Metrics for 2atan (example 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample2.0s (36.2%)

Memory

-185.6MiB live, 1 851.6MiB allocated

Samples

1.1s	7 453×	1	valid
92.0ms	399×	2	valid
31.0ms	404×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 977.0ms

ival-atan: 359.0ms (36.7% of total)

adjust: 218.0ms (22.3% of total)

const: 121.0ms (12.4% of total)

ival-sub: 110.0ms (11.3% of total)

ival-add: 92.0ms (9.4% of total)

ival-<: 29.0ms (3% of total)

ival->: 24.0ms (2.5% of total)

ival-and: 12.0ms (1.2% of total)

exact: 8.0ms (0.8% of total)

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

Bogosity

explain134.0ms (2.4%)

Memory

23.6MiB live, 213.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
253	1	(16.265296218883723)	-	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
0	0	-	-	`N`
0	0	-	-	`(+.f64 N #s(literal 1 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(atan.f64 N)`
0	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 -
+	253	0
-	1	2

Precision

0.9960629921259843

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	1	0	2

Precision?

0.9960629921259843

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

65.0ms	456×	1	valid
5.0ms	28×	2	valid
2.0ms	28×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-atan: 19.0ms (35.7% of total)

adjust: 16.0ms (30.1% of total)

ival-sub: 12.0ms (22.6% of total)

ival-add: 5.0ms (9.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess16.0ms (0.3%)

Memory

-4.1MiB live, 34.6MiB 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

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.3%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB 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)

localize62.0ms (1.1%)

Memory

-14.6MiB live, 71.1MiB 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	58.06696980648091	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Samples

52.0ms	228×	1	valid
2.0ms	14×	2	valid
1.0ms	14×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-atan: 9.0ms (35.9% of total)

adjust: 7.0ms (27.9% of total)

ival-sub: 6.0ms (24% of total)

ival-add: 3.0ms (12% 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

1.8MiB live, 1.8MiB 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

8.6MiB live, 8.6MiB 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)))

rewrite200.0ms (3.6%)

Memory

-7.2MiB live, 257.5MiB 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))))))))
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(-.f64 (*.f64 N (/.f64 N (-.f64 N #s(literal 1 binary64)))) (pow.f64 (-.f64 N #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 N))
(+.f64 (pow.f64 (fma.f64 N N (-.f64 #s(literal 1 binary64) N)) #s(literal -1 binary64)) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N N (-.f64 #s(literal 1 binary64) N))))
(+.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N N (-.f64 #s(literal 1 binary64) N))) (pow.f64 (fma.f64 N N (-.f64 #s(literal 1 binary64) N)) #s(literal -1 binary64)))
(+.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)))

eval16.0ms (0.3%)

Memory: 24.2MiB live, 24.2MiB allocated
Compiler: Compiled 3 055 to 504 computations (83.5% saved)

prune3.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB 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

99.6%

Counts

124 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify38.0ms (0.7%)

Memory

-28.6MiB live, 34.0MiB 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

localize23.0ms (0.4%)

Memory

-4.6MiB live, 31.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(+.f64 #s(literal 1 binary64) N)
accuracy	0.00390625	(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

New

Metric

Score

Program

accuracy

0.0

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

accuracy

0.00390625

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

accuracy

0.28125

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

Samples

16.0ms

256×

valid

Compiler

Compiled 23 to 8 computations (65.2% saved)

Precisions

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

ival-add: 3.0ms (48.3% of total)

ival-atan2: 2.0ms (32.2% of total)

ival-mult: 2.0ms (32.2% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.0MiB live, 2.0MiB 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))

simplify109.0ms (1.9%)

Memory

-10.6MiB live, 110.1MiB 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)))

rewrite155.0ms (2.8%)

Memory

17.6MiB live, 174.3MiB 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)))
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(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (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 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (neg.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)) (pow.f64 (neg.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) (pow.f64 N #s(literal 3 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (neg.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 (*.f64 (neg.f64 N) N) (-.f64 #s(literal 1 binary64) N)))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 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) (pow.f64 N #s(literal 3 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 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 (*.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 (.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)

eval44.0ms (0.8%)

Memory: 3.4MiB live, 78.3MiB allocated
Compiler: Compiled 6 027 to 955 computations (84.2% saved)

prune18.0ms (0.3%)

Memory

-3.2MiB live, 35.0MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	236	19	255
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	236	20	256

Accuracy

99.8%

Counts

256 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	91.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (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))) N #s(literal 1 binary64)))
	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))
	45.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) N #s(literal 1 binary64)))
	75.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (*.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))) N #s(literal 1 binary64)))
	92.1%	(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)))
	99.1%	(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 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	92.1%	(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)))
	46.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))))) (fabs.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
▶	92.0%	(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)))
▶	93.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
	75.5%	(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
	68.1%	(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))))
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	53.7%	(atan2.f64 #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))))
	95.9%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	7.9%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
	92.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
▶	6.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 674 to 393 computations (41.7% saved)

simplify165.0ms (2.9%)

Memory

-65.1MiB live, 217.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(log1p.f64 N)
cost-diff	0	(exp.f64 (log1p.f64 N))
cost-diff	0	(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
cost-diff	0	(-.f64 #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	(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))
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	(sqrt.f64 N)
cost-diff	0	(hypot.f64 (sqrt.f64 N) N)
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))
cost-diff	4	(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	172
0	55	162
1	103	162
2	275	162
3	922	162
4	2900	162
0	8407	162

Stop Event

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

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(hypot.f64 (sqrt.f64 N) N)
(sqrt.f64 N)
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) (+.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) (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)
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(log1p.f64 N)
N

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(hypot.f64 (sqrt.f64 N) N)
(sqrt.f64 N)
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) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
#s(literal 1 binary64)
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(fma.f64 N N #s(literal 1 binary64))
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 (+.f64 (fma.f64 N N N) #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 (+.f64 (fma.f64 N N N) #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))))
(/.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)
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(+.f64 N #s(literal 1 binary64))
(log1p.f64 N)
N

localize124.0ms (2.2%)

Memory

35.1MiB live, 110.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
accuracy	0.01171875	(log1p.f64 N)
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
accuracy	4.345086022398723	(exp.f64 (log1p.f64 N))
accuracy	0.0078125	(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
accuracy	0.26171875	(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	0.2890625	(/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
accuracy	0.3991012695368841	(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	0.0	(fma.f64 N N #s(literal 1 binary64))
accuracy	0.0546875	(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
accuracy	59.69685826911379	#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 N)
accuracy	0.0078125	(hypot.f64 (sqrt.f64 N) N)
accuracy	0.046875	(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))

Samples

102.0ms	253×	0	valid
2.0ms	1×	5	exit
1.0ms	2×	1	valid

Compiler

Compiled 223 to 33 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-atan2: 37.0ms (40.9% of total)

ival-add: 23.0ms (25.4% of total)

ival-mult: 7.0ms (7.7% of total)

ival-hypot: 5.0ms (5.5% of total)

ival-log1p: 4.0ms (4.4% of total)

ival-exp: 3.0ms (3.3% of total)

ival-pow: 3.0ms (3.3% of total)

ival-div: 2.0ms (2.2% of total)

ival-sqrt: 2.0ms (2.2% of total)

ival-fabs: 2.0ms (2.2% of total)

adjust: 1.0ms (1.1% of total)

ival-sub: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

19 → 60

Calls

Call 1

Inputs
(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))
(hypot.f64 (sqrt.f64 N) N)
(sqrt.f64 N)
(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) (+.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) (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)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(log1p.f64 N)
(/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))

Outputs
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(sqrt N)
(+ (sqrt N) (* 1/2 (sqrt (pow N 3))))
(+ (sqrt N) (* (pow N 2) (+ (* -1/8 (sqrt N)) (* 1/2 (sqrt (/ 1 N))))))
(+ (sqrt N) (* (pow N 2) (+ (* 1/2 (sqrt (/ 1 N))) (* (pow N 2) (+ (* -1/8 (sqrt (/ 1 (pow N 3)))) (* 1/16 (sqrt (/ 1 N))))))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(+ 1 (pow N 2))
(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)))
N
(* N (+ 1 (* -1/2 N)))
(* N (+ 1 (* N (- (* 1/3 N) 1/2))))
(* N (+ 1 (* N (- (* N (+ 1/3 (* -1/4 N))) 1/2))))
(* N (+ 1 (* -1 N)))
(* N (+ 1 (* N (- (pow N 2) 1))))
(* N (+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* N (+ 1 (* 1/2 (/ 1 N))))
(* N (- (+ 1 (* 1/2 (/ 1 N))) (/ 1/8 (pow N 2))))
(* N (- (+ 1 (+ (* 1/2 (/ 1 N)) (* 1/16 (/ 1 (pow N 3))))) (/ 1/8 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* -1 (pow N 3))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(* N (+ 1 (/ 1 N)))
(* -1 (log (/ 1 N)))
(+ (* -1 (log (/ 1 N))) (/ 1 N))
(- (+ (* -1 (log (/ 1 N))) (/ 1 N)) (/ 1/2 (pow N 2)))
(- (+ (* -1 (log (/ 1 N))) (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3))))) (/ 1/2 (pow N 2)))
(/ 1 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)
(* (pow N 2) (+ 1 (* -1 (/ (pow (sqrt -1) 2) N))))
(* (pow N 2) (+ 1 (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N))))
(atan2 1 (+ 1 (+ (* -1 (* N (pow (sqrt -1) 2))) (pow N 2))))
(* -1 N)
(* -1 (* N (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) N))) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(* -1 (* (sqrt N) (pow (sqrt -1) 2)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(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)))))
(+ (log -1) (* -1 (log (/ -1 N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (/ 1 N)))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* 1/2 (/ 1 N)) 1) N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 N)) 1/2) N)) 1) N))))
(* -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

4.0ms

-inf

((+ (* (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N)))) 1) (atan2 1 (+ (* (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N)))) 1)) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt N) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (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)) (atan2 1 (+ (* (exp (log (+ 1 N))) N) 1)) (+ (* (exp (log (+ 1 N))) N) 1) (exp (log (+ 1 N))) (log (+ 1 N)) (/ N (+ (+ (* N N) N) 1)) (+ (+ (* N N) N) 1))

2.0ms

((+ (* (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N)))) 1) (atan2 1 (+ (* (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N)))) 1)) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt N) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (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)) (atan2 1 (+ (* (exp (log (+ 1 N))) N) 1)) (+ (* (exp (log (+ 1 N))) N) 1) (exp (log (+ 1 N))) (log (+ 1 N)) (/ N (+ (+ (* N N) N) 1)) (+ (+ (* N N) N) 1))

2.0ms

inf

((+ (* (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N)))) 1) (atan2 1 (+ (* (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N)))) 1)) (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (sqrt N) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (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)) (atan2 1 (+ (* (exp (log (+ 1 N))) N) 1)) (+ (* (exp (log (+ 1 N))) N) 1) (exp (log (+ 1 N))) (log (+ 1 N)) (/ N (+ (+ (* N N) N) 1)) (+ (+ (* N N) N) 1))

simplify302.0ms (5.4%)

Memory

-12.4MiB live, 186.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	218	657
1	672	607
2	2100	588
3	7479	586
0	8500	550

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

Inputs
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(sqrt N)
(+ (sqrt N) (* 1/2 (sqrt (pow N 3))))
(+ (sqrt N) (* (pow N 2) (+ (* -1/8 (sqrt N)) (* 1/2 (sqrt (/ 1 N))))))
(+ (sqrt N) (* (pow N 2) (+ (* 1/2 (sqrt (/ 1 N))) (* (pow N 2) (+ (* -1/8 (sqrt (/ 1 (pow N 3)))) (* 1/16 (sqrt (/ 1 N))))))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(+ 1 (pow N 2))
(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)))
N
(* N (+ 1 (* -1/2 N)))
(* N (+ 1 (* N (- (* 1/3 N) 1/2))))
(* N (+ 1 (* N (- (* N (+ 1/3 (* -1/4 N))) 1/2))))
(* N (+ 1 (* -1 N)))
(* N (+ 1 (* N (- (pow N 2) 1))))
(* N (+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* N (+ 1 (* 1/2 (/ 1 N))))
(* N (- (+ 1 (* 1/2 (/ 1 N))) (/ 1/8 (pow N 2))))
(* N (- (+ 1 (+ (* 1/2 (/ 1 N)) (* 1/16 (/ 1 (pow N 3))))) (/ 1/8 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* -1 (pow N 3))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(* N (+ 1 (/ 1 N)))
(* -1 (log (/ 1 N)))
(+ (* -1 (log (/ 1 N))) (/ 1 N))
(- (+ (* -1 (log (/ 1 N))) (/ 1 N)) (/ 1/2 (pow N 2)))
(- (+ (* -1 (log (/ 1 N))) (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3))))) (/ 1/2 (pow N 2)))
(/ 1 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)
(* (pow N 2) (+ 1 (* -1 (/ (pow (sqrt -1) 2) N))))
(* (pow N 2) (+ 1 (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N))))
(atan2 1 (+ 1 (+ (* -1 (* N (pow (sqrt -1) 2))) (pow N 2))))
(* -1 N)
(* -1 (* N (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) N))) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(* -1 (* (sqrt N) (pow (sqrt -1) 2)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(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)))))
(+ (log -1) (* -1 (log (/ -1 N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (/ 1 N)))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* 1/2 (/ 1 N)) 1) N))))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 N)) 1/2) N)) 1) N))))
(* -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))
(+ 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)))
(sqrt N)
(sqrt.f64 N)
(+ (sqrt N) (* 1/2 (sqrt (pow N 3))))
(fma.f64 (sqrt.f64 (pow.f64 N #s(literal 3 binary64))) #s(literal 1/2 binary64) (sqrt.f64 N))
(+ (sqrt N) (* (pow N 2) (+ (* -1/8 (sqrt N)) (* 1/2 (sqrt (/ 1 N))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 N))) (.f64 N N) (sqrt.f64 N))
(+ (sqrt N) (* (pow N 2) (+ (* 1/2 (sqrt (/ 1 N))) (* (pow N 2) (+ (* -1/8 (sqrt (/ 1 (pow N 3)))) (* 1/16 (sqrt (/ 1 N))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64))) (.f64 N N)) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) (fma.f64 #s(literal 1/16 binary64) (.f64 N N) #s(literal 1/2 binary64)))) (*.f64 N N) (sqrt.f64 N))
(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 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(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 #s(literal -1 binary64) (pow.f64 N #s(literal 3 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 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64))
(fabs (- 1 (pow N 3)))
(fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))))
(+ 1 (* -1 (pow N 3)))
(-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))
N
(* N (+ 1 (* -1/2 N)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) N #s(literal 1 binary64)) N)
(* N (+ 1 (* N (- (* 1/3 N) 1/2))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) N) #s(literal 1/2 binary64)) N #s(literal 1 binary64)) N)
(* N (+ 1 (* N (- (* N (+ 1/3 (* -1/4 N))) 1/2))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) N #s(literal 1/3 binary64)) N) #s(literal 1/2 binary64)) N #s(literal 1 binary64)) N)
(* 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 (fma.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)) (fma.f64 N N #s(literal -1 binary64))) N #s(literal 1 binary64)) N)
(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 (+ 1 (* 1/2 (/ 1 N))))
(-.f64 N #s(literal -1/2 binary64))
(* N (- (+ 1 (* 1/2 (/ 1 N))) (/ 1/8 (pow N 2))))
(+.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 N N))) N))
(* N (- (+ 1 (+ (* 1/2 (/ 1 N)) (* 1/16 (/ 1 (pow N 3))))) (/ 1/8 (pow N 2))))
(fma.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) N) #s(literal -1/2 binary64)) N)) N N)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(* -1 (pow N 3))
(pow.f64 (neg.f64 N) #s(literal 3 binary64))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 N #s(literal 3 binary64)))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* -1 (log (/ 1 N)))
(log.f64 N)
(+ (* -1 (log (/ 1 N))) (/ 1 N))
(-.f64 (log.f64 N) (/.f64 #s(literal -1 binary64) N))
(- (+ (* -1 (log (/ 1 N))) (/ 1 N)) (/ 1/2 (pow N 2)))
(-.f64 (-.f64 (log.f64 N) (/.f64 #s(literal -1 binary64) N)) (/.f64 (/.f64 #s(literal 1/2 binary64) N) N))
(- (+ (* -1 (log (/ 1 N))) (+ (/ 1 N) (* 1/3 (/ 1 (pow N 3))))) (/ 1/2 (pow N 2)))
(+.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) N) #s(literal 1/2 binary64)) N) #s(literal 1 binary64)) N) (log.f64 N))
(/ 1 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 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) N) (*.f64 N N))
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) N)
(+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64)) #s(literal 1 binary64)) N)) N))
(* (pow N 2) (+ 1 (* -1 (/ (pow (sqrt -1) 2) N))))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(atan2 1 (+ 1 (+ (* -1 (* N (pow (sqrt -1) 2))) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(* -1 N)
(neg.f64 N)
(* -1 (* N (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) N)))))
(-.f64 #s(literal -1/2 binary64) N)
(* -1 (* N (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) N) #s(literal 1/8 binary64) #s(literal -1/2 binary64)) N)
(* -1 (* N (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) N))) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(-.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)) N) #s(literal -1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal -1/8 binary64))) N)) N)
(* -1 (* (sqrt N) (pow (sqrt -1) 2)))
(sqrt.f64 N)
(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 (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 (* (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 #s(literal -1 binary64) (pow.f64 N #s(literal 3 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 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64))
(fabs (+ 1 (* -1 (pow N 3))))
(fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64))) (pow.f64 (neg.f64 N) #s(literal 3 binary64)))
(+ (log -1) (* -1 (log (/ -1 N))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) N)))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (/ 1 N)))
(-.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) N))) (/.f64 #s(literal -1 binary64) N))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* 1/2 (/ 1 N)) 1) N))))
(-.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) N) #s(literal 1 binary64)) N)) (log.f64 (/.f64 #s(literal -1 binary64) N)))
(+ (log -1) (+ (* -1 (log (/ -1 N))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 N)) 1/2) N)) 1) N))))
(-.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) N) #s(literal 1/2 binary64)) N) #s(literal -1 binary64) #s(literal -1 binary64)) N)) (log.f64 (/.f64 #s(literal -1 binary64) N)))
(* -1 (/ (- (/ 1 N) 1) N))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) (neg.f64 N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) 1) N)) 1) N))
(/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) N) (*.f64 N N))
(* -1 (/ (- (* -1 (/ (- (/ 1 (pow N 2)) (+ 1 (/ 1 (pow N 3)))) N)) 1) N))
(+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64)) #s(literal 1 binary64)) N)) N))

rewrite135.0ms (2.4%)

Memory

13.4MiB live, 171.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	146
0	55	113
1	243	113
2	1706	113
0	11344	113

Stop Event

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

Counts

19 → 779

Calls

Call 1

Inputs
(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64)))
(hypot.f64 (sqrt.f64 N) N)
(sqrt.f64 N)
(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) (+.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) (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)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64))
(exp.f64 (log1p.f64 N))
(log1p.f64 N)
(/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))

Outputs
(/.f64 (fma.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) (.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal 1 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 N #s(literal 3 binary64)))) (.f64 (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64))) (-.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(/.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
(/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 3 binary64))) (+.f64 (pow.f64 N #s(literal 4 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64)) (.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
(/.f64 (neg.f64 (-.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 (neg.f64 (pow.f64 (-.f64 (fma.f64 N N #s(literal 1 binary64)) N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N 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 (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 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 (pow.f64 (-.f64 (fma.f64 N N #s(literal 1 binary64)) N) #s(literal 2 binary64)) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
(/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)))
(/.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 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64))) (fma.f64 N N (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 N N #s(literal 1 binary64)) N))))
(/.f64 (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64))) (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))))
(fma.f64 (fabs.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (sqrt.f64 N))) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) N)) N #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 N N N) (-.f64 #s(literal 1 binary64) N))) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 N N N) N)) (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64))) N #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 (fma.f64 N N N) #s(literal 3/2 binary64))) (sqrt.f64 (hypot.f64 (sqrt.f64 N) N)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 N N N) (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)))) (sin.f64 (acos.f64 (pow.f64 N #s(literal 3/2 binary64)))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 N N N) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))) (sqrt.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 N #s(literal 3/2 binary64))) (pow.f64 N #s(literal 1/4 binary64)) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (pow.f64 (*.f64 (fma.f64 N N N) (-.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 (fma.f64 N N N) N) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (pow.f64 (fma.f64 N N N) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (hypot.f64 (sqrt.f64 N) N)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64)) #s(literal 1/2 binary64)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (sqrt.f64 N)) #s(literal 1 binary64)) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) N #s(literal 1 binary64))
(fma.f64 (pow.f64 (pow.f64 N #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 N #s(literal 1/4 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) N))
(fma.f64 (pow.f64 (pow.f64 N #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 N #s(literal 1/4 binary64)) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) N (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (sqrt.f64 N)) (sqrt.f64 N) #s(literal 1 binary64))
(fma.f64 (+.f64 N (sqrt.f64 N)) (-.f64 N (sqrt.f64 N)) #s(literal 1 binary64))
(fma.f64 (+.f64 (sqrt.f64 N) N) (-.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(fma.f64 (sin.f64 (acos.f64 (pow.f64 N #s(literal 3/2 binary64)))) (sqrt.f64 (*.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (fma.f64 N N N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 N N N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 N) N)) (sqrt.f64 (pow.f64 (fma.f64 N N N) #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 N) N)) (pow.f64 (pow.f64 (fma.f64 N N N) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) (hypot.f64 N (pow.f64 N #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) (pow.f64 (*.f64 N (fma.f64 N N N)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 N #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 N #s(literal 3/2 binary64))) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (pow.f64 N #s(literal 1/4 binary64)) (pow.f64 (pow.f64 N #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N))
(fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
(fma.f64 (*.f64 N N) #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N))
(fma.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (fabs.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 N N N) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (fabs.f64 (*.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (*.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 N N) (-.f64 #s(literal 1 binary64) N))
(fma.f64 #s(literal 1 binary64) (fma.f64 N N N) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) N (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (fabs.f64 (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (fma.f64 N N N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (fma.f64 N N N)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 1 binary64) N))
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 N (fabs.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 N (fabs.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 N (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 N (*.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (-.f64 N #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))
(fma.f64 N #s(literal 1 binary64) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 N N (-.f64 #s(literal 1 binary64) N))
(-.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 2 binary64)) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (/.f64 (*.f64 N N) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)))
(-.f64 (-.f64 #s(literal 1 binary64) N) (*.f64 N N))
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(fma.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (fabs.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 N N N) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (fabs.f64 (*.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (*.f64 (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 N N) (-.f64 #s(literal 1 binary64) N))
(fma.f64 #s(literal 1 binary64) (fma.f64 N N N) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) N (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) N) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (fabs.f64 (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (fma.f64 N N N))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) (fma.f64 N N N)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 N) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 1 binary64) N))
(fma.f64 (sqrt.f64 N) (sqrt.f64 N) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 N (fabs.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 N (fabs.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 N (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 N (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 N (*.f64 (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (-.f64 N #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 N (-.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))
(fma.f64 N #s(literal 1 binary64) (fma.f64 N N #s(literal 1 binary64)))
(fma.f64 N N (-.f64 #s(literal 1 binary64) N))
(-.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 2 binary64)) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (/.f64 (*.f64 N N) (-.f64 (fma.f64 N N #s(literal 1 binary64)) N)))
(-.f64 (-.f64 #s(literal 1 binary64) N) (*.f64 N N))
(-.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) N)) N))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (/.f64 N (-.f64 (fma.f64 N N #s(literal 1 binary64)) N))))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(-.f64 N (-.f64 (*.f64 N N) #s(literal 1 binary64)))
(+.f64 (fma.f64 N N (cosh.f64 (log1p.f64 N))) (sinh.f64 (log1p.f64 N)))
(+.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))) (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))))
(+.f64 (-.f64 #s(literal 1 binary64) N) (*.f64 N N))
(+.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(+.f64 #s(literal 1 binary64) (fma.f64 N N N))
(+.f64 N (fma.f64 N N #s(literal 1 binary64)))

eval104.0ms (1.8%)

Memory: -12.4MiB live, 219.3MiB allocated
Compiler: Compiled 9 248 to 1 750 computations (81.1% saved)

prune19.0ms (0.3%)

Memory

9.3MiB live, 48.2MiB allocated

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	458	8	466
Fresh	8	6	14
Picked	3	2	5
Done	0	1	1
Total	469	17	486

Accuracy

99.8%

Counts

486 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	92.0%	(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)))
▶	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
▶	96.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	45.7%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) N #s(literal 1 binary64)))
	99.1%	(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 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	91.8%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (fabs.f64 (fma.f64 (sqrt.f64 N) N #s(literal 1 binary64))) (fabs.f64 (-.f64 (pow.f64 N #s(literal 3/2 binary64)) #s(literal 1 binary64)))) (fabs.f64 (/.f64 N (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) #s(literal 1 binary64)))
	91.9%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 N) (fabs.f64 (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64)))
▶	96.7%	(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 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64)))
	92.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fabs.f64 #s(approx (/ N (+ (+ (* N N) N) 1)) (/.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64)))
▶	99.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	75.4%	(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))
	95.9%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
▶	7.9%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
	92.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
✓	6.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 519 to 330 computations (36.4% saved)

simplify160.0ms (2.9%)

Memory

16.6MiB live, 174.9MiB 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 (fma.f64 (-.f64 #s(literal 1 binary64) 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 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 N)
cost-diff	0	(hypot.f64 (sqrt.f64 N) N)
cost-diff	0	(fma.f64 (hypot.f64 (sqrt.f64 N) N) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 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 (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64)))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
cost-diff	0	(pow.f64 N #s(literal 3/2 binary64))
cost-diff	0	(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64))
cost-diff	0	(+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N)
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	225
0	69	214
1	110	214
2	278	214
3	832	214
4	1884	214
5	3677	214
6	7587	214
0	8054	214

Stop Event

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

Calls

Call 1

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

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

localize117.0ms (2.1%)

Memory

-26.5MiB live, 136.3MiB 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	0.265625	(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 (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64)))
accuracy	0.27734375	(/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))
accuracy	0.38119125976844204	(fma.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64))
accuracy	0.0078125	(hypot.f64 (sqrt.f64 N) N)
accuracy	0.046875	(fma.f64 (hypot.f64 (sqrt.f64 N) N) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64))
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64)))
accuracy	2.1450031057617207	#s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 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	0.28125	(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	0.4609375	(fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64))
accuracy	0.0	(-.f64 N #s(literal -1 binary64))
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
accuracy	58.700528589071176	#s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64)))
accuracy	0.00390625	(pow.f64 N #s(literal 3/2 binary64))
accuracy	0.0546875	(+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N)
accuracy	0.28125	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N))
accuracy	0.35384750976844204	(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64))

Samples

69.0ms	253×	0	valid
1.0ms	1×	5	exit
1.0ms	2×	1	valid

Compiler

Compiled 260 to 40 computations (84.6% saved)

Precisions

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

ival-mult: 11.0ms (20.1% of total)

ival-add: 10.0ms (18.3% of total)

ival-pow: 9.0ms (16.5% of total)

ival-atan2: 7.0ms (12.8% of total)

ival-hypot: 5.0ms (9.2% of total)

ival-sub: 5.0ms (9.2% of total)

ival-fabs: 3.0ms (5.5% of total)

ival-sqrt: 2.0ms (3.7% of total)

ival-div: 2.0ms (3.7% of total)

adjust: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series9.0ms (0.2%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

20 → 62

Calls

Call 1

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

Outputs
(atan2 1 (+ 1 (+ N (pow N 2))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (pow N 2))
(sqrt (pow N 3))
(atan2 1 (+ 1 (* N (+ 1 N))))
(sqrt N)
(+ (sqrt N) (* 1/2 (sqrt (pow N 3))))
(+ (sqrt N) (* (pow N 2) (+ (* -1/8 (sqrt N)) (* 1/2 (sqrt (/ 1 N))))))
(+ (sqrt N) (* (pow N 2) (+ (* 1/2 (sqrt (/ 1 N))) (* (pow N 2) (+ (* -1/8 (sqrt (/ 1 (pow N 3)))) (* 1/16 (sqrt (/ 1 N))))))))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- (* N (- 1 N)) 1))))))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- (* N (- 1 N)) 1)))))
(fabs (- 1 (pow N 3)))
(+ 1 (* -1 (pow N 3)))
(* -1 N)
(* N (- (* -1 N) 1))
(* N (- (* N (- (pow N 2) 1)) 1))
(* N (- (* N (- (* (pow N 2) (+ 1 N)) 1)) 1))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
N
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (* 1/2 (/ 1 N))))
(* N (- (+ 1 (* 1/2 (/ 1 N))) (/ 1/8 (pow N 2))))
(* N (- (+ 1 (+ (* 1/2 (/ 1 N)) (* 1/16 (/ 1 (pow N 3))))) (/ 1/8 (pow N 2))))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- N (+ 1 (pow N 2))))))))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- N (+ 1 (pow N 2)))))))
(* -1 (pow N 3))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(/ -1 N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/ (- (/ 1 (pow N 3)) (+ 1 (/ 1 N))) N)
(/ (- (+ (/ 1 (pow N 3)) (/ 1 (pow N 4))) (+ 1 (/ 1 N))) N)
(atan2 1 (- (+ 1 (* (pow N 2) (pow (sqrt -1) 2))) (* -1 N)))
(* (pow N 2) (pow (sqrt -1) 2))
(* (pow N 2) (+ (/ 1 N) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (/ 1 N) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2))))
(* (pow N 2) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2)))
(* (sqrt (pow N 3)) (pow (sqrt -1) 2))
(atan2 1 (+ 1 (* N (- 1 (* -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))) (pow N 2))))
(* (pow N 2) (+ 1 (* -1 (/ (pow (sqrt -1) 2) N))))
(* (pow N 2) (+ 1 (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N))))
(* -1 (* N (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) N))) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(atan2 1 (+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (* N (+ 1 (* -1 N))) 1))))))
(+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (* N (+ 1 (* -1 N))) 1)))))
(fabs (+ 1 (* -1 (pow N 3))))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(* -1 (/ (+ 1 (* -1 (/ (- (/ 1 (pow N 2)) 1) N))) N))
(* -1 (/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow N 2)) (/ 1 (pow N 3))) 1) N))) N))

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify124.0ms (2.2%)

Memory

8.2MiB live, 162.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	202	654
1	604	576
2	2100	552
3	7835	552
0	8037	513

Stop Event

1×	iter limit
1×	node limit

Counts

62 → 61

Calls

Call 1

Inputs
(atan2 1 (+ 1 (+ N (pow N 2))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (pow N 2))
(sqrt (pow N 3))
(atan2 1 (+ 1 (* N (+ 1 N))))
(sqrt N)
(+ (sqrt N) (* 1/2 (sqrt (pow N 3))))
(+ (sqrt N) (* (pow N 2) (+ (* -1/8 (sqrt N)) (* 1/2 (sqrt (/ 1 N))))))
(+ (sqrt N) (* (pow N 2) (+ (* 1/2 (sqrt (/ 1 N))) (* (pow N 2) (+ (* -1/8 (sqrt (/ 1 (pow N 3)))) (* 1/16 (sqrt (/ 1 N))))))))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- (* N (- 1 N)) 1))))))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- (* N (- 1 N)) 1)))))
(fabs (- 1 (pow N 3)))
(+ 1 (* -1 (pow N 3)))
(* -1 N)
(* N (- (* -1 N) 1))
(* N (- (* N (- (pow N 2) 1)) 1))
(* N (- (* N (- (* (pow N 2) (+ 1 N)) 1)) 1))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
N
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (* 1/2 (/ 1 N))))
(* N (- (+ 1 (* 1/2 (/ 1 N))) (/ 1/8 (pow N 2))))
(* N (- (+ 1 (+ (* 1/2 (/ 1 N)) (* 1/16 (/ 1 (pow N 3))))) (/ 1/8 (pow N 2))))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- N (+ 1 (pow N 2))))))))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- N (+ 1 (pow N 2)))))))
(* -1 (pow N 3))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(/ -1 N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/ (- (/ 1 (pow N 3)) (+ 1 (/ 1 N))) N)
(/ (- (+ (/ 1 (pow N 3)) (/ 1 (pow N 4))) (+ 1 (/ 1 N))) N)
(atan2 1 (- (+ 1 (* (pow N 2) (pow (sqrt -1) 2))) (* -1 N)))
(* (pow N 2) (pow (sqrt -1) 2))
(* (pow N 2) (+ (/ 1 N) (pow (sqrt -1) 2)))
(* (pow N 2) (+ (/ 1 N) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2))))
(* (pow N 2) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2)))
(* (sqrt (pow N 3)) (pow (sqrt -1) 2))
(atan2 1 (+ 1 (* N (- 1 (* -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))) (pow N 2))))
(* (pow N 2) (+ 1 (* -1 (/ (pow (sqrt -1) 2) N))))
(* (pow N 2) (+ 1 (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N))))
(* -1 (* N (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(* -1 (* N (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) N))) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(atan2 1 (+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (* N (+ 1 (* -1 N))) 1))))))
(+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (* N (+ 1 (* -1 N))) 1)))))
(fabs (+ 1 (* -1 (pow N 3))))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(* -1 (/ (+ 1 (* -1 (/ (- (/ 1 (pow N 2)) 1) N))) N))
(* -1 (/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow N 2)) (/ 1 (pow N 3))) 1) N))) 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))
(sqrt (pow N 3))
(sqrt.f64 (pow.f64 N #s(literal 3 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)
(+ (sqrt N) (* 1/2 (sqrt (pow N 3))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 N #s(literal 3 binary64))) (sqrt.f64 N))
(+ (sqrt N) (* (pow N 2) (+ (* -1/8 (sqrt N)) (* 1/2 (sqrt (/ 1 N))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 N))) (.f64 N N) (sqrt.f64 N))
(+ (sqrt N) (* (pow N 2) (+ (* 1/2 (sqrt (/ 1 N))) (* (pow N 2) (+ (* -1/8 (sqrt (/ 1 (pow N 3)))) (* 1/16 (sqrt (/ 1 N))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 N N)) (sqrt.f64 (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) N)) (fma.f64 #s(literal 1/16 binary64) (.f64 N N) #s(literal 1/2 binary64)))) (*.f64 N N) (sqrt.f64 N))
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- (* N (- 1 N)) 1))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) (fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64)))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- (* N (- 1 N)) 1)))))
(fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) (fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64))
(fabs (- 1 (pow N 3)))
(fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))))
(+ 1 (* -1 (pow N 3)))
(-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))
(* -1 N)
(neg.f64 N)
(* N (- (* -1 N) 1))
(*.f64 N (-.f64 #s(literal -1 binary64) N))
(* N (- (* N (- (pow N 2) 1)) 1))
(.f64 (-.f64 (.f64 (fma.f64 N N #s(literal -1 binary64)) N) #s(literal 1 binary64)) N)
(* N (- (* N (- (* (pow N 2) (+ 1 N)) 1)) 1))
(.f64 (-.f64 (.f64 (fma.f64 N N (-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))) N) #s(literal 1 binary64)) N)
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (* 1/2 (/ 1 N))))
(-.f64 N #s(literal -1/2 binary64))
(* N (- (+ 1 (* 1/2 (/ 1 N))) (/ 1/8 (pow N 2))))
(+.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 N N))) N))
(* N (- (+ 1 (+ (* 1/2 (/ 1 N)) (* 1/16 (/ 1 (pow N 3))))) (/ 1/8 (pow N 2))))
(fma.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 N #s(literal 3 binary64))) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) N)) N)) N N)
(atan2 1 (+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- N (+ 1 (pow N 2))))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) (fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64)))
(+ 1 (* (fabs (- 1 (pow N 3))) (fabs (/ N (- N (+ 1 (pow N 2)))))))
(fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) (fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64))
(* -1 (pow N 3))
(pow.f64 (neg.f64 N) #s(literal 3 binary64))
(* (pow N 3) (- (/ 1 (pow N 3)) 1))
(*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 N #s(literal 3 binary64)))
(/ -1 N)
(/.f64 #s(literal -1 binary64) N)
(* -1 (/ (+ 1 (/ 1 N)) N))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) N)) N)
(/ (- (/ 1 (pow N 3)) (+ 1 (/ 1 N))) N)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(/ (- (+ (/ 1 (pow N 3)) (/ 1 (pow N 4))) (+ 1 (/ 1 N))) N)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(atan2 1 (- (+ 1 (* (pow N 2) (pow (sqrt -1) 2))) (* -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 N) (pow (sqrt -1) 2)))
(*.f64 (-.f64 #s(literal 1 binary64) N) N)
(* (pow N 2) (+ (/ 1 N) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2))))
(fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
(* (pow N 2) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2)))
(fma.f64 (neg.f64 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))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(* -1 (* 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))) (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) (+ 1 (* -1 (/ (pow (sqrt -1) 2) N))))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (* -1 (/ (- (pow (sqrt -1) 2) (/ 1 N)) N))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* -1 (* N (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) N)))))
(-.f64 #s(literal -1/2 binary64) N)
(* -1 (* N (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) N) #s(literal 1/8 binary64) #s(literal -1/2 binary64)) N)
(* -1 (* N (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) N))) N)) (* 1/2 (pow (sqrt -1) 2))) N)))))
(-.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)) N) #s(literal -1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal -1/8 binary64))) N)) N)
(atan2 1 (+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (* N (+ 1 (* -1 N))) 1))))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) (fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64)))
(+ 1 (* (fabs (+ 1 (* -1 (pow N 3)))) (fabs (/ N (- (* N (+ 1 (* -1 N))) 1)))))
(fma.f64 (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) (fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) #s(literal 1 binary64))
(fabs (+ 1 (* -1 (pow N 3))))
(fabs.f64 (+.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64))))
(* -1 (* (pow N 3) (- 1 (/ 1 (pow N 3)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal 3 binary64))) (pow.f64 (neg.f64 N) #s(literal 3 binary64)))
(* -1 (/ (+ 1 (* -1 (/ (- (/ 1 (pow N 2)) 1) N))) N))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)
(* -1 (/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow N 2)) (/ 1 (pow N 3))) 1) N))) N))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) N) N) #s(literal 1 binary64)) N) #s(literal 1 binary64)) N)

rewrite206.0ms (3.7%)

Memory

-2.5MiB live, 243.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	182
0	69	176
1	270	162
2	2007	158
0	10024	157

Stop Event

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

Counts

20 → 807

Calls

Call 1

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

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (fma.f64 N N N)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (neg.f64 (fma.f64 N N N)) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 N N N)) #s(literal 1 binary64))) (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (fma.f64 N N N)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (.f64 (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))))) (.f64 (/.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 N #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))) (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))) (-.f64 (.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64))) (.f64 (/.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))) (pow.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal -1 binary64))))))
(/.f64 (+.f64 (pow.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 6 binary64))) (+.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 (pow.f64 N #s(literal 4 binary64)) (.f64 (-.f64 N #s(literal -1 binary64)) (.f64 N N)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) (fma.f64 N N #s(literal 1 binary64)))) (neg.f64 (-.f64 (*.f64 N N) (-.f64 N #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 N (fma.f64 N N #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) (pow.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) (-.f64 (fma.f64 N N #s(literal 1 binary64)) (.f64 (.f64 N N) (-.f64 N #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))))
(/.f64 (neg.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 (neg.f64 (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)))))
(/.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 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))) (.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)) (*.f64 N N))) (pow.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.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))) (*.f64 (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(/.f64 (pow.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 N #s(literal 3 binary64)))) (.f64 (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) (.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) #s(literal 1 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N)) (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))))
(/.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 N (fma.f64 N N #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 N #s(literal 4 binary64)) (fma.f64 N N #s(literal 1 binary64))) (-.f64 (*.f64 N N) (-.f64 N #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 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64))) (fma.f64 N N (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 N N #s(literal 1 binary64)) N))))
(/.f64 (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64))) (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 N #s(literal 6 binary64)) (pow.f64 (-.f64 N #s(literal -1 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 N #s(literal 4 binary64)) (-.f64 (fma.f64 N N #s(literal 1 binary64)) (.f64 (.f64 N N) (-.f64 N #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N))))
(/.f64 (neg.f64 (pow.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)) #s(literal 2 binary64))) (neg.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))))
(/.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 (fma.f64 N N #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 N #s(literal 3 binary64)))) (neg.f64 (fma.f64 N N (-.f64 (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 N N #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 (fma.f64 N (-.f64 N (fma.f64 N N #s(literal 1 binary64))) (pow.f64 (fma.f64 N N #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.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 (neg.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (fma.f64 N N N)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 N N N))))
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eval146.0ms (2.6%)

Memory: -15.2MiB live, 137.9MiB allocated
Compiler: Compiled 18 028 to 2 622 computations (85.5% saved)

prune98.0ms (1.7%)

Memory

-6.1MiB live, 67.6MiB allocated

Pruning

17 alts after pruning (11 fresh and 6 done)

	Pruned	Kept	Total
New	658	8	666
Fresh	6	3	9
Picked	2	3	5
Done	0	3	3
Total	666	17	683

Accuracy

99.8%

Counts

683 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (*.f64 N N) N #s(literal 1 binary64)) (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64)))
✓	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 N) (sqrt.f64 N) #s(literal 1 binary64)) N #s(literal 1 binary64)))
	99.1%	(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)))
	92.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (sqrt.f64 (.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (sqrt.f64 (-.f64 N #s(literal -1 binary64)))) #s(approx (sqrt (+ ( (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 N (+.f64 (sqrt.f64 N) #s(literal 1 binary64))) (/.f64 (-.f64 (*.f64 N N) #s(literal 1 binary64)) (-.f64 (sqrt.f64 N) #s(literal 1 binary64))) #s(literal 1 binary64)))
	99.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64)))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
	92.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fabs.f64 #s(approx (/ N (+ (+ (* N N) N) 1)) (/.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64)))
	96.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	99.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N))
	99.1%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 (sqrt.f64 N) N) (sqrt.f64 N) #s(literal 1 binary64)) N))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	75.4%	(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))
	95.9%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (fma.f64 N N N)))
	92.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (*.f64 N N)))
✓	7.9%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
✓	6.4%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 949 to 364 computations (61.6% saved)

regimes20.0ms (0.4%)

Memory

24.4MiB live, 24.4MiB allocated

Counts

37 → 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 (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (fma.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) (fma.f64 #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #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) (+.f64 (fma.f64 (*.f64 (sqrt.f64 N) N) (sqrt.f64 N) #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 N) (fabs.f64 (*.f64 (sqrt.f64 N) (-.f64 #s(literal 1 binary64) 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 (fma.f64 (*.f64 N N) N #s(literal 1 binary64)) (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (sqrt.f64 (.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (sqrt.f64 (-.f64 N #s(literal -1 binary64)))) #s(approx (sqrt (+ ( (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 N (+.f64 (sqrt.f64 N) #s(literal 1 binary64))) (/.f64 (-.f64 (*.f64 N N) #s(literal 1 binary64)) (-.f64 (sqrt.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) (+.f64 (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (sqrt.f64 N) #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) #s(approx (sqrt (+ (* (sqrt N) (sqrt N)) (* N N))) (-.f64 N #s(literal -1/2 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 #s(approx (/ N (+ (+ (* N N) N) 1)) (/.f64 #s(literal 1 binary64) 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) (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 N N N) #s(literal 1 binary64))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) N) N #s(literal -1 binary64)))) #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 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64)))) (fabs.f64 (/.f64 N (fma.f64 (-.f64 #s(literal 1 binary64) 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 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (*.f64 (fma.f64 N N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))) 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) (fma.f64 (*.f64 (fabs.f64 (fma.f64 (sqrt.f64 N) N #s(literal 1 binary64))) (fabs.f64 (-.f64 (pow.f64 N #s(literal 3/2 binary64)) #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 (exp.f64 (log1p.f64 N)) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (hypot.f64 (sqrt.f64 N) N) (hypot.f64 (sqrt.f64 N) 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 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fabs.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 3 binary64))))) (fabs.f64 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (*.f64 (/.f64 (-.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))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (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))) N #s(literal 1 binary64)))

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

Calls

2 calls:

10.0ms	N
8.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB 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 (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`N`
99.5%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes28.0ms (0.5%)

Memory

-37.1MiB live, 12.0MiB 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 (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (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:

25.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
3.0ms	N

Results

Accuracy	Segments	Branch
95.9%	1	`N`
95.9%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

4 → 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 (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (+ (* (pow N 3/2) (sqrt N)) 1) N) (*.f64 N N)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
92.5%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
92.5%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Counts

2 → 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))))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #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
7.9%	1	`N`
7.9%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB 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
6.4%	1	`N`
6.4%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify30.0ms (0.5%)

Memory

-17.7MiB live, 20.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness875.0ms (15.6%)

Memory

-2.7MiB live, 402.0MiB 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	6	16
0	10	16
1	43	16
2	266	16
3	2561	16
0	9660	16
0	25	61
1	71	57
2	192	57
3	676	57
4	3357	57
0	8117	51

Stop Event

1×	fuel
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 192 to 96 computations (50% saved)

preprocess57.0ms (1%)

Memory: -4.3MiB live, 74.4MiB allocated
Compiler: Compiled 164 to 70 computations (57.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze2.0ms (0%)

sample2.0s (36.2%)

explain134.0ms (2.4%)

preprocess16.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize62.0ms (1.1%)

series1.0ms (0%)

simplify6.0ms (0.1%)

rewrite200.0ms (3.6%)

eval16.0ms (0.3%)

prune3.0ms (0.1%)

simplify38.0ms (0.7%)

localize23.0ms (0.4%)

series1.0ms (0%)

simplify109.0ms (1.9%)

rewrite155.0ms (2.8%)

eval44.0ms (0.8%)

prune18.0ms (0.3%)

simplify165.0ms (2.9%)

localize124.0ms (2.2%)

series10.0ms (0.2%)

simplify302.0ms (5.4%)

rewrite135.0ms (2.4%)

eval104.0ms (1.8%)

prune19.0ms (0.3%)

simplify160.0ms (2.9%)

localize117.0ms (2.1%)

series9.0ms (0.2%)

simplify124.0ms (2.2%)

rewrite206.0ms (3.7%)

eval146.0ms (2.6%)

prune98.0ms (1.7%)

regimes20.0ms (0.4%)

regimes5.0ms (0.1%)

regimes28.0ms (0.5%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

simplify30.0ms (0.5%)

soundness875.0ms (15.6%)

preprocess57.0ms (1%)

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