)) 1)
(atan2 1 (+ 1 (* -1 (/ (* N (+ 1 (pow N 3))) (- (* -1 (+ N (pow N 2))) 1)))))
(+ 1 (* -1 N))
(+ 1 (* N (- (* 2 (pow N 2)) 1)))
(+ 1 (* N (- (* (pow N 2) (+ 2 (* -2 N))) 1)))
(* N (+ 1 (* -1/2 N)))
(* N (+ 1 (* N (- (* 1/3 N) 1/2))))
(* N (+ 1 (* N (- (* N (+ 1/3 (* -1/4 N))) 1/2))))
(- (* -1 (pow N 3)) 1)
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (- 1 (/ 1 N)))
(* (pow N 2) (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)))
(* (pow N 2) (- (+ 1 (+ (/ 1 (pow N 2)) (* 2 (/ 1 (pow N 3))))) (/ 1 N)))
(* -1 (pow N 2))
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(* (pow N 2) (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1))
(* N (- 1 (/ 1 N)))
(* N (- (+ 1 (/ 2 (pow N 3))) (/ 1 N)))
(* N (- (+ 1 (/ 2 (pow N 3))) (+ (/ 1 N) (* 2 (/ 1 (pow N 4))))))
(* N (+ 1 (/ 1 N)))
(* -1 (log (/ 1 N)))
(+ (* -1 (log (/ 1 N))) (/ 1 N))
(- (+ (* -1 (log (/ 1 N))) (/ 1 N)) (/ 1/2 (pow N 2)))
(- (+ (* -1 (log (/ 1 N))) (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3))))) (/ 1/2 (pow N 2)))
(* -1 (pow N 3))
(* -1 (* (pow N 3) (+ 1 (/ 1 (pow N 3)))))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(* (pow N 2) (+ 1 (* -1 (/ (- 1 (/ 1 N)) N))))
(* (pow N 2) (+ 1 (* -1 (/ (+ 1 (* -1 (/ (+ 1 (* 2 (/ 1 N))) N))) N))))
(atan2 1 (+ 1 (/ (* N (- (* -1 (pow N 3)) 1)) (- (* -1 (- (pow N 2) (* -1 N))) 1))))
(* -1 (* N (- (/ 1 N) 1)))
(* -1 (* N (- (* -1 (/ (- (* 2 (/ 1 (pow N 2))) 1) N)) 1)))
(* -1 (* N (- (* -1 (/ (- (* 2 (/ 1 (pow N 2))) (+ 1 (/ 2 (pow N 3)))) N)) 1)))
(+ (log -1) (* -1 (log (/ -1 N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (/ 1 N)))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* 1/2 (/ 1 N)) 1) N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 N)) 1/2) N)) 1) N))))

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

rewrite227.0ms (4%)

Memory

-9.6MiB live, 293.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	146
0	45	132
1	194	129
2	1448	111
0	9444	111

Stop Event

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

Counts

17 → 934

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 N N #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
(fma.f64 N N N)
(fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(log1p.f64 N)
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(/.f64 (-.f64 (fma.f64 N N #s(literal 1 binary64)) (pow.f64 N #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) N) (*.f64 N N)))
(/.f64 (-.f64 (*.f64 (fma.f64 N N (cosh.f64 (log1p.f64 N))) (fma.f64 N N (cosh.f64 (log1p.f64 N)))) (pow.f64 (sinh.f64 (log1p.f64 N)) #s(literal 2 binary64))) (-.f64 (fma.f64 N N (cosh.f64 (log1p.f64 N))) (sinh.f64 (log1p.f64 N))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)))) (.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64)))) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))))) (.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))))) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
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(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 N #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (fma.f64 (/.f64 (pow.f64 N #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (/.f64 (pow.f64 N #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (/.f64 (pow.f64 N #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64))))))))
(/.f64 (+.f64 (pow.f64 N #s(literal 9 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 N #s(literal 6 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64))) (.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64)))) (.f64 #s(literal -1 binary64) (.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 9 binary64)))) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 9 binary64))))) (neg.f64 (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) (.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (pow.f64 N #s(literal 6 binary64)))) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64))) (pow.f64 N #s(literal 9 binary64)))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64)))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 9 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64)))) (neg.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 9 binary64)))) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 9 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))))
(fma.f64 (neg.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64)))) (neg.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (neg.f64 (neg.f64 N)) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (neg.f64 N)) #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (neg.f64 N) #s(literal 3/2 binary64)) (pow.f64 (*.f64 (neg.f64 N) #s(literal 1 binary64)) #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (neg.f64 N) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 N) #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) #s(literal -1 binary64))
(fma.f64 (*.f64 (neg.f64 N) N) (neg.f64 N) #s(literal -1 binary64))
(fma.f64 (*.f64 (neg.f64 N) N) N #s(literal -1 binary64))
(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 (neg.f64 N) (*.f64 (neg.f64 N) N) #s(literal -1 binary64))
(fma.f64 (neg.f64 N) (*.f64 N N) #s(literal -1 binary64))
(fma.f64 (*.f64 N N) (neg.f64 N) #s(literal -1 binary64))
(fma.f64 (*.f64 N N) N #s(literal -1 binary64))
(fma.f64 (pow.f64 N #s(literal 3 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(fma.f64 N (*.f64 N N) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(-.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 6 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (/.f64 (pow.f64 N #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64))))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
(+.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 6 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))))
(+.f64 (/.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))) (/.f64 (pow.f64 N #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (pow.f64 N #s(literal 3 binary64)))))
(+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 3/2 binary64))))
(+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))

eval125.0ms (2.2%)

Memory: -12.4MiB live, 168.6MiB allocated
Compiler: Compiled 21 016 to 3 149 computations (85% saved)

prune54.0ms (1%)

Memory

17.4MiB live, 64.4MiB allocated

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	750	9	759
Fresh	6	4	10
Picked	2	3	5
Done	0	1	1
Total	758	17	775

Accuracy

99.8%

Counts

775 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
	46.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) N #s(literal 1 binary64)))
	94.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(approx (+ (* -1 (+ (* N N) N)) -1) (*.f64 (neg.f64 N) N))) N #s(literal 1 binary64)))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	94.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N)) (sqrt.f64 N) #s(literal 1 binary64)))
	47.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))))) (fabs.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	93.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
	76.9%	(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 N N) #s(literal 1 binary64))) N))
▶	52.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
▶	7.7%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
	94.7%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (*.f64 N N)))
	97.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 (/.f64 N N) (/.f64 (pow.f64 N #s(literal 3 binary64)) (-.f64 N #s(literal 1 binary64))) (/.f64 (*.f64 N N) (fma.f64 N N N)))))
✓	97.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
▶	75.0%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
	97.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))
▶	97.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
✓	6.2%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 587 to 350 computations (40.4% saved)

simplify103.0ms (1.8%)

Memory

6.9MiB live, 106.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	2	(.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))
cost-diff	2	(neg.f64 (neg.f64 N))
cost-diff	2	(pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))
cost-diff	6	(fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))
cost-diff	0	(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
cost-diff	0	#s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
cost-diff	2	(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
cost-diff	0	(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
cost-diff	0	#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
cost-diff	7	(/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))
cost-diff	0	(-.f64 N #s(literal -1 binary64))
cost-diff	0	#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 N)
cost-diff	0	(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
cost-diff	3	(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	405
0	74	317
1	152	300
2	507	272
3	3069	264
0	8369	257

Stop Event

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

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
(sqrt.f64 N)
N
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
#s(literal 1 binary64)
#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
(-.f64 N #s(literal -1 binary64))
N
#s(literal -1 binary64)
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))
(/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
(fma.f64 N N N)
N
#s(literal 2 binary64)
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))))
(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
#s(literal -1 binary64)
(pow.f64 N #s(literal 3 binary64))
N
#s(literal 3 binary64)
(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) N)
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
#s(literal 1 binary64)
(+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N)
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))))
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64)))
(pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))
(*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))
(neg.f64 (neg.f64 N))
(neg.f64 N)
N
#s(literal 3 binary64)
(+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))
(fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))
(.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
(fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
(+.f64 N #s(literal 1 binary64))
(sqrt.f64 N)
N
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
#s(literal 1 binary64)
#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
#s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64)))
(-.f64 N #s(literal -1 binary64))
N
#s(literal -1 binary64)
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))
#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
(/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))
(fma.f64 N N N)
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
(fma.f64 N N N)
N
#s(literal 2 binary64)
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (+.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64)))))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))))
#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (+.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (+.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64)))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
#s(literal -1 binary64)
(pow.f64 N #s(literal 3 binary64))
N
#s(literal 3 binary64)
(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) N)
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) N) N #s(literal 1 binary64))) N))
#s(literal 1 binary64)
(+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N)
(+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) N) N #s(literal 1 binary64))) N)
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))))
(/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) N) N #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64)))
(+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))
(neg.f64 (pow.f64 N #s(literal 6 binary64)))
(*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))
(*.f64 (neg.f64 N) N)
(neg.f64 (neg.f64 N))
N
(neg.f64 N)
N
#s(literal 3 binary64)
(+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))
(fma.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) N) N #s(literal 1 binary64))
(fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))
(*.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) N) N)
(.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))
(*.f64 (neg.f64 N) N)

localize145.0ms (2.6%)

Memory

3.9MiB live, 137.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
accuracy	0.39040766606351435	(pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))
accuracy	0.39748002930532605	(fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))
accuracy	29.74658963743504	(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
accuracy	0.2578125	(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
accuracy	0.3359375	(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
accuracy	1.2878078304564844	#s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
accuracy	0.39976503907376804	(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
accuracy	1.2878078304564844	#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))
accuracy	14.857466424886855	(/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))
accuracy	0.0	(-.f64 N #s(literal -1 binary64))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
accuracy	59.06188186507497	#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
accuracy	0.0	(sqrt.f64 N)
accuracy	0.0078125	(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
accuracy	0.2578125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
accuracy	0.53125	(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))

Samples

119.0ms

256×

valid

Compiler

Compiled 362 to 44 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-atan2: 24.0ms (30.4% of total)

ival-add: 16.0ms (20.3% of total)

ival-mult: 13.0ms (16.5% of total)

ival-pow: 8.0ms (10.1% of total)

ival-sub: 5.0ms (6.3% of total)

ival-div: 4.0ms (5.1% of total)

ival-sqrt: 2.0ms (2.5% of total)

ival-neg: 2.0ms (2.5% of total)

ival-pow2: 2.0ms (2.5% of total)

exact: 1.0ms (1.3% of total)

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

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

series13.0ms (0.2%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

22 → 49

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
(sqrt.f64 N)
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
(-.f64 N #s(literal -1 binary64))
(/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
#s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
(fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))
(pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))
(neg.f64 (neg.f64 N))
(.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))
(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))

Outputs
1
(+ 1 N)
(atan2 1 (+ 1 (* N (+ 1 N))))
(+ 1 (* N (+ 1 N)))
(sqrt N)
(atan2 1 (+ 1 (+ N (pow N 2))))
N
(* N (+ 1 N))
(pow N 2)
(* (pow N 2) (+ 1 (* 2 N)))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
-1
(- (* -1 (pow N 3)) 1)
(* -1 (pow N 2))
(* (pow N 2) (- (pow N 2) 1))
(* -1 (pow N 6))
(* -1 N)
(* N (- (* -1 N) 1))
(* N (- (* N (- (pow N 2) 1)) 1))
(* N (- (* N (- (* (pow N 2) (+ 1 N)) 1)) 1))
(+ 1 (pow N 2))
(atan2 1 (- (+ N (/ 1 (+ 1 (+ (* -1 (pow N 2)) (pow N 4))))) (* -1 (/ (pow N 6) (+ 1 (+ (* -1 (pow N 2)) (pow N 4)))))))
(* N (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 4)
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(* -1 (pow N 3))
(* -1 (* (pow N 3) (+ 1 (/ 1 (pow N 3)))))
(* (pow N 4) (- 1 (/ 1 (pow N 2))))
(/ -1 N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/ (- (/ 1 (pow N 3)) (+ 1 (/ 1 N))) N)
(/ (- (+ (/ 1 (pow N 3)) (/ 1 (pow N 4))) (+ 1 (/ 1 N))) N)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(atan2 1 (+ N (+ (/ 1 (- (+ 1 (pow N 4)) (pow N 2))) (/ (pow N 6) (- (+ 1 (pow N 4)) (pow N 2))))))
(* -1 (* N (pow (sqrt -1) 2)))
(* -1 (* N (- (pow (sqrt -1) 2) (/ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 (* -1 (* N (pow (sqrt -1) 2)))))))
(* -1 (* (pow N 2) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (* -1 (pow (sqrt -1) 2)) (/ 1 N)))
(* (pow N 2) (+ (* -1 (pow (sqrt -1) 2)) (+ (/ 1 N) (/ 1 (pow N 2)))))
(* -1 (* (sqrt N) (pow (sqrt -1) 2)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(* -1 (/ (+ 1 (* -1 (/ (- (/ 1 (pow N 2)) 1) N))) N))
(* -1 (/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow N 2)) (/ 1 (pow N 3))) 1) N))) N))
(atan2 1 (- (+ (/ 1 (- (+ 1 (pow N 4)) (pow N 2))) (/ (pow N 6) (- (+ 1 (pow N 4)) (pow N 2)))) (* -1 N)))

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

((+ (* (sqrt N) (sqrt N)) 1) (atan2 1 (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1)) (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (sqrt N) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (- N -1) (/ (pow (+ (* N N) N) 2) (+ (* N N) N)) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (pow (+ (* N N) N) 2) (* (- -1 (pow N 3)) (/ N (+ (* (- 1 N) N) -1))) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (- -1 (pow N 3)) (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))) (pow (* (neg (neg N)) (neg N)) 3) (neg (neg N)) (* 1 (* (neg (neg N)) (neg N))) (/ N (+ (* (- 1 N) N) -1)) (/ (- 1 (pow (* (neg (neg N)) (neg N)) 3)) (+ 1 (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))))) (atan2 1 (+ (/ (- 1 (pow (* (neg (neg N)) (neg N)) 3)) (+ 1 (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))))) N)))

4.0ms

((+ (* (sqrt N) (sqrt N)) 1) (atan2 1 (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1)) (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (sqrt N) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (- N -1) (/ (pow (+ (* N N) N) 2) (+ (* N N) N)) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (pow (+ (* N N) N) 2) (* (- -1 (pow N 3)) (/ N (+ (* (- 1 N) N) -1))) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (- -1 (pow N 3)) (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))) (pow (* (neg (neg N)) (neg N)) 3) (neg (neg N)) (* 1 (* (neg (neg N)) (neg N))) (/ N (+ (* (- 1 N) N) -1)) (/ (- 1 (pow (* (neg (neg N)) (neg N)) 3)) (+ 1 (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))))) (atan2 1 (+ (/ (- 1 (pow (* (neg (neg N)) (neg N)) 3)) (+ 1 (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))))) N)))

3.0ms

inf

((+ (* (sqrt N) (sqrt N)) 1) (atan2 1 (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1)) (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (sqrt N) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (- N -1) (/ (pow (+ (* N N) N) 2) (+ (* N N) N)) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (pow (+ (* N N) N) 2) (* (- -1 (pow N 3)) (/ N (+ (* (- 1 N) N) -1))) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (- -1 (pow N 3)) (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))) (pow (* (neg (neg N)) (neg N)) 3) (neg (neg N)) (* 1 (* (neg (neg N)) (neg N))) (/ N (+ (* (- 1 N) N) -1)) (/ (- 1 (pow (* (neg (neg N)) (neg N)) 3)) (+ 1 (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))))) (atan2 1 (+ (/ (- 1 (pow (* (neg (neg N)) (neg N)) 3)) (+ 1 (+ (* (* (neg (neg N)) (neg N)) (* (neg (neg N)) (neg N))) (* 1 (* (neg (neg N)) (neg N)))))) N)))

simplify125.0ms (2.2%)

Memory

-27.4MiB live, 124.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	406
1	380	367
2	1136	358
0	5043	335

Stop Event

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

Counts

49 → 48

Calls

Call 1

Inputs
1
(+ 1 N)
(atan2 1 (+ 1 (* N (+ 1 N))))
(+ 1 (* N (+ 1 N)))
(sqrt N)
(atan2 1 (+ 1 (+ N (pow N 2))))
N
(* N (+ 1 N))
(pow N 2)
(* (pow N 2) (+ 1 (* 2 N)))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
-1
(- (* -1 (pow N 3)) 1)
(* -1 (pow N 2))
(* (pow N 2) (- (pow N 2) 1))
(* -1 (pow N 6))
(* -1 N)
(* N (- (* -1 N) 1))
(* N (- (* N (- (pow N 2) 1)) 1))
(* N (- (* N (- (* (pow N 2) (+ 1 N)) 1)) 1))
(+ 1 (pow N 2))
(atan2 1 (- (+ N (/ 1 (+ 1 (+ (* -1 (pow N 2)) (pow N 4))))) (* -1 (/ (pow N 6) (+ 1 (+ (* -1 (pow N 2)) (pow N 4)))))))
(* N (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 4)
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(* -1 (pow N 3))
(* -1 (* (pow N 3) (+ 1 (/ 1 (pow N 3)))))
(* (pow N 4) (- 1 (/ 1 (pow N 2))))
(/ -1 N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/ (- (/ 1 (pow N 3)) (+ 1 (/ 1 N))) N)
(/ (- (+ (/ 1 (pow N 3)) (/ 1 (pow N 4))) (+ 1 (/ 1 N))) N)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(atan2 1 (+ N (+ (/ 1 (- (+ 1 (pow N 4)) (pow N 2))) (/ (pow N 6) (- (+ 1 (pow N 4)) (pow N 2))))))
(* -1 (* N (pow (sqrt -1) 2)))
(* -1 (* N (- (pow (sqrt -1) 2) (/ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 (* -1 (* N (pow (sqrt -1) 2)))))))
(* -1 (* (pow N 2) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (* -1 (pow (sqrt -1) 2)) (/ 1 N)))
(* (pow N 2) (+ (* -1 (pow (sqrt -1) 2)) (+ (/ 1 N) (/ 1 (pow N 2)))))
(* -1 (* (sqrt N) (pow (sqrt -1) 2)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(* -1 (/ (+ 1 (* -1 (/ (- (/ 1 (pow N 2)) 1) N))) N))
(* -1 (/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow N 2)) (/ 1 (pow N 3))) 1) N))) N))
(atan2 1 (- (+ (/ 1 (- (+ 1 (pow N 4)) (pow N 2))) (/ (pow N 6) (- (+ 1 (pow N 4)) (pow N 2)))) (* -1 N)))

Outputs
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(sqrt N)
(sqrt.f64 N)
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
N
(* N (+ 1 N))
(fma.f64 N N N)
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (* 2 N)))
(fma.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 2 binary64) (*.f64 N N))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
-1
#s(literal -1 binary64)
(- (* -1 (pow N 3)) 1)
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
(* -1 (pow N 2))
(*.f64 (neg.f64 N) N)
(* (pow N 2) (- (pow N 2) 1))
(.f64 (.f64 (fma.f64 N N #s(literal -1 binary64)) N) N)
(* -1 (pow N 6))
(neg.f64 (pow.f64 N #s(literal 6 binary64)))
(* -1 N)
(neg.f64 N)
(* N (- (* -1 N) 1))
(neg.f64 (fma.f64 N N N))
(* N (- (* N (- (pow N 2) 1)) 1))
(.f64 (-.f64 (.f64 (fma.f64 N N #s(literal -1 binary64)) N) #s(literal 1 binary64)) N)
(* N (- (* N (- (* (pow N 2) (+ 1 N)) 1)) 1))
(.f64 (-.f64 (.f64 (fma.f64 N N (-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))) N) #s(literal 1 binary64)) N)
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(atan2 1 (- (+ N (/ 1 (+ 1 (+ (* -1 (pow N 2)) (pow N 4))))) (* -1 (/ (pow N 6) (+ 1 (+ (* -1 (pow N 2)) (pow N 4)))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 N #s(literal 4 binary64)) (fma.f64 N N #s(literal -1 binary64)))) N))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(pow N 4)
(pow.f64 N #s(literal 4 binary64))
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(*.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 #s(literal 2 binary64) N))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
(* -1 (pow N 3))
(pow.f64 (neg.f64 N) #s(literal 3 binary64))
(* -1 (* (pow N 3) (+ 1 (/ 1 (pow N 3)))))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
(* (pow N 4) (- 1 (/ 1 (pow N 2))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) N) N)) (pow.f64 N #s(literal 4 binary64)))
(/ -1 N)
(/.f64 #s(literal -1 binary64) N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N)
(/ (- (/ 1 (pow N 3)) (+ 1 (/ 1 N))) N)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(/ (- (+ (/ 1 (pow N 3)) (/ 1 (pow N 4))) (+ 1 (/ 1 N))) N)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(atan2 1 (+ N (+ (/ 1 (- (+ 1 (pow N 4)) (pow N 2))) (/ (pow N 6) (- (+ 1 (pow N 4)) (pow N 2))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 N #s(literal 4 binary64)) (fma.f64 N N #s(literal -1 binary64)))) N))
(* -1 (* N (pow (sqrt -1) 2)))
N
(* -1 (* N (- (pow (sqrt -1) 2) (/ 1 N))))
(-.f64 N #s(literal -1 binary64))
(atan2 1 (+ 1 (* N (+ 1 (* -1 (* N (pow (sqrt -1) 2)))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(* -1 (* (pow N 2) (pow (sqrt -1) 2)))
(*.f64 N N)
(* (pow N 2) (+ (* -1 (pow (sqrt -1) 2)) (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ (* -1 (pow (sqrt -1) 2)) (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* -1 (* (sqrt N) (pow (sqrt -1) 2)))
(sqrt.f64 N)
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(* -1 (/ (+ 1 (* -1 (/ (- (/ 1 (pow N 2)) 1) N))) N))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(* -1 (/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow N 2)) (/ 1 (pow N 3))) 1) N))) N))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(atan2 1 (- (+ (/ 1 (- (+ 1 (pow N 4)) (pow N 2))) (/ (pow N 6) (- (+ 1 (pow N 4)) (pow N 2)))) (* -1 N)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 N #s(literal 4 binary64)) (fma.f64 N N #s(literal -1 binary64)))) N))

rewrite153.0ms (2.7%)

Memory

-8.0MiB live, 218.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	297
0	74	219
1	339	198
2	2554	175
0	9857	174

Stop Event

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

Counts

22 → 734

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
(sqrt.f64 N)
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
(-.f64 N #s(literal -1 binary64))
(/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
#s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
#s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))))
(-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))
(fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))
(pow.f64 (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))
(neg.f64 (neg.f64 N))
(.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))
(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))

Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 N N #s(literal 1 binary64)) (fma.f64 N N #s(literal 1 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))
(*.f64 (pow.f64 (/.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 (.f64 N N) #s(literal 1 binary64))) (-.f64 N #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 N N #s(literal 1 binary64)) (fma.f64 N N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) N))
(*.f64 (/.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64)))) (.f64 (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64))) #s(literal -1 binary64))) (*.f64 (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64))) (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 N N) (-.f64 N #s(literal 1 binary64))) (.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 N #s(literal 1 binary64)) (-.f64 N #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (.f64 (-.f64 #s(literal 1 binary64) N) (*.f64 N N))) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (pow.f64 N #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (pow.f64 N #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 N N) #s(literal 1 binary64))) (neg.f64 (-.f64 N #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 N N #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) N)))
(/.f64 (-.f64 (*.f64 N N) #s(literal 1 binary64)) (-.f64 N #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(/.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))
(fma.f64 (sqrt.f64 (*.f64 #s(literal -1 binary64) N)) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) N #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 #s(literal -1 binary64) N) #s(literal 1/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (pow.f64 (pow.f64 N #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 N #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 N #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 N #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 N #s(literal 1/4 binary64)) (pow.f64 (pow.f64 N #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) N #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 N (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 N #s(literal 1 binary64) #s(literal 1 binary64))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 N N (fma.f64 #s(literal -1 binary64) N #s(literal 1 binary64)))))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (/.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N)))
(-.f64 (/.f64 (*.f64 N N) (-.f64 N #s(literal 1 binary64))) (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) N)
(-.f64 N #s(literal -1 binary64))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) N)
(+.f64 N #s(literal 1 binary64))
(exp.f64 (*.f64 (log1p.f64 N) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N (-.f64 N #s(literal 1 binary64)))) (.f64 (fma.f64 N N (-.f64 N #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (fma.f64 N N (-.f64 N #s(literal 1 binary64))) (fma.f64 N N (-.f64 N #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (*.f64 N N))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #s(literal 1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 N #s(literal 3 binary64)))) (.f64 (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64))) (-.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N)))
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(*.f64 (sqrt.f64 N) (/.f64 (sqrt.f64 N) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
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(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(neg.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 4 binary64)))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 4 binary64))) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
(*.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 N #s(literal 4 binary64)) (-.f64 (.f64 N N) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 N N) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) (pow.f64 N #s(literal 6 binary64)))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) (pow.f64 N #s(literal 6 binary64)))) (*.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) (pow.f64 N #s(literal 6 binary64)))) (*.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))))
(/.f64 (fma.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))))
(/.f64 (fma.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) (*.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 6 binary64))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))) #s(literal 2 binary64))) (+.f64 (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -3 binary64)) (/.f64 (pow.f64 N #s(literal 18 binary64)) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))))) (neg.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (*.f64 N N) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))) (.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) (pow.f64 N #s(literal 6 binary64)))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (fma.f64 N N #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 12 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 N N) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 18 binary64))) (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 12 binary64))) (pow.f64 N #s(literal 6 binary64))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64)))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64)))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))))
(fma.f64 (fabs.f64 (*.f64 #s(literal -1 binary64) N)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 #s(literal -1 binary64) N) #s(literal 1 binary64)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 (pow.f64 N #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 N #s(literal 1/4 binary64)) #s(literal 4 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (pow.f64 N #s(literal 6 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 4 binary64)))) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (/.f64 (pow.f64 N #s(literal 6 binary64)) (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 4 binary64))) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 N #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 N #s(literal 7/2 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(fma.f64 (pow.f64 N #s(literal 4 binary64)) (/.f64 (*.f64 N N) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 N #s(literal 3 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 N N) #s(literal 1 binary64))
(fma.f64 (*.f64 N N) (/.f64 (pow.f64 N #s(literal 4 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 N N) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 N N) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 N N) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 N #s(literal 3/2 binary64)) #s(literal 1 binary64))
(fma.f64 N N #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 N #s(literal 4 binary64)) (-.f64 (.f64 N N) #s(literal 1 binary64))) (pow.f64 (-.f64 (.f64 N N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(+.f64 (/.f64 (pow.f64 N #s(literal 6 binary64)) (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal -1 binary64))) (pow.f64 (fma.f64 N (+.f64 (pow.f64 N #s(literal 3 binary64)) N) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (*.f64 N N) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 N N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

eval110.0ms (1.9%)

Memory: 41.5MiB live, 235.5MiB allocated
Compiler: Compiled 19 094 to 3 228 computations (83.1% saved)

prune60.0ms (1.1%)

Memory

-25.5MiB live, 76.1MiB allocated

Pruning

17 alts after pruning (12 fresh and 5 done)

	Pruned	Kept	Total
New	725	10	735
Fresh	6	2	8
Picked	3	2	5
Done	1	3	4
Total	735	17	752

Accuracy

99.8%

Counts

752 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	52.1%	(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 N #s(literal 6 binary64)))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
✓	7.7%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
	94.7%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (*.f64 N N)))
	97.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) N)))
✓	97.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	71.8%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (fma.f64 (sqrt.f64 N) (pow.f64 N #s(literal 7/2 binary64)) (*.f64 N N)) (fma.f64 N N N))))
	97.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (.f64 (-.f64 (.f64 N N) #s(literal 1 binary64)) N) (-.f64 N #s(literal 1 binary64)))))
	71.8%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (.f64 N (.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (fma.f64 N N N))))
	71.8%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 #s(approx (pow (+ (* N N) N) 2) (pow.f64 N #s(literal 4 binary64))) (fma.f64 N N N))))
	97.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))
	97.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (fma.f64 (.f64 #s(literal -1 binary64) N) (*.f64 N N) #s(literal -1 binary64)) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
	94.6%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(approx (/ N (+ ( (- 1 N) N) -1)) (/.f64 #s(literal -1 binary64) N)))))
	94.1%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (sqrt.f64 N) (fabs.f64 (.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N))))))
	91.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (exp.f64 (log1p.f64 N)) N)))
✓	6.2%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 1 029 to 399 computations (61.2% saved)

regimes38.0ms (0.7%)

Memory

-14.3MiB live, 31.1MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (.f64 (-.f64 (.f64 N N) #s(literal 1 binary64)) N) (-.f64 N #s(literal 1 binary64)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (.f64 N (.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (fma.f64 N N N))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (sqrt.f64 N) (fabs.f64 (.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N))))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (fma.f64 (.f64 #s(literal -1 binary64) N) (*.f64 N N) #s(literal -1 binary64)) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 #s(approx (pow (+ (* N N) N) 2) (pow.f64 N #s(literal 4 binary64))) (fma.f64 N N N))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(approx (/ N (+ ( (- 1 N) N) -1)) (/.f64 #s(literal -1 binary64) N)))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 N N) #s(literal 1 binary64))) N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(approx (+ (* -1 (+ (* N N) N)) -1) (*.f64 (neg.f64 N) N))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64))))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 N N N) #s(literal -1 binary64))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fabs.f64 (/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N)) (sqrt.f64 N) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (fma.f64 (sqrt.f64 N) (pow.f64 N #s(literal 7/2 binary64)) (*.f64 N N)) (fma.f64 N N N))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 (/.f64 N N) (/.f64 (pow.f64 N #s(literal 3 binary64)) (-.f64 N #s(literal 1 binary64))) (/.f64 (*.f64 N N) (fma.f64 N N N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 N #s(literal 6 binary64)))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 N)) (neg.f64 N)))))) N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 (exp.f64 (log1p.f64 N)) N)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))))) (fabs.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))))

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Calls

2 calls:

28.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
9.0ms	N

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
99.6%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Outputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Calls

2 calls:

3.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
99.6%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))

Calls

2 calls:

2.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
97.6%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
97.6%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (*.f64 N N)))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))

Calls

2 calls:

2.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
94.7%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
94.7%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.1%)

Memory

-36.8MiB live, 7.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))

(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))

Calls

2 calls:

5.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
7.7%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
7.7%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Calls

2 calls:

1.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
6.2%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
6.2%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify18.0ms (0.3%)

Memory

34.6MiB live, 34.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	67
1	30	67
2	46	67
3	89	67
4	200	67
5	413	67
6	628	67
7	660	67
8	669	67

Stop Event

1×

saturated

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

soundness831.0ms (14.6%)

Memory

-45.1MiB live, 396.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	9	17
1	38	17
2	261	17
3	2707	17
0	8997	17
0	25	61
1	71	57
2	192	57
3	676	57
4	3357	57
0	8117	51
0	6	16
0	10	16
1	43	16
2	266	16
3	2561	16
0	9660	16

Stop Event

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

Compiler

Compiled 192 to 96 computations (50% saved)

preprocess49.0ms (0.9%)

Memory: 29.3MiB live, 72.8MiB allocated
Compiler: Compiled 164 to 70 computations (57.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	5	19
0	9	19
1	14	19
2	27	19
3	70	19
4	172	19
5	275	19
6	415	19
7	512	19
8	603	19
9	678	19
10	687	19
0	687	19

Iter	Nodes	Cost
0	5	19
0	9	19
1	14	19
2	27	19
3	70	19
4	172	19
5	275	19
6	415	19
7	512	19
8	603	19
9	678	19
10	687	19
0	687	19

start0.0ms (0%)

analyze2.0ms (0%)

sample2.3s (39.8%)

explain157.0ms (2.8%)

preprocess19.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize42.0ms (0.7%)

series1.0ms (0%)

simplify6.0ms (0.1%)

rewrite173.0ms (3.1%)

eval35.0ms (0.6%)

prune2.0ms (0%)

simplify25.0ms (0.4%)

localize17.0ms (0.3%)

series1.0ms (0%)

simplify146.0ms (2.6%)

rewrite159.0ms (2.8%)

eval35.0ms (0.6%)

prune59.0ms (1%)

simplify136.0ms (2.4%)

localize92.0ms (1.6%)

series17.0ms (0.3%)

simplify214.0ms (3.8%)

rewrite227.0ms (4%)

eval125.0ms (2.2%)

prune54.0ms (1%)

simplify103.0ms (1.8%)

localize145.0ms (2.6%)

series13.0ms (0.2%)

simplify125.0ms (2.2%)

rewrite153.0ms (2.7%)

eval110.0ms (1.9%)

prune60.0ms (1.1%)

regimes38.0ms (0.7%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

simplify18.0ms (0.3%)

soundness831.0ms (14.6%)

preprocess49.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	5	19
0	9	19
1	14	19
2	27	19
3	70	19
4	172	19
5	275	19
6	415	19
7	512	19
8	603	19
9	678	19
10	687	19
0	687	19