Metrics for arccos

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze4.0ms (0.1%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
33.3%	25%	50%	0%	0%	25%	0%	4
60%	37.5%	25%	0%	0%	37.5%	0%	5
77.8%	43.7%	12.5%	0%	0%	43.7%	0%	6
88.2%	46.9%	6.2%	0%	0%	46.9%	0%	7
93.9%	48.4%	3.1%	0%	0%	48.4%	0%	8
96.9%	49.2%	1.6%	0%	0%	49.2%	0%	9
98.4%	49.6%	0.8%	0%	0%	49.6%	0%	10
99.2%	49.8%	0.4%	0%	0%	49.8%	0%	11
99.6%	49.9%	0.2%	0%	0%	49.9%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample660.0ms (21.6%)

Memory

13.0MiB live, 231.6MiB allocated

Samples

446.0ms	8 256×	0	valid
1.0ms	16×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 310.0ms

ival-atan: 65.0ms (20.9% of total)

ival-sqrt: 52.0ms (16.8% of total)

ival-mult: 48.0ms (15.5% of total)

ival-sub: 48.0ms (15.5% of total)

ival-div: 46.0ms (14.8% of total)

ival-add: 38.0ms (12.2% of total)

exact: 6.0ms (1.9% of total)

ival-true: 5.0ms (1.6% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

explain77.0ms (2.5%)

Memory

-4.3MiB live, 50.5MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
-	-	`#s(literal 1 binary64)`
-	-	`(-.f64 #s(literal 1 binary64) x)`
-	-	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
-	-	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
-	-	`(+.f64 #s(literal 1 binary64) x)`
-	-	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
-	-	`#s(literal 2 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Total Time

17.80078125

Average Time

0.0695343017578125

Samples

32.0ms

512×

valid

Compiler

Compiled 147 to 40 computations (72.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-atan: 5.0ms (24.7% of total)

ival-div: 3.0ms (14.8% of total)

ival-add: 3.0ms (14.8% of total)

ival-mult: 3.0ms (14.8% of total)

ival-sub: 3.0ms (14.8% of total)

ival-sqrt: 3.0ms (14.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess27.0ms (0.9%)

Memory

-1.6MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Stop Event

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

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Outputs

(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))

Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify11.0ms (0.4%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))

localize24.0ms (0.8%)

Memory

1.9MiB live, 9.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
accuracy	0.01171875	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy	0.015625	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy	0.02734375	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Samples

16.0ms

256×

valid

Compiler

Compiled 90 to 20 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-atan: 2.0ms (21% of total)

ival-sqrt: 2.0ms (21% of total)

ival-div: 1.0ms (10.5% of total)

ival-add: 1.0ms (10.5% of total)

ival-mult: 1.0ms (10.5% of total)

ival-sub: 1.0ms (10.5% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated

Counts

4 → 23

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))
1.0ms	x	@	inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))
1.0ms	x	@	0	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))

Time

Variable

Point

Expression

1.0ms

-inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))

1.0ms

inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))

1.0ms

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))

simplify104.0ms (3.4%)

Memory

0.2MiB live, 29.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	323
1	276	262
2	764	248
3	2111	236
4	6140	230
0	8112	219

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 23

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)

Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* 2 x) 2)))
(fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x)) (/.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x))

rewrite84.0ms (2.8%)

Memory

2.5MiB live, 26.0MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	15	34
1	52	34
2	339	34
3	4589	8
0	9824	8

Stop Event

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

Counts

4 → 7

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(neg.f64 (atan.f64 (/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(neg.f64 (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)

eval3.0ms (0.1%)

Memory: -5.7MiB live, 2.0MiB allocated
Compiler: Compiled 424 to 136 computations (67.9% saved)

prune2.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Accuracy

100.0%

Counts

25 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 71 to 58 computations (18.3% saved)

simplify94.0ms (3.1%)

Memory

0.5MiB live, 8.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(atan.f64 #s(literal 1 binary64))
cost-diff	0	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	210
0	46	210
1	68	210
2	92	210
3	181	210
4	345	210
5	613	210
6	1149	210
7	2060	210
8	2506	210
9	2667	210
10	2740	210
11	2839	210
12	2885	210
13	2885	210
0	2885	210

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)

localize58.0ms (1.9%)

Memory

-2.9MiB live, 22.8MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy	0	(atan.f64 #s(literal 1 binary64))
accuracy	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy	0.19360019752224977	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy	0.24163708810170448	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy	0.5133264709473986	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))

Samples

44.0ms

256×

valid

Compiler

Compiled 362 to 54 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 9.0ms (29% of total)

ival-sqrt: 9.0ms (29% of total)

ival-add: 6.0ms (19.3% of total)

ival-atan: 3.0ms (9.7% of total)

ival-div: 1.0ms (3.2% of total)

ival-sub: 1.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Counts

16 → 38

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))

Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-1
(- (* 1/2 x) 1)
1/2
(+ 1/2 (* -1/2 x))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (- 1/2 (/ 1 x)))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 1) (* (atan 1) 2) (atan 1) (+ (* 1/2 x) -1) (+ (* -1/2 x) 1/2))
1.0ms	x	@	-inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 1) (* (atan 1) 2) (atan 1) (+ (* 1/2 x) -1) (+ (* -1/2 x) 1/2))
1.0ms	x	@	0	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 1) (* (atan 1) 2) (atan 1) (+ (* 1/2 x) -1) (+ (* -1/2 x) 1/2))

Time

Variable

Point

Expression

2.0ms

inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 1) (* (atan 1) 2) (atan 1) (+ (* 1/2 x) -1) (+ (* -1/2 x) 1/2))

1.0ms

-inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 1) (* (atan 1) 2) (atan 1) (+ (* 1/2 x) -1) (+ (* -1/2 x) 1/2))

1.0ms

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 1) (* (atan 1) 2) (atan 1) (+ (* 1/2 x) -1) (+ (* -1/2 x) 1/2))

simplify140.0ms (4.6%)

Memory

-0.1MiB live, 37.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	391
1	338	326
2	1115	318
3	3741	306
4	7777	306
0	8155	275

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 38

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-1
(- (* 1/2 x) 1)
1/2
(+ 1/2 (* -1/2 x))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (- 1/2 (/ 1 x)))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))

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

rewrite124.0ms (4%)

Memory

2.6MiB live, 44.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	187
0	46	187
1	151	187
2	1041	187
0	8475	187

Stop Event

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

Counts

16 → 255

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))

Outputs
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) (+.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (.f64 x x) x) #s(literal 2 binary64)))) (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (.f64 x x) x) #s(literal 3 binary64)))) (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (-.f64 (.f64 x x) x) #s(literal 2 binary64)) (-.f64 (.f64 x x) x)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(neg.f64 (+.f64 #s(literal -1 binary64) x))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x) (neg.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))))
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(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/4 binary64))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x #s(literal 1/4 binary64)) x (.f64 x #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x #s(literal 1/4 binary64)) x (.f64 x #s(literal 1/4 binary64)))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))

eval39.0ms (1.3%)

Memory: -0.8MiB live, 29.6MiB allocated
Compiler: Compiled 9 311 to 1 663 computations (82.1% saved)

prune6.0ms (0.2%)

Memory

3.9MiB live, 11.6MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	275	3	278
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	275	8	283

Accuracy

100.0%

Counts

283 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
▶	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
✓	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))))

Compiler

Compiled 155 to 113 computations (27.1% saved)

simplify127.0ms (4.1%)

Memory

-13.6MiB live, 34.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
cost-diff	128	(-.f64 (neg.f64 x) #s(literal 1 binary64))
cost-diff	1088	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
cost-diff	8064	(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))))
cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))))
cost-diff	128	(-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))
cost-diff	8384	(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	390
0	54	402
1	91	386
2	160	381
3	514	380
4	2189	272
5	4589	272
0	8319	263

Stop Event

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

Calls

Call 1

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

Outputs
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)))
#s(literal 1 binary64)
(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))
(/.f64 #s(literal -1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) x)
(neg.f64 x)
#s(literal 1 binary64)

localize64.0ms (2.1%)

Memory

4.7MiB live, 29.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
accuracy	0.0234375	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
accuracy	0.5133264709473986	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
accuracy	0.01953125	(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
accuracy	0.03515625	(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
accuracy	0.24163708810170448	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
accuracy	0.03515625	(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
accuracy	0.24163708810170448	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))

Samples

45.0ms

256×

valid

Compiler

Compiled 648 to 62 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-div: 7.0ms (22.4% of total)

ival-mult: 7.0ms (22.4% of total)

ival-sub: 6.0ms (19.2% of total)

ival-add: 4.0ms (12.8% of total)

ival-atan: 2.0ms (6.4% of total)

ival-sqrt: 2.0ms (6.4% of total)

ival-pow2: 2.0ms (6.4% of total)

ival-neg: 1.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory

-3.7MiB live, 3.5MiB allocated

Counts

18 → 44

Calls

Call 1

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

Outputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 x)
(+ 1 (* x (+ 1 (* -1/2 x))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-1
(- (* -1 x) 1)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 1/4 x) 1))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(+ 1 (* x (- (* 3/2 x) 1)))
(+ 1 (* x (- (* x (+ 3/2 (* -2 x))) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (+ (/ 1 x) (/ 1 (pow x 2))) 1/2))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* x (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 x))))
(* 1/4 (pow x 4))
(* (pow x 4) (- 1/4 (/ 1 x)))
(* (pow x 4) (- (+ 1/4 (/ 1 (pow x 2))) (/ 1 x)))
(/ -2 (pow x 2))
(* -1 (/ (+ 2 (* 4 (/ 1 x))) (pow x 2)))
(/ (- (* -1 (/ (+ 4 (* 12 (/ 1 x))) x)) 2) (pow x 2))
(/ (- (* -1 (/ (+ 12 (* 32 (/ 1 x))) (pow x 2))) (+ 2 (* 4 (/ 1 x)))) (pow x 2))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(/ (- (* -1 (/ (+ 4 (+ (* 12 (/ 1 x)) (/ 32 (pow x 2)))) x)) 2) (pow x 2))

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

((* (- 1 (pow (* (+ (* 1/2 x) -1) x) 2)) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x)))) (- 1 (* (+ (* 1/2 x) -1) x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (/ (- (pow (* (+ (* 1/2 x) -1) x) 2) 1) (+ (* (+ (* 1/2 x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (pow (* (+ (* 1/2 x) -1) x) 2) (* (+ (* 1/2 x) -1) x) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x))) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))

2.0ms

-inf

((* (- 1 (pow (* (+ (* 1/2 x) -1) x) 2)) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x)))) (- 1 (* (+ (* 1/2 x) -1) x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (/ (- (pow (* (+ (* 1/2 x) -1) x) 2) 1) (+ (* (+ (* 1/2 x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (pow (* (+ (* 1/2 x) -1) x) 2) (* (+ (* 1/2 x) -1) x) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x))) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))

2.0ms

((* (- 1 (pow (* (+ (* 1/2 x) -1) x) 2)) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x)))) (- 1 (* (+ (* 1/2 x) -1) x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (/ (- (pow (* (+ (* 1/2 x) -1) x) 2) 1) (+ (* (+ (* 1/2 x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (pow (* (+ (* 1/2 x) -1) x) 2) (* (+ (* 1/2 x) -1) x) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x))) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))

simplify94.0ms (3.1%)

Memory

7.1MiB live, 28.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	481
1	422	420
2	1199	402
3	3906	392
0	8236	369

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

Inputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 x)
(+ 1 (* x (+ 1 (* -1/2 x))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-1
(- (* -1 x) 1)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 1/4 x) 1))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(+ 1 (* x (- (* 3/2 x) 1)))
(+ 1 (* x (- (* x (+ 3/2 (* -2 x))) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (+ (/ 1 x) (/ 1 (pow x 2))) 1/2))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* x (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 x))))
(* 1/4 (pow x 4))
(* (pow x 4) (- 1/4 (/ 1 x)))
(* (pow x 4) (- (+ 1/4 (/ 1 (pow x 2))) (/ 1 x)))
(/ -2 (pow x 2))
(* -1 (/ (+ 2 (* 4 (/ 1 x))) (pow x 2)))
(/ (- (* -1 (/ (+ 4 (* 12 (/ 1 x))) x)) 2) (pow x 2))
(/ (- (* -1 (/ (+ 12 (* 32 (/ 1 x))) (pow x 2))) (+ 2 (* 4 (/ 1 x)))) (pow x 2))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(/ (- (* -1 (/ (+ 4 (+ (* 12 (/ 1 x)) (/ 32 (pow x 2)))) x)) 2) (pow x 2))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* -1/2 x))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) x) x) x)
(* (pow x 2) (+ 1 (* x (- (* 1/4 x) 1))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) x) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 x) 1))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(+ 1 (* x (- (* 3/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 3/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/2 (* -2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 3/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 x) 1/2))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (- (+ (/ 1 x) (/ 1 (pow x 2))) 1/2))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x)))
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* 1/4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(* (pow x 4) (- 1/4 (/ 1 x)))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/4 (/ 1 (pow x 2))) (/ 1 x)))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (pow.f64 x #s(literal 4 binary64)))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(* -1 (/ (+ 2 (* 4 (/ 1 x))) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) x)) x) x)
(/ (- (* -1 (/ (+ 4 (* 12 (/ 1 x))) x)) 2) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 12 binary64) x) #s(literal 4 binary64)) x)) x) x)
(/ (- (* -1 (/ (+ 12 (* 32 (/ 1 x))) (pow x 2))) (+ 2 (* 4 (/ 1 x)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) x)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 12 binary64)) x) x)) (*.f64 x x))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* (pow x 4) (+ 1/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* -1 (/ (+ 4 (+ (* 12 (/ 1 x)) (/ 32 (pow x 2)))) x)) 2) (pow x 2))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 12 binary64)) x) #s(literal 4 binary64)) x)) (*.f64 x x))

rewrite166.0ms (5.4%)

Memory

-7.2MiB live, 69.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	323
0	54	297
1	212	206
2	1652	142
0	9338	133

Stop Event

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

Counts

18 → 1 174

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)))) (fma.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (pow.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64))) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)))) (pow.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64)))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -3 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -2 binary64)) (/.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)))))))
(.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))))))
(.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))))
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(/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
(neg.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))) (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 (/.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log1p.f64 (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(/.f64 (*.f64 (neg.f64 x) x) x)
(/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 x x) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (pow.f64 x #s(literal 3 binary64))))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 x x) x))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (neg.f64 x))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))

eval104.0ms (3.4%)

Memory: 5.7MiB live, 88.0MiB allocated
Compiler: Compiled 32 881 to 4 640 computations (85.9% saved)

prune13.0ms (0.4%)

Memory

-5.8MiB live, 30.9MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	824	4	828
Fresh	0	0	0
Picked	3	0	3
Done	0	5	5
Total	827	9	836

Accuracy

100.0%

Counts

836 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
▶	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))))
▶	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
✓	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))))

Compiler

Compiled 187 to 142 computations (24.1% saved)

simplify120.0ms (3.9%)

Memory

6.6MiB live, 29.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
cost-diff	1088	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
cost-diff	0	(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64)))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))))
cost-diff	0	(/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))))
cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))))
cost-diff	128	(-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))
cost-diff	320	(.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	518
0	65	530
1	104	509
2	168	509
3	417	508
4	1052	480
5	2570	480
6	5690	480
0	8033	479

Stop Event

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

Calls

Call 1

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

Outputs
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))))
(.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)))
#s(literal 1 binary64)
#s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))
(*.f64 x x)
x
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))
(/.f64 #s(literal -1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64))
#s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (- (neg x) 1) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 #s(literal -1 binary64) x)

localize70.0ms (2.3%)

Memory

0.7MiB live, 32.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
accuracy	0.0234375	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
accuracy	0.5133264709473986	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64)))))
accuracy	0.0234375	(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64)))
accuracy	0.5133264709473986	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))
accuracy	1.3570611539816055	#s(approx (- (neg x) 1) #s(literal -1 binary64))
accuracy	0.01171875	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
accuracy	0.01953125	(/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
accuracy	0.24163708810170448	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
accuracy	1.356688629159276	#s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
accuracy	0.24163708810170448	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)))))
accuracy	1.356688629159276	#s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x))

Samples

47.0ms

256×

valid

Compiler

Compiled 832 to 78 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-div: 7.0ms (22% of total)

ival-mult: 7.0ms (22% of total)

ival-sub: 7.0ms (22% of total)

ival-add: 4.0ms (12.6% of total)

ival-atan: 2.0ms (6.3% of total)

ival-sqrt: 2.0ms (6.3% of total)

ival-pow2: 2.0ms (6.3% of total)

ival-neg: 1.0ms (3.1% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

-4.3MiB live, 3.1MiB allocated

Counts

21 → 44

Calls

Call 1

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

Outputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 x)
(+ 1 (* x (+ 1 (* -1/2 x))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 1/4 x) 1))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(+ 1 (* x (- (* 3/2 x) 1)))
(+ 1 (* x (- (* x (+ 3/2 (* -2 x))) 1)))
-1
(- (* -1 x) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (+ (/ 1 x) (/ 1 (pow x 2))) 1/2))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* x (- (/ 1 x) 1))
(* 1/4 (pow x 4))
(* (pow x 4) (- 1/4 (/ 1 x)))
(* (pow x 4) (- (+ 1/4 (/ 1 (pow x 2))) (/ 1 x)))
(/ -2 (pow x 2))
(* -1 (/ (+ 2 (* 4 (/ 1 x))) (pow x 2)))
(/ (- (* -1 (/ (+ 4 (* 12 (/ 1 x))) x)) 2) (pow x 2))
(/ (- (* -1 (/ (+ 12 (* 32 (/ 1 x))) (pow x 2))) (+ 2 (* 4 (/ 1 x)))) (pow x 2))
(* -1 (* x (+ 1 (/ 1 x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(/ (- (* -1 (/ (+ 4 (+ (* 12 (/ 1 x)) (/ 32 (pow x 2)))) x)) 2) (pow x 2))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

((* (- 1 (pow (* (+ (* 1/2 x) -1) x) 2)) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x)))) (- 1 (* (+ (* 1/2 x) -1) x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- (pow (* (+ (* 1/2 x) -1) x) 2) 1) (+ (* (+ (* 1/2 x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (/ (+ (* x x) -1) (- -1 x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (pow (* (+ (* 1/2 x) -1) x) 2) (sqrt (/ (- 1 x) (+ 1 x))) (* (+ (* 1/2 x) -1) x) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x))) (- (neg x) 1))

1.0ms

inf

((* (- 1 (pow (* (+ (* 1/2 x) -1) x) 2)) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x)))) (- 1 (* (+ (* 1/2 x) -1) x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- (pow (* (+ (* 1/2 x) -1) x) 2) 1) (+ (* (+ (* 1/2 x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (/ (+ (* x x) -1) (- -1 x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (pow (* (+ (* 1/2 x) -1) x) 2) (sqrt (/ (- 1 x) (+ 1 x))) (* (+ (* 1/2 x) -1) x) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x))) (- (neg x) 1))

1.0ms

-inf

((* (- 1 (pow (* (+ (* 1/2 x) -1) x) 2)) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x)))) (- 1 (* (+ (* 1/2 x) -1) x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- (pow (* (+ (* 1/2 x) -1) x) 2) 1) (+ (* (+ (* 1/2 x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (/ (+ (* x x) -1) (- -1 x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (pow (* (+ (* 1/2 x) -1) x) 2) (sqrt (/ (- 1 x) (+ 1 x))) (* (+ (* 1/2 x) -1) x) (/ 1 (- 1 (* (+ (* 1/2 x) -1) x))) (- (neg x) 1))

simplify99.0ms (3.2%)

Memory

4.5MiB live, 28.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	481
1	422	420
2	1199	402
3	3904	392
0	8262	369

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

Inputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 x)
(+ 1 (* x (+ 1 (* -1/2 x))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 1/4 x) 1))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(+ 1 (* x (- (* 3/2 x) 1)))
(+ 1 (* x (- (* x (+ 3/2 (* -2 x))) 1)))
-1
(- (* -1 x) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (+ (/ 1 x) (/ 1 (pow x 2))) 1/2))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* x (- (/ 1 x) 1))
(* 1/4 (pow x 4))
(* (pow x 4) (- 1/4 (/ 1 x)))
(* (pow x 4) (- (+ 1/4 (/ 1 (pow x 2))) (/ 1 x)))
(/ -2 (pow x 2))
(* -1 (/ (+ 2 (* 4 (/ 1 x))) (pow x 2)))
(/ (- (* -1 (/ (+ 4 (* 12 (/ 1 x))) x)) 2) (pow x 2))
(/ (- (* -1 (/ (+ 12 (* 32 (/ 1 x))) (pow x 2))) (+ 2 (* 4 (/ 1 x)))) (pow x 2))
(* -1 (* x (+ 1 (/ 1 x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 4) (+ 1/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(/ (- (* -1 (/ (+ 4 (+ (* 12 (/ 1 x)) (/ 32 (pow x 2)))) x)) 2) (pow x 2))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* -1/2 x))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) x) x) x)
(* (pow x 2) (+ 1 (* x (- (* 1/4 x) 1))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) x) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 x) 1))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)
(+ 1 (* x (- (* 3/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 3/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/2 (* -2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 3/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 x) 1/2))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (- (+ (/ 1 x) (/ 1 (pow x 2))) 1/2))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x)))
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* 1/4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(* (pow x 4) (- 1/4 (/ 1 x)))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/4 (/ 1 (pow x 2))) (/ 1 x)))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (pow.f64 x #s(literal 4 binary64)))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(* -1 (/ (+ 2 (* 4 (/ 1 x))) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) x)) x) x)
(/ (- (* -1 (/ (+ 4 (* 12 (/ 1 x))) x)) 2) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 12 binary64) x) #s(literal 4 binary64)) x)) x) x)
(/ (- (* -1 (/ (+ 12 (* 32 (/ 1 x))) (pow x 2))) (+ 2 (* 4 (/ 1 x)))) (pow x 2))
(/.f64 (-.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 4 binary64) x)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 12 binary64)) x) x)) (*.f64 x x))
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* (pow x 4) (+ 1/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* -1 (/ (+ 4 (+ (* 12 (/ 1 x)) (/ 32 (pow x 2)))) x)) 2) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 12 binary64)) x) #s(literal 4 binary64)) x)) x) x)

rewrite132.0ms (4.3%)

Memory

-8.3MiB live, 57.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	430
0	65	426
1	240	393
2	1777	393
0	9083	393

Stop Event

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

Counts

21 → 682

Calls

Call 1

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

Outputs
(.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1 binary64)) (+.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64))) (/.f64 (-.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (+.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
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(+.f64 (neg.f64 x) (.f64 (.f64 x #s(literal 1/2 binary64)) x))
(+.f64 (neg.f64 x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log1p.f64 (*.f64 (neg.f64 x) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))) #s(literal -1 binary64))
(pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)))) #s(literal -1 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x)))
(neg.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log1p.f64 (.f64 (neg.f64 x) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))) #s(literal -1 binary64)))
#s(approx (- (neg x) 1) #s(literal -1 binary64))

eval70.0ms (2.3%)

Memory: 7.5MiB live, 58.9MiB allocated
Compiler: Compiled 24 702 to 3 210 computations (87% saved)

prune11.0ms (0.4%)

Memory

-3.2MiB live, 22.6MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	542	1	543
Fresh	0	0	0
Picked	1	3	4
Done	0	5	5
Total	543	9	552

Accuracy

100.0%

Counts

552 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
✓	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))))
✓	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow ( (+ (* 1/2 x) -1) x) 2) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
✓	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (.f64 (-.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* 1/2 x) -1) x) 2) (.f64 x x))) #s(approx (/ 1 (- 1 ( (+ (* 1/2 x) -1) x))) (fma.f64 (fma.f64 #s(literal 3/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))))

Compiler

Compiled 514 to 239 computations (53.5% saved)

regimes17.0ms (0.6%)

Memory

2.3MiB live, 9.9MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Calls

5 calls:

4.0ms	x
3.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
3.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
100.0%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes23.0ms (0.7%)

Memory

-3.2MiB live, 8.0MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))

Calls

5 calls:

9.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
3.0ms	x
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.7%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.7%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes9.0ms (0.3%)

Memory

-1.3MiB live, 6.6MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) #s(literal -1 binary64))))))

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))

Calls

5 calls:

2.0ms	x
2.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.6%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.6%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Calls

5 calls:

1.0ms	x
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.2%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.2%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.2%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes5.0ms (0.2%)

Memory

-2.6MiB live, 5.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

Calls

5 calls:

1.0ms	x
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
97.9%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
97.9%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
97.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify20.0ms (0.7%)

Memory

2.1MiB live, 18.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	71
1	43	71
2	46	71
3	48	71
4	49	71

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

soundness401.0ms (13.1%)

Memory

-5.8MiB live, 2.1MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	323
1	276	262
2	764	248
3	2111	236
4	6140	230
0	8112	219
0	9	35
0	15	34
1	52	34
2	339	34
3	4589	8
0	9824	8

Stop Event

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

Compiler

Compiled 100 to 59 computations (41% saved)

preprocess35.0ms (1.1%)

Memory: 5.2MiB live, 20.3MiB allocated
Compiler: Compiled 164 to 84 computations (48.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

start0.0ms (0%)

analyze4.0ms (0.1%)

sample660.0ms (21.6%)

explain77.0ms (2.5%)

preprocess27.0ms (0.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify11.0ms (0.4%)

localize24.0ms (0.8%)

series3.0ms (0.1%)

simplify104.0ms (3.4%)

rewrite84.0ms (2.8%)

eval3.0ms (0.1%)

prune2.0ms (0.1%)

simplify94.0ms (3.1%)

localize58.0ms (1.9%)

series4.0ms (0.1%)

simplify140.0ms (4.6%)

rewrite124.0ms (4%)

eval39.0ms (1.3%)

prune6.0ms (0.2%)

simplify127.0ms (4.1%)

localize64.0ms (2.1%)

series8.0ms (0.2%)

simplify94.0ms (3.1%)

rewrite166.0ms (5.4%)

eval104.0ms (3.4%)

prune13.0ms (0.4%)

simplify120.0ms (3.9%)

localize70.0ms (2.3%)

series5.0ms (0.2%)

simplify99.0ms (3.2%)

rewrite132.0ms (4.3%)

eval70.0ms (2.3%)

prune11.0ms (0.4%)

regimes17.0ms (0.6%)

regimes23.0ms (0.7%)

regimes9.0ms (0.3%)

regimes6.0ms (0.2%)

regimes5.0ms (0.2%)

simplify20.0ms (0.7%)

soundness401.0ms (13.1%)

preprocess35.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44