Metrics for 2atan (example 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.4MiB live, 2.4MiB 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)

sample1.8s (31.8%)

Memory

68.7MiB live, 1 950.1MiB allocated

Samples

1.2s	7 419×	1	valid
191.0ms	399×	2	valid
46.0ms	438×	0	valid

Precisions

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

ival-atan: 476.0ms (40.1% of total)

adjust: 226.0ms (19.1% of total)

const: 190.0ms (16% of total)

ival-add: 123.0ms (10.4% of total)

ival-sub: 80.0ms (6.7% of total)

ival->: 43.0ms (3.6% of total)

ival-<: 24.0ms (2% of total)

ival-and: 13.0ms (1.1% of total)

exact: 8.0ms (0.7% of total)

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

Bogosity

explain179.0ms (3.1%)

Memory

-23.1MiB live, 128.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
254	-	-	`(-.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	254	0

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	0	2

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

108.0ms	464×	1	valid
4.0ms	22×	2	valid
1.0ms	26×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-atan: 38.0ms (62.2% of total)

adjust: 12.0ms (19.6% of total)

ival-add: 5.0ms (8.2% of total)

ival-sub: 5.0ms (8.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess12.0ms (0.2%)

Memory

15.6MiB live, 15.6MiB 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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.1%	(-.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

3.4MiB live, 3.4MiB 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)

localize67.0ms (1.2%)

Memory

-4.0MiB live, 40.8MiB 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	58.20726245684741	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Samples

57.0ms	232×	1	valid
3.0ms	11×	2	valid
1.0ms	13×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-sub: 33.0ms (63.3% of total)

ival-atan: 9.0ms (17.3% of total)

adjust: 7.0ms (13.4% of total)

ival-add: 3.0ms (5.8% 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

1.3MiB live, 1.3MiB 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

5.9MiB live, 5.9MiB 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)))

rewrite264.0ms (4.6%)

Memory

-20.1MiB live, 180.7MiB 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)))

eval27.0ms (0.5%)

Memory: -11.6MiB live, 33.8MiB allocated
Compiler: Compiled 3 055 to 504 computations (83.5% saved)

prune2.0ms (0%)

Memory

7.9MiB live, 7.9MiB 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

99.7%

Counts

124 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(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)

simplify17.0ms (0.3%)

Memory

17.3MiB live, 17.3MiB 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

localize33.0ms (0.6%)

Memory

-29.2MiB live, 16.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
accuracy	0.0	(+.f64 #s(literal 1 binary64) N)
accuracy	0.22265625	(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

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

accuracy

0.0

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

accuracy

0.22265625

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

Samples

11.0ms

256×

valid

Compiler

Compiled 23 to 8 computations (65.2% saved)

Precisions

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

ival-atan2: 2.0ms (32.6% of total)

ival-add: 2.0ms (32.6% of total)

ival-mult: 2.0ms (32.6% 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

1.3MiB live, 1.3MiB 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))

simplify151.0ms (2.6%)

Memory

4.4MiB live, 104.1MiB 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 (2.7%)

Memory

20.8MiB live, 111.9MiB 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)

eval66.0ms (1.1%)

Memory: 0.6MiB live, 61.4MiB allocated
Compiler: Compiled 6 027 to 955 computations (84.2% saved)

prune41.0ms (0.7%)

Memory

-19.7MiB live, 26.6MiB 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
	99.2%	(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)))
	54.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (*.f64 (+.f64 (fma.f64 N N (pow.f64 N #s(literal 4 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))) N #s(literal 1 binary64)))
	92.0%	(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)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))
▶	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
✓	99.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
▶	91.8%	(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)))
	92.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) (*.f64 N N)))) (fabs.f64 (-.f64 N #s(literal 1 binary64))) #s(literal 1 binary64)))
	91.8%	(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)))
	72.4%	(atan2.f64 #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))))
	27.8%	(atan2.f64 #s(literal 1 binary64) (/.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)))))))
▶	99.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
▶	96.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	8.0%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
	92.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
▶	6.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 608 to 337 computations (44.6% saved)

simplify148.0ms (2.6%)

Memory

-19.9MiB live, 126.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N)
cost-diff	0	(sqrt.f64 (*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N))
cost-diff	0	(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))
cost-diff	0	(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)))
cost-diff	0	(pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64))
cost-diff	0	(fma.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
cost-diff	10	(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N))))
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: 7 (0.0ms)

Iter	Nodes	Cost
0	29	197
0	52	173
1	79	173
2	154	170
3	365	169
4	789	169
5	1714	169
6	2269	169
7	3213	163
8	4584	163
9	7124	163
0	8108	163

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

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

localize99.0ms (1.7%)

Memory

44.0MiB live, 89.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.140625	(sqrt.f64 (*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N))
accuracy	0.20703125	(*.f64 (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal 2 binary64)) N)
accuracy	0.21875	(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)))
accuracy	0.36328125	(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))
accuracy	0.0	(-.f64 #s(literal 1 binary64) N)
accuracy	0.00390625	(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N))))
accuracy	0.06640625	(*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))
accuracy	0.22265625	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
accuracy	0.0	(fma.f64 N N N)
accuracy	0.22265625	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
accuracy	2.1058248932251167	#s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N))
accuracy	0.22265625	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
accuracy	59.87394217261007	#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 N N #s(literal 1 binary64))
accuracy	0.04296875	(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
accuracy	0.22265625	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Samples

69.0ms

256×

valid

Compiler

Compiled 193 to 31 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-sub: 19.0ms (34.3% of total)

ival-mult: 9.0ms (16.3% of total)

ival-add: 7.0ms (12.7% of total)

ival-atan2: 6.0ms (10.8% of total)

ival-pow: 6.0ms (10.8% of total)

ival-sqrt: 3.0ms (5.4% of total)

ival-div: 2.0ms (3.6% of total)

ival-pow2: 2.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.5%)

Memory

-35.0MiB live, 12.0MiB allocated

Counts

18 → 59

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

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

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

2.0ms

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

simplify158.0ms (2.7%)

Memory

20.8MiB live, 118.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	574
1	436	516
2	1600	482
0	6462	456

Stop Event

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

Counts

59 → 58

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

rewrite260.0ms (4.5%)

Memory

13.7MiB live, 247.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	171
0	52	147
1	196	131
2	1510	125
0	8646	123

Stop Event

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

Counts

18 → 639

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

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

eval137.0ms (2.4%)

Memory: -20.5MiB live, 123.9MiB allocated
Compiler: Compiled 17 041 to 2 653 computations (84.4% saved)

prune27.0ms (0.5%)

Memory

-2.0MiB live, 45.7MiB allocated

Pruning

20 alts after pruning (16 fresh and 4 done)

	Pruned	Kept	Total
New	603	12	615
Fresh	6	4	10
Picked	2	3	5
Done	0	1	1
Total	611	20	631

Accuracy

99.8%

Counts

631 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(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)))
	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (fma.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N) (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) N)) (-.f64 #s(literal 1 binary64) N))) N #s(literal 1 binary64)))
	99.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 N (-.f64 N #s(literal 1 binary64)) #s(literal 1 binary64))) N #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))
▶	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
✓	99.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	99.0%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 (+.f64 N #s(literal 1 binary64)) (sqrt.f64 (-.f64 N #s(literal 1 binary64)))) (/.f64 (-.f64 N #s(literal 1 binary64)) (sqrt.f64 (-.f64 N #s(literal 1 binary64))))) N #s(literal 1 binary64)))
	91.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 N #s(literal 1 binary64)) (sqrt.f64 N)) (sqrt.f64 N) #s(literal 1 binary64)))
	81.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 N)) #s(literal 1 binary64)))
▶	91.8%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))) (sqrt.f64 (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
▶	91.8%	(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)))
✓	99.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	79.9%	(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))
▶	8.0%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
✓	96.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	96.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) N))))
	96.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))
	96.1%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (fma.f64 N (-.f64 N #s(literal 1 binary64)) #s(literal 1 binary64))))))
	92.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
✓	6.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 645 to 369 computations (42.8% saved)

simplify297.0ms (5.1%)

Memory

35.8MiB live, 177.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))
cost-diff	0	(fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))
cost-diff	0	(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))
cost-diff	0	(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)))
cost-diff	0	(.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N)))
cost-diff	0	(fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))) (sqrt.f64 (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))) (sqrt.f64 (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))) #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))
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	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N))
cost-diff	0	(fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
cost-diff	5	(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	289
0	73	278
1	124	278
2	323	269
3	1041	266
4	2936	264
5	7596	264
0	9185	263

Stop Event

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

Calls

Call 1

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

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

localize232.0ms (4%)

Memory

-38.8MiB live, 187.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))
accuracy	0.2109375	(/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
accuracy	0.21875	(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)))
accuracy	0.3203125	(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))
accuracy	0.21875	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))) (sqrt.f64 (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
accuracy	0.25390625	(*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))
accuracy	0.34603500976844204	(.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))
accuracy	0.35546875	(fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (sqrt.f64 N))) (sqrt.f64 (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 N)
accuracy	0.22265625	(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	0.44140625	(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
accuracy	0.0	(-.f64 N #s(literal -1 binary64))
accuracy	0.22265625	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
accuracy	58.87377541621345	#s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64)))
accuracy	0.0	(-.f64 #s(literal 1 binary64) N)
accuracy	0.00390625	(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N))))
accuracy	0.06640625	(*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))
accuracy	0.22265625	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))

Samples

108.0ms

256×

valid

Compiler

Compiled 300 to 44 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-mult: 39.0ms (50.2% of total)

ival-add: 10.0ms (12.9% of total)

ival-atan2: 7.0ms (9% of total)

ival-sub: 6.0ms (7.7% of total)

ival-div: 5.0ms (6.4% of total)

ival-sqrt: 5.0ms (6.4% of total)

ival-pow: 3.0ms (3.9% of total)

ival-fabs: 2.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.5%)

Memory

-17.4MiB live, 29.9MiB allocated

Counts

23 → 94

Calls

Call 1

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

Outputs
1
(+ 1 N)
(atan2 1 (+ 1 (* N (- (/ 1 (- 1 N)) (/ (pow N 2) (- 1 N))))))
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 (* N (+ 1 N)))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(sqrt N)
(atan2 1 (+ 1 (* N (- N 1))))
(+ 1 (* -1 N))
(+ 1 (* N (- N 1)))
(* (pow (* 1 (pow N 3)) 1/4) (sqrt -1))
(+ (* 1/2 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (sqrt -1)))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(+ (* N (+ (* -1/8 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (sqrt -1)))))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(+ (* N (+ (* 1/2 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (sqrt -1)))) (* N (+ (* -1/8 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (pow (sqrt -1) 5)))))))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(* -1 (sqrt (pow N 3)))
(* N (+ (sqrt (pow N 3)) (* -1 (sqrt N))))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (+ 1 (+ N (pow N 2))))))))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (+ 1 (+ N (pow N 2)))))))
(fabs (- 1 (pow N 3)))
(+ 1 (* -1 (pow N 3)))
(pow N 2)
(* (pow N 2) (+ 1 N))
(* (pow N 2) (+ 1 (* N (+ 1 N))))
(* (pow N 2) (+ 1 (* N (+ 1 (* N (+ 1 N))))))
(* -1 (sqrt N))
(+ (sqrt (pow N 3)) (* -1 (sqrt N)))
N
(* N (+ 1 (* -1 N)))
(* N (+ 1 (* N (- (pow N 2) 1))))
(* N (+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1))))
(* N (+ 1 (/ 1 N)))
(atan2 1 (- (+ 1 (/ N (- 1 N))) (/ (pow N 3) (- 1 N))))
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(/ -1 N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N)
(/ (- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N))) N)
(atan2 1 (- (+ 1 (pow N 2)) N))
(* (pow N 2) (- 1 (/ 1 N)))
(* (pow N 2) (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)))
(pow (* 1 (pow N 5)) 1/4)
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (pow (* 1 N) 1/4)))
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (+ (* -1/8 (pow (/ 1 (pow N 7)) 1/4)) (pow (* 1 N) 1/4))))
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (+ (* -1/8 (pow (/ 1 (pow N 7)) 1/4)) (+ (* -1/16 (pow (/ 1 (pow N 11)) 1/4)) (pow (* 1 N) 1/4)))))
(sqrt (pow N 5))
(* (pow N 3) (+ (sqrt (/ 1 N)) (* -1 (sqrt (/ 1 (pow N 3))))))
(* -1 (pow N 3))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(* -1 N)
(* -1 (* N (+ 1 (/ 1 N))))
(* N (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1))
(* N (- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N))))
(* N (- (/ 1 N) 1))
(sqrt (pow N 3))
(* (pow N 2) (+ (sqrt (/ 1 N)) (* -1 (sqrt (/ 1 (pow N 3))))))
(/ 1 N)
(/ (- 1 (/ 1 N)) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) N)
(atan2 1 (+ 1 (* N (- (/ 1 (+ 1 (* -1 N))) (/ (pow N 2) (+ 1 (* -1 N)))))))
(* -1 (/ (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))) N))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N))) N))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(* -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 (* -1 (* N (* (pow (sqrt -1) 2) (+ 1 (* -1 N)))))))
(* (pow N 2) (pow (sqrt -1) 2))
(* (pow N 2) (+ (* -1 (/ (pow (sqrt -1) 2) N)) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N)) (pow (sqrt -1) 2)))
(* -1 (* (pow (* -1 (pow N 5)) 1/4) (sqrt (sqrt -1))))
(* -1 (* N (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1))))))
(* -1 (* N (+ (* -1/8 (* (pow (/ -1 (pow N 7)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1)))))))
(* -1 (* N (+ (* -1/8 (* (pow (/ -1 (pow N 7)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/16 (* (pow (/ -1 (pow N 11)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1))))))))
(* -1 (* (sqrt (pow N 5)) (pow (sqrt -1) 2)))
(* -1 (* (pow N 3) (+ (* -1 (* (sqrt (/ 1 (pow N 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 N)) (pow (sqrt -1) 2)))))
(atan2 1 (+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (+ 1 (pow N 2)) (* -1 N)))))))
(+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (+ 1 (pow N 2)) (* -1 N))))))
(fabs (+ 1 (* -1 (pow N 3))))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(* -1 (* N (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))))
(* -1 (* N (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N)))))
(* -1 (* N (- 1 (/ 1 N))))
(* -1 (* (sqrt (pow N 3)) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (* -1 (* (sqrt (/ 1 N)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (pow N 3))) (pow (sqrt -1) 2))))
(* -1 (/ (- (/ 1 N) 1) N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) 1) N)) 1) N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) (+ 1 (/ 1 (pow N 3)))) N)) 1) N))

Calls

3 calls:

Time

Variable

Point

Expression

16.0ms

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

5.0ms

-inf

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

4.0ms

inf

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

simplify145.0ms (2.5%)

Memory

-1.2MiB live, 232.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	292	1138
1	902	1058
2	3580	1034
0	8612	980

Stop Event

1×	iter limit
1×	node limit

Counts

94 → 93

Calls

Call 1

Inputs
1
(+ 1 N)
(atan2 1 (+ 1 (* N (- (/ 1 (- 1 N)) (/ (pow N 2) (- 1 N))))))
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 (* N (+ 1 N)))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(sqrt N)
(atan2 1 (+ 1 (* N (- N 1))))
(+ 1 (* -1 N))
(+ 1 (* N (- N 1)))
(* (pow (* 1 (pow N 3)) 1/4) (sqrt -1))
(+ (* 1/2 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (sqrt -1)))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(+ (* N (+ (* -1/8 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (sqrt -1)))))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(+ (* N (+ (* 1/2 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (sqrt -1)))) (* N (+ (* -1/8 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (pow (sqrt -1) 5)))))))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(* -1 (sqrt (pow N 3)))
(* N (+ (sqrt (pow N 3)) (* -1 (sqrt N))))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (+ 1 (+ N (pow N 2))))))))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (+ 1 (+ N (pow N 2)))))))
(fabs (- 1 (pow N 3)))
(+ 1 (* -1 (pow N 3)))
(pow N 2)
(* (pow N 2) (+ 1 N))
(* (pow N 2) (+ 1 (* N (+ 1 N))))
(* (pow N 2) (+ 1 (* N (+ 1 (* N (+ 1 N))))))
(* -1 (sqrt N))
(+ (sqrt (pow N 3)) (* -1 (sqrt N)))
N
(* N (+ 1 (* -1 N)))
(* N (+ 1 (* N (- (pow N 2) 1))))
(* N (+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1))))
(* N (+ 1 (/ 1 N)))
(atan2 1 (- (+ 1 (/ N (- 1 N))) (/ (pow N 3) (- 1 N))))
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(/ -1 N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N)
(/ (- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N))) N)
(atan2 1 (- (+ 1 (pow N 2)) N))
(* (pow N 2) (- 1 (/ 1 N)))
(* (pow N 2) (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)))
(pow (* 1 (pow N 5)) 1/4)
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (pow (* 1 N) 1/4)))
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (+ (* -1/8 (pow (/ 1 (pow N 7)) 1/4)) (pow (* 1 N) 1/4))))
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (+ (* -1/8 (pow (/ 1 (pow N 7)) 1/4)) (+ (* -1/16 (pow (/ 1 (pow N 11)) 1/4)) (pow (* 1 N) 1/4)))))
(sqrt (pow N 5))
(* (pow N 3) (+ (sqrt (/ 1 N)) (* -1 (sqrt (/ 1 (pow N 3))))))
(* -1 (pow N 3))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(* -1 N)
(* -1 (* N (+ 1 (/ 1 N))))
(* N (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1))
(* N (- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N))))
(* N (- (/ 1 N) 1))
(sqrt (pow N 3))
(* (pow N 2) (+ (sqrt (/ 1 N)) (* -1 (sqrt (/ 1 (pow N 3))))))
(/ 1 N)
(/ (- 1 (/ 1 N)) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) N)
(atan2 1 (+ 1 (* N (- (/ 1 (+ 1 (* -1 N))) (/ (pow N 2) (+ 1 (* -1 N)))))))
(* -1 (/ (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))) N))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N))) N))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(* -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 (* -1 (* N (* (pow (sqrt -1) 2) (+ 1 (* -1 N)))))))
(* (pow N 2) (pow (sqrt -1) 2))
(* (pow N 2) (+ (* -1 (/ (pow (sqrt -1) 2) N)) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N)) (pow (sqrt -1) 2)))
(* -1 (* (pow (* -1 (pow N 5)) 1/4) (sqrt (sqrt -1))))
(* -1 (* N (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1))))))
(* -1 (* N (+ (* -1/8 (* (pow (/ -1 (pow N 7)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1)))))))
(* -1 (* N (+ (* -1/8 (* (pow (/ -1 (pow N 7)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/16 (* (pow (/ -1 (pow N 11)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1))))))))
(* -1 (* (sqrt (pow N 5)) (pow (sqrt -1) 2)))
(* -1 (* (pow N 3) (+ (* -1 (* (sqrt (/ 1 (pow N 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 N)) (pow (sqrt -1) 2)))))
(atan2 1 (+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (+ 1 (pow N 2)) (* -1 N)))))))
(+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (+ 1 (pow N 2)) (* -1 N))))))
(fabs (+ 1 (* -1 (pow N 3))))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(* -1 (* N (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))))
(* -1 (* N (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N)))))
(* -1 (* N (- 1 (/ 1 N))))
(* -1 (* (sqrt (pow N 3)) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (* -1 (* (sqrt (/ 1 N)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (pow N 3))) (pow (sqrt -1) 2))))
(* -1 (/ (- (/ 1 N) 1) N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) 1) N)) 1) N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) (+ 1 (/ 1 (pow N 3)))) N)) 1) N))

Outputs
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(atan2 1 (+ 1 (* N (- (/ 1 (- 1 N)) (/ (pow N 2) (- 1 N))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 (* N (+ 1 N)))))
(fma.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) 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)))
(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)))
(sqrt N)
(sqrt.f64 N)
(atan2 1 (+ 1 (* N (- N 1))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(+ 1 (* N (- N 1)))
(fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(* (pow (* 1 (pow N 3)) 1/4) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64)))
(+ (* 1/2 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (sqrt -1)))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64)) (/.f64 (*.f64 (pow.f64 (pow.f64 N #s(literal 7 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* N (+ (* -1/8 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (sqrt -1)))))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (pow.f64 N #s(literal 7 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) N (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64))))
(+ (* N (+ (* 1/2 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (sqrt -1)))) (* N (+ (* -1/8 (* (pow (* 1 (pow N 3)) 1/4) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (pow (* 1 (pow N 7)) 1/4) (/ 1 (pow (sqrt -1) 5)))))))) (* (pow (* 1 (pow N 3)) 1/4) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (pow.f64 N #s(literal 7 binary64)) #s(literal 1/4 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) N (/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) N (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1/4 binary64))))
(* -1 (sqrt (pow N 3)))
(neg.f64 (sqrt.f64 (pow.f64 N #s(literal 3 binary64))))
(* N (+ (sqrt (pow N 3)) (* -1 (sqrt N))))
(*.f64 (-.f64 (sqrt.f64 (pow.f64 N #s(literal 3 binary64))) (sqrt.f64 N)) N)
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (+ 1 (+ N (pow N 2))))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))) (fabs.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64)))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (+ 1 (+ N (pow N 2)))))))
(fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))) (fabs.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fabs (- 1 (pow N 3)))
(fabs.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64)))
(+ 1 (* -1 (pow N 3)))
(-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 N))
(*.f64 (fma.f64 N N N) N)
(* (pow N 2) (+ 1 (* N (+ 1 N))))
(*.f64 (fma.f64 (fma.f64 N N N) N N) N)
(* (pow N 2) (+ 1 (* N (+ 1 (* N (+ 1 N))))))
(*.f64 N (fma.f64 (fma.f64 (fma.f64 N N N) N N) N N))
(* -1 (sqrt N))
(neg.f64 (sqrt.f64 N))
(+ (sqrt (pow N 3)) (* -1 (sqrt N)))
(-.f64 (sqrt.f64 (pow.f64 N #s(literal 3 binary64))) (sqrt.f64 N))
N
(* N (+ 1 (* -1 N)))
(*.f64 (-.f64 #s(literal 1 binary64) N) N)
(* N (+ 1 (* N (- (pow N 2) 1))))
(*.f64 (fma.f64 (fma.f64 N N #s(literal -1 binary64)) N #s(literal 1 binary64)) N)
(* N (+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1))))
(*.f64 (fma.f64 (-.f64 (fma.f64 N N (pow.f64 (neg.f64 N) #s(literal 3 binary64))) #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 N))) (/ (pow N 3) (- 1 N))))
(atan2.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) 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))
(/ -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 (/ (+ 1 (/ 1 N)) N)) 1) N)
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N) #s(literal 1 binary64)) N)
(/ (- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N))) N)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(atan2 1 (- (+ 1 (pow N 2)) 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 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 N (fma.f64 N (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) N) N))
(pow (* 1 (pow N 5)) 1/4)
(pow.f64 (pow.f64 N #s(literal 5 binary64)) #s(literal 1/4 binary64))
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (pow (* 1 N) 1/4)))
(*.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64) (pow.f64 N #s(literal 1/4 binary64))) N)
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (+ (* -1/8 (pow (/ 1 (pow N 7)) 1/4)) (pow (* 1 N) 1/4))))
(*.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64) (pow.f64 N #s(literal 1/4 binary64)))) N)
(* N (+ (* -1/2 (pow (/ 1 (pow N 3)) 1/4)) (+ (* -1/8 (pow (/ 1 (pow N 7)) 1/4)) (+ (* -1/16 (pow (/ 1 (pow N 11)) 1/4)) (pow (* 1 N) 1/4)))))
(*.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 11 binary64))) #s(literal 1/4 binary64)) #s(literal -1/16 binary64) (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -1/8 binary64) (pow.f64 N #s(literal 1/4 binary64))))) N)
(sqrt (pow N 5))
(sqrt.f64 (pow.f64 N #s(literal 5 binary64)))
(* (pow N 3) (+ (sqrt (/ 1 N)) (* -1 (sqrt (/ 1 (pow N 3))))))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))) (pow.f64 N #s(literal 3 binary64)))
(* -1 (pow N 3))
(pow.f64 (neg.f64 N) #s(literal 3 binary64))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 N #s(literal 3 binary64)))
(* -1 N)
(neg.f64 N)
(* -1 (* N (+ 1 (/ 1 N))))
(-.f64 #s(literal -1 binary64) N)
(* N (- (* -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)) N)
(* N (- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N))))
(*.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(* N (- (/ 1 N) 1))
(-.f64 #s(literal 1 binary64) N)
(sqrt (pow N 3))
(sqrt.f64 (pow.f64 N #s(literal 3 binary64)))
(* (pow N 2) (+ (sqrt (/ 1 N)) (* -1 (sqrt (/ 1 (pow N 3))))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))) (.f64 N N))
(/ 1 N)
(/.f64 #s(literal 1 binary64) N)
(/ (- 1 (/ 1 N)) N)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) N)
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) N)) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) N)
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) N))) N)
(atan2 1 (+ 1 (* N (- (/ 1 (+ 1 (* -1 N))) (/ (pow N 2) (+ 1 (* -1 N)))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
(* -1 (/ (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))) N))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N) #s(literal 1 binary64)) N)
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N))) N))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) N) #s(literal -1 binary64)) N)) 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)))
(* -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 (* -1 (* N (* (pow (sqrt -1) 2) (+ 1 (* -1 N)))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(* (pow N 2) (pow (sqrt -1) 2))
(*.f64 (neg.f64 N) N)
(* (pow N 2) (+ (* -1 (/ (pow (sqrt -1) 2) N)) (pow (sqrt -1) 2)))
(*.f64 (-.f64 #s(literal 1 binary64) N) N)
(* (pow N 2) (+ (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N)) (pow (sqrt -1) 2)))
(fma.f64 (neg.f64 N) N (-.f64 N #s(literal -1 binary64)))
(* -1 (* (pow (* -1 (pow N 5)) 1/4) (sqrt (sqrt -1))))
(*.f64 (neg.f64 (pow.f64 (neg.f64 (pow.f64 N #s(literal 5 binary64))) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* N (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1))))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64) (pow.f64 (neg.f64 N) #s(literal 1/4 binary64)))) (neg.f64 N))
(* -1 (* N (+ (* -1/8 (* (pow (/ -1 (pow N 7)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1)))))))
(.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64) (pow.f64 (neg.f64 N) #s(literal 1/4 binary64))))) (neg.f64 N))
(* -1 (* N (+ (* -1/8 (* (pow (/ -1 (pow N 7)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/16 (* (pow (/ -1 (pow N 11)) 1/4) (sqrt (sqrt -1)))) (+ (* 1/2 (* (pow (/ -1 (pow N 3)) 1/4) (sqrt (sqrt -1)))) (* (pow (* -1 N) 1/4) (sqrt (sqrt -1))))))))
(.f64 (fma.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -1/8 binary64) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 11 binary64))) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64) (pow.f64 (neg.f64 N) #s(literal 1/4 binary64))))) (neg.f64 N))
(* -1 (* (sqrt (pow N 5)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 N #s(literal 5 binary64))) #s(literal 1 binary64))
(* -1 (* (pow N 3) (+ (* -1 (* (sqrt (/ 1 (pow N 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 N)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))) (pow.f64 N #s(literal 3 binary64)))
(atan2 1 (+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (+ 1 (pow N 2)) (* -1 N)))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))) (fabs.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64)))
(+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (+ 1 (pow N 2)) (* -1 N))))))
(fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))) (fabs.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64))
(fabs (+ 1 (* -1 (pow N 3))))
(fabs.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64)))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (pow.f64 (neg.f64 N) #s(literal 3 binary64)))
(* -1 (* N (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))))
(fma.f64 (neg.f64 N) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) #s(literal -1 binary64))
(* -1 (* N (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 N)) N)) 1) N)))))
(neg.f64 (fma.f64 (neg.f64 (-.f64 (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N) #s(literal 1 binary64))) #s(literal 1 binary64) N))
(* -1 (* N (- 1 (/ 1 N))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) (neg.f64 N))
(* -1 (* (sqrt (pow N 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64))
(* (pow N 2) (+ (* -1 (* (sqrt (/ 1 N)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 (pow N 3))) (pow (sqrt -1) 2))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))) (.f64 N N))
(* -1 (/ (- (/ 1 N) 1) N))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N)
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) 1) N)) 1) N))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) N)) #s(literal 1 binary64)) (neg.f64 N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) (+ 1 (/ 1 (pow N 3)))) N)) 1) N))
(/.f64 (-.f64 (/.f64 (-.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (neg.f64 N)) #s(literal 1 binary64)) (neg.f64 N))

rewrite145.0ms (2.5%)

Memory

19.0MiB live, 212.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	233
0	73	229
1	290	159
2	2230	147
0	9160	146

Stop Event

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

Counts

23 → 814

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (.f64 N N) #s(literal 1 binary64)) (-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(.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)) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(.f64 (/.f64 (-.f64 (.f64 N N) #s(literal 1 binary64)) (-.f64 (*.f64 N N) #s(literal 1 binary64))) (-.f64 N #s(literal -1 binary64)))
(*.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (fma.f64 (pow.f64 N #s(literal 3 binary64)) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N) (*.f64 (-.f64 (fma.f64 N N #s(literal 1 binary64)) N) #s(literal 1 binary64))) (pow.f64 (-.f64 (fma.f64 N N #s(literal 1 binary64)) N) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 N N) (neg.f64 (-.f64 N #s(literal -1 binary64))) (.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))) #s(literal -1 binary64))) (pow.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 N N) (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64)))) (.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))) (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))))))
(/.f64 (fma.f64 (.f64 N N) (-.f64 N #s(literal -1 binary64)) (.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))) (-.f64 N #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 (-.f64 N #s(literal -1 binary64))) (.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))) (.f64 N N))) (pow.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (-.f64 N #s(literal -1 binary64))) (.f64 (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64)))) (.f64 N N))) (*.f64 (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64)))) (neg.f64 (-.f64 N #s(literal -1 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (-.f64 N #s(literal -1 binary64))) (.f64 (-.f64 N #s(literal -1 binary64)) (.f64 N N))) (*.f64 (-.f64 N #s(literal -1 binary64)) (neg.f64 (-.f64 N #s(literal -1 binary64)))))
(/.f64 (fma.f64 (.f64 N N) (neg.f64 (-.f64 N #s(literal -1 binary64))) (.f64 (-.f64 N #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (-.f64 N #s(literal -1 binary64)) (neg.f64 (-.f64 N #s(literal -1 binary64)))))
(/.f64 (fma.f64 (.f64 N N) (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64)))) (-.f64 N #s(literal -1 binary64))) (.f64 (-.f64 N #s(literal -1 binary64)) (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64))))))
(/.f64 (fma.f64 (*.f64 N N) (-.f64 N #s(literal -1 binary64)) (-.f64 N #s(literal -1 binary64))) (pow.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (-.f64 N #s(literal -1 binary64)) (.f64 (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64)))) (.f64 N N))) (*.f64 (neg.f64 (neg.f64 (-.f64 N #s(literal -1 binary64)))) (-.f64 N #s(literal -1 binary64))))
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eval110.0ms (1.9%)

Memory: -11.2MiB live, 214.5MiB allocated
Compiler: Compiled 12 681 to 2 312 computations (81.8% saved)

prune54.0ms (0.9%)

Memory

7.9MiB live, 65.5MiB allocated

Pruning

21 alts after pruning (14 fresh and 7 done)

	Pruned	Kept	Total
New	545	6	551
Fresh	3	8	11
Picked	2	3	5
Done	0	4	4
Total	550	21	571

Accuracy

99.8%

Counts

571 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	91.9%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (*.f64 N N) N #s(literal 1 binary64)) (fabs.f64 (/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) #s(literal 1 binary64)))
✓	99.2%	(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)))
	99.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) (-.f64 N #s(literal -1 binary64))))
	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (fma.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N) (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) N)) (-.f64 #s(literal 1 binary64) N))) N #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (*.f64 N (/.f64 N (-.f64 #s(literal 1 binary64) N)))) N #s(literal 1 binary64)))
✓	99.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	99.0%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 (+.f64 N #s(literal 1 binary64)) (sqrt.f64 (-.f64 N #s(literal 1 binary64)))) (/.f64 (-.f64 N #s(literal 1 binary64)) (sqrt.f64 (-.f64 N #s(literal 1 binary64))))) N #s(literal 1 binary64)))
	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (-.f64 N #s(literal -1 binary64)) (sqrt.f64 N)) (sqrt.f64 N) #s(literal 1 binary64)))
	91.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) (sqrt.f64 N)) N)) (sqrt.f64 (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
	81.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (.f64 (.f64 (-.f64 N #s(literal 1 binary64)) N) (*.f64 (sqrt.f64 N) (-.f64 N #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 N)) #s(literal 1 binary64)))
	96.8%	(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 (sqrt.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))) (sqrt.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))))) #s(literal 1 binary64)))
✓	99.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	79.9%	(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))
✓	8.0%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* N N) 1) N) (-.f64 N #s(literal -1 binary64))))
	92.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (*.f64 N N)))
✓	96.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	96.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) N))))
	96.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (+.f64 (*.f64 N N) N)))
	96.1%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (.f64 (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (fma.f64 N (-.f64 N #s(literal 1 binary64)) #s(literal 1 binary64))))))
✓	6.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 1 031 to 402 computations (61% saved)

regimes18.0ms (0.3%)

Memory

-24.2MiB live, 23.9MiB allocated

Counts

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

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

Calls

2 calls:

9.0ms	N
8.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
99.7%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
99.7%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB 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 (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (*.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) (+.f64 (*.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
96.4%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
96.4%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

6 → 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 (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.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
96.4%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
96.4%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB 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 (+ (* (+ (* (sqrt N) (sqrt N)) 1) N) 1) (*.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
92.4%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
92.4%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

5.7MiB live, 5.8MiB 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:

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

Results

Accuracy	Segments	Branch
8.0%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
8.0%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory

4.4MiB live, 4.4MiB 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
6.5%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
6.5%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify18.0ms (0.3%)

Memory

-33.5MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	74
1	30	74
2	46	74
3	89	74
4	200	74
5	413	74
6	628	74
7	660	74
8	669	74

Stop Event

1×

saturated

Calls

Call 1

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

soundness889.0ms (15.4%)

Memory

40.8MiB live, 552.0MiB 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	29	171
0	52	147
1	196	131
2	1510	125
0	8646	123
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
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 219 to 109 computations (50.2% saved)

preprocess93.0ms (1.6%)

Memory: 27.0MiB live, 117.4MiB allocated
Compiler: Compiled 178 to 70 computations (60.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.1MiB 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%)

sample1.8s (31.8%)

explain179.0ms (3.1%)

preprocess12.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize67.0ms (1.2%)

series1.0ms (0%)

simplify6.0ms (0.1%)

rewrite264.0ms (4.6%)

eval27.0ms (0.5%)

prune2.0ms (0%)

simplify17.0ms (0.3%)

localize33.0ms (0.6%)

series1.0ms (0%)

simplify151.0ms (2.6%)

rewrite159.0ms (2.7%)

eval66.0ms (1.1%)

prune41.0ms (0.7%)

simplify148.0ms (2.6%)

localize99.0ms (1.7%)

series31.0ms (0.5%)

simplify158.0ms (2.7%)

rewrite260.0ms (4.5%)

eval137.0ms (2.4%)

prune27.0ms (0.5%)

simplify297.0ms (5.1%)

localize232.0ms (4%)

series26.0ms (0.5%)

simplify145.0ms (2.5%)

rewrite145.0ms (2.5%)

eval110.0ms (1.9%)

prune54.0ms (0.9%)

regimes18.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

simplify18.0ms (0.3%)

soundness889.0ms (15.4%)

preprocess93.0ms (1.6%)

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