Metrics for arccos

start0.0ms (0%)

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

analyze24.0ms (0.5%)

Memory

-32.3MiB live, 11.4MiB allocated; 9ms collecting garbage

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)

sample943.0ms (19.5%)

Memory

73.8MiB live, 1 354.9MiB allocated; 316ms collecting garbage

Samples

654.0ms	8 256×	0	valid
1.0ms	18×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 479.0ms

ival-mult: 103.0ms (21.5% of total)

ival-div: 86.0ms (17.9% of total)

ival-atan: 80.0ms (16.7% of total)

ival-sub: 79.0ms (16.5% of total)

ival-sqrt: 65.0ms (13.6% of total)

ival-add: 46.0ms (9.6% of total)

exact: 8.0ms (1.7% of total)

ival-true: 6.0ms (1.3% of total)

adjust: 3.0ms (0.6% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain102.0ms (2.1%)

Memory

7.1MiB live, 150.0MiB allocated; 27ms collecting garbage

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

Samples

42.0ms

512×

valid

Compiler

Compiled 103 to 31 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sub: 8.0ms (28.3% of total)

ival-atan: 5.0ms (17.7% of total)

ival-mult: 4.0ms (14.1% of total)

ival-sqrt: 4.0ms (14.1% of total)

ival-div: 3.0ms (10.6% of total)

ival-add: 3.0ms (10.6% of total)

exact: 1.0ms (3.5% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess14.0ms (0.3%)

Memory

21.3MiB live, 21.3MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	25	26
2	30	26
3	32	26
4	37	26
5	39	26
6	42	26
7	45	26
8	46	26
9	50	26
10	56	26
11	62	26
12	66	26
0	9	11
0	15	11
1	24	11
0	24	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 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))

Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

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)

simplify8.0ms (0.2%)

Memory

-39.9MiB live, 4.5MiB allocated; 10ms collecting garbage

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
0	24	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 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #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 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(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 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))

localize26.0ms (0.5%)

Memory

39.1MiB live, 39.1MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
accuracy	0.0078125	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy	0.0078125	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy	0.0234375	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Samples

18.0ms

256×

valid

Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-div: 2.0ms (17.3% of total)

ival-mult: 2.0ms (17.3% of total)

ival-atan: 2.0ms (17.3% of total)

ival-sub: 2.0ms (17.3% of total)

ival-sqrt: 2.0ms (17.3% of total)

ival-add: 1.0ms (8.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

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)))

simplify125.0ms (2.6%)

Memory

-3.6MiB live, 182.6MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	324
1	307	262
2	1011	242
3	3679	224
0	8337	217

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

rewrite378.0ms (7.8%)

Memory

-70.5MiB live, 214.4MiB allocated; 635ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	15	34
1	50	34
2	273	26
3	2956	5
0	9204	5

Stop Event

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

Counts

4 → 6

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
#s(literal 2 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: 6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 415 to 143 computations (65.5% saved)

prune4.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	18	5	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	6	24

Accuracy

100.0%

Counts

24 → 6

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)))))
▶	99.9%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (.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 (-.f64 (.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))))
▶	98.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
▶	20.7%	#s(literal 2 binary64)

Compiler

Compiled 155 to 123 computations (20.6% saved)

simplify265.0ms (5.5%)

Memory

14.4MiB live, 106.2MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	256
0	48	256
1	71	256
2	92	256
3	134	256
4	245	256
5	395	256
6	666	256
7	1165	256
8	1614	256
9	2139	256
10	2602	256
11	3199	256
12	3759	256
13	4631	256
14	5632	256
15	5851	256
16	5853	256
17	5857	256
18	5865	256
19	5865	256
20	5865	256
21	5969	256
22	6293	256
23	6293	256
0	6293	247

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

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

localize69.0ms (1.4%)

Memory

12.4MiB live, 97.3MiB allocated; 23ms collecting garbage

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64))))
accuracy	0.23855707976793572	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	0.0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy	0.5378447791757264	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
accuracy	0.0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
accuracy	1.2579734430220804	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
accuracy	0.0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (.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	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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	0.01953125	(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.04839909748515697	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))

Samples

46.0ms

256×

valid

Compiler

Compiled 183 to 23 computations (87.4% saved)

Precisions

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

ival-mult: 9.0ms (35.6% of total)

ival-add: 5.0ms (19.8% of total)

ival-sub: 4.0ms (15.8% of total)

ival-div: 2.0ms (7.9% of total)

ival-atan: 2.0ms (7.9% of total)

ival-sqrt: 2.0ms (7.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Counts

17 → 30

Calls

Call 1

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

Outputs
-1
(- (* 1/2 x) 1)
(- (* x (+ 1/2 (* -1/2 x))) 1)
(* 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)
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow 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 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)))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) 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))))

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify178.0ms (3.7%)

Memory

-25.1MiB live, 313.7MiB allocated; 58ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	364
1	290	302
2	940	282
3	3348	271
0	9581	266

Stop Event

1×	iter limit
1×	node limit

Counts

30 → 30

Calls

Call 1

Inputs
-1
(- (* 1/2 x) 1)
(- (* x (+ 1/2 (* -1/2 x))) 1)
(* 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)
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow 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 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)))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) 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))))

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

rewrite220.0ms (4.5%)

Memory

-9.6MiB live, 375.5MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	221
0	48	242
1	150	242
2	989	162
0	8752	162

Stop Event

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

Counts

17 → 303

Calls

Call 1

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

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

eval39.0ms (0.8%)

Memory: 26.4MiB live, 68.2MiB allocated; 11ms collecting garbage
Compiler: Compiled 8 594 to 1 274 computations (85.2% saved)

prune10.0ms (0.2%)

Memory

-28.5MiB live, 16.9MiB allocated; 8ms collecting garbage

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	226	7	233

Accuracy

100.0%

Counts

233 → 7

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)))))
✓	99.9%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (.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 (-.f64 (.f64 #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))) (/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.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))))
✓	98.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
✓	20.7%	#s(literal 2 binary64)

Compiler

Compiled 116 to 85 computations (26.7% saved)

simplify201.0ms (4.1%)

Memory

13.2MiB live, 161.9MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))))))
cost-diff	13	(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	163
0	27	163
1	42	163
2	62	163
3	135	123
4	379	115
5	1250	115
6	3416	115
7	7036	115
0	8093	111

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

localize83.0ms (1.7%)

Memory

3.9MiB live, 100.4MiB allocated; 21ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
accuracy	0.0234375	(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64)))
accuracy	0.03125	(pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))
accuracy	0.23855707976793572	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))))

Samples

45.0ms

256×

valid

Compiler

Compiled 99 to 19 computations (80.8% saved)

Precisions

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

ival-sub: 8.0ms (24.7% of total)

ival-mult: 7.0ms (21.6% of total)

ival-div: 5.0ms (15.4% of total)

ival-pow2: 4.0ms (12.3% of total)

ival-atan: 3.0ms (9.3% of total)

ival-sqrt: 3.0ms (9.3% of total)

ival-add: 2.0ms (6.2% of total)

exact: 1.0ms (3.1% of total)

adjust: 0.0ms (0% of total)

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

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

series8.0ms (0.2%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Counts

6 → 27

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))))
(pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

((/ (- (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))) (pow (* (- (* 1/2 x) 1) x) 2) (* (- (* 1/2 x) 1) x))

2.0ms

inf

((/ (- (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))) (pow (* (- (* 1/2 x) 1) x) 2) (* (- (* 1/2 x) 1) x))

2.0ms

((/ (- (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))) (pow (* (- (* 1/2 x) 1) x) 2) (* (- (* 1/2 x) 1) x))

simplify213.0ms (4.4%)

Memory

-2.6MiB live, 180.1MiB allocated; 34ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	356
1	303	293
2	1022	269
3	3636	259
0	8519	255

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

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

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

rewrite222.0ms (4.6%)

Memory

-30.0MiB live, 219.7MiB allocated; 59ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	131
0	27	131
1	107	83
2	735	65
0	8495	62

Stop Event

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

Counts

6 → 277

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))))
(pow.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)

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

eval79.0ms (1.6%)

Memory: 2.0MiB live, 93.2MiB allocated; 9ms collecting garbage
Compiler: Compiled 16 672 to 2 108 computations (87.4% saved)

prune7.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	0	0	0
Picked	1	0	1
Done	0	6	6
Total	347	7	354

Accuracy

100.0%

Counts

354 → 7

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)))))
✓	99.9%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (.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 (-.f64 (.f64 #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))) (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.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))))
✓	98.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
✓	20.7%	#s(literal 2 binary64)

Compiler

Compiled 120 to 92 computations (23.3% saved)

simplify143.0ms (2.9%)

Memory

4.2MiB live, 149.5MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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)) (-.f64 (.f64 (-.f64 (*.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)) (-.f64 (.f64 (-.f64 (*.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)) (-.f64 (.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))))))
cost-diff	1	(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	190
0	32	190
1	51	190
2	79	190
3	163	190
4	382	190
5	702	190
6	822	190
7	1282	190
8	3824	190
9	5650	190
10	7967	190
0	8005	178

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(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.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)) (-.f64 (.f64 (-.f64 (*.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)) (-.f64 (.f64 (-.f64 (*.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)) (-.f64 (.f64 (-.f64 (*.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)
(-.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

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

localize104.0ms (2.1%)

Memory

-30.8MiB live, 70.9MiB allocated; 16ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
accuracy	0.0234375	(/.f64 (-.f64 #s(approx (pow (* (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64)))
accuracy	0.23855707976793572	#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)) (-.f64 (.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1 binary64))))
accuracy	1.242318362562951	#s(approx (pow (* (- (* 1/2 x) 1) x) 2) (*.f64 x x))

Samples

68.0ms

256×

valid

Compiler

Compiled 102 to 20 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 41.0ms (70.3% of total)

ival-sub: 5.0ms (8.6% of total)

ival-div: 3.0ms (5.1% of total)

ival-pow2: 3.0ms (5.1% of total)

ival-atan: 2.0ms (3.4% of total)

ival-sqrt: 2.0ms (3.4% of total)

ival-add: 1.0ms (1.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Counts

6 → 27

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((* (- (* 1/2 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) (/ (- (pow (* (- (* 1/2 x) 1) x) 2) 1) (- (* (- (* 1/2 x) 1) x) 1)))

1.0ms

-inf

((* (- (* 1/2 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) (/ (- (pow (* (- (* 1/2 x) 1) x) 2) 1) (- (* (- (* 1/2 x) 1) x) 1)))

1.0ms

((* (- (* 1/2 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) (/ (- (pow (* (- (* 1/2 x) 1) x) 2) 1) (- (* (- (* 1/2 x) 1) x) 1)))

simplify181.0ms (3.7%)

Memory

4.7MiB live, 232.2MiB allocated; 41ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	356
1	303	293
2	1022	269
3	3627	259
0	8515	255

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

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

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

rewrite149.0ms (3.1%)

Memory

33.9MiB live, 124.1MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	151
0	32	151
1	117	151
2	739	117
0	8094	117

Stop Event

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

Counts

6 → 159

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) x) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) x) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(.f64 (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))))
(.f64 (fabs.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) (fabs.f64 (sqrt.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))))
(.f64 (fabs.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) x)
(.f64 (exp.f64 (log.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (exp.f64 (log.f64 x)))
(.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) (sqrt.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 x (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 x #s(literal 1 binary64)))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(.f64 #s(literal 1 binary64) (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
(.f64 x (fabs.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 x (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(/.f64 (.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64))) x) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1 binary64)))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) x) (neg.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (.f64 x (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1 binary64)))
(/.f64 (.f64 x (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1 binary64)))
(/.f64 (fabs.f64 (.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) x)) (fabs.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(/.f64 (fabs.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) x)) (fabs.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) x) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(sqrt.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)))
(fabs.f64 (.f64 (neg.f64 x) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(fabs.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
(exp.f64 (log.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(+.f64 (cosh.f64 (log.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) (sinh.f64 (log.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))))
(atan2.f64 (.f64 #s(literal 2 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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (pow.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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64)))) #s(literal 2 binary64))))
(.f64 (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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #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 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (pow.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 3 binary64)) (+.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 2 binary64)) #s(literal 0 binary64))) (/.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 3 binary64)) (+.f64 (pow.f64 (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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(+.f64 (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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #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)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #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)) (-.f64 (.f64 (-.f64 (*.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 #s(literal 1 binary64) #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (*.f64 x x)))
#s(approx (pow (* (- (* 1/2 x) 1) x) 2) (*.f64 x x))
(.f64 (/.f64 (neg.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64))) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (neg.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64))) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (+.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) 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)) (neg.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (fma.f64 (neg.f64 x) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (neg.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (+.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) 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)) (+.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64))) (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x #s(literal 1 binary64)))
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(+.f64 (.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.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(approx (pow (* (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(+.f64 (.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) 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)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(+.f64 (.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x #s(literal 1 binary64))) (.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (.f64 (/.f64 (-.f64 #s(approx (pow (* (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (.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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))) (.f64 (neg.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (fma.f64 (-.f64 (*.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)) (-.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1 binary64))) (.f64 (neg.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (fma.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (+.f64 (pow.f64 (.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))))

eval69.0ms (1.4%)

Memory: -16.7MiB live, 84.0MiB allocated; 25ms collecting garbage
Compiler: Compiled 10 982 to 1 107 computations (89.9% saved)

prune6.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	180	7	187

Accuracy

100.0%

Counts

187 → 7

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)))))
✓	99.9%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (.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 (-.f64 (.f64 #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))) (/.f64 (-.f64 #s(approx (pow ( (- (* 1/2 x) 1) x) 2) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 (*.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))))
✓	98.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
✓	20.7%	#s(literal 2 binary64)

Compiler

Compiled 273 to 148 computations (45.8% saved)

regimes14.0ms (0.3%)

Memory

-11.4MiB live, 32.0MiB allocated; 6ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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:

5.0ms	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))))
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
100.0%	1	`(/.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	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) 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	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes8.0ms (0.2%)

Memory

19.2MiB live, 19.2MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

2.0ms	x
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) 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	(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
99.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
99.9%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.9%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.9%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.9%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes8.0ms (0.2%)

Memory

-30.0MiB live, 16.8MiB allocated; 2ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

Calls

5 calls:

3.0ms	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	(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	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

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

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

#s(literal 2 binary64)

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

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

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 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	(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
98.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.1%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.1%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.1%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.1%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes8.0ms (0.2%)

Memory

-53.2MiB live, 9.9MiB allocated; 6ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)

Outputs
#s(literal 2 binary64)

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
20.7%	1	`x`
20.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
20.7%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
20.7%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
20.7%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify11.0ms (0.2%)

Memory

16.4MiB live, 16.4MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	83
1	46	83
2	53	83
3	57	83
4	61	83
5	76	83

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

derivations863.0ms (17.8%)

Memory

-11.7MiB live, 267.9MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	15	34
1	50	34
2	273	26
3	2956	5
0	9204	5
0	107	324
1	307	262
2	1011	242
3	3679	224
0	8337	217

Stop Event

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

Compiler

Compiled 83 to 35 computations (57.8% saved)

preprocess35.0ms (0.7%)

Memory: 35.0MiB live, 77.0MiB allocated; 7ms collecting garbage
Compiler: Compiled 188 to 88 computations (53.2% saved)

end0.0ms (0%)

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

Iter	Nodes	Cost
0	11	26
1	25	26
2	30	26
3	32	26
4	37	26
5	39	26
6	42	26
7	45	26
8	46	26
9	50	26
10	56	26
11	62	26
12	66	26
0	9	11
0	15	11
1	24	11
0	24	11

Iter	Nodes	Cost
0	11	26
1	25	26
2	30	26
3	32	26
4	37	26
5	39	26
6	42	26
7	45	26
8	46	26
9	50	26
10	56	26
11	62	26
12	66	26
0	9	11
0	15	11
1	24	11
0	24	11

start0.0ms (0%)

analyze24.0ms (0.5%)

sample943.0ms (19.5%)

explain102.0ms (2.1%)

preprocess14.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify8.0ms (0.2%)

localize26.0ms (0.5%)

series4.0ms (0.1%)

simplify125.0ms (2.6%)

rewrite378.0ms (7.8%)

eval3.0ms (0.1%)

prune4.0ms (0.1%)

simplify265.0ms (5.5%)

localize69.0ms (1.4%)

series6.0ms (0.1%)

simplify178.0ms (3.7%)

rewrite220.0ms (4.5%)

eval39.0ms (0.8%)

prune10.0ms (0.2%)

simplify201.0ms (4.1%)

localize83.0ms (1.7%)

series8.0ms (0.2%)

simplify213.0ms (4.4%)

rewrite222.0ms (4.6%)

eval79.0ms (1.6%)

prune7.0ms (0.1%)

simplify143.0ms (2.9%)

localize104.0ms (2.1%)

series3.0ms (0.1%)

simplify181.0ms (3.7%)

rewrite149.0ms (3.1%)

eval69.0ms (1.4%)

prune6.0ms (0.1%)

regimes14.0ms (0.3%)

regimes8.0ms (0.2%)

regimes8.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes8.0ms (0.2%)

simplify11.0ms (0.2%)

derivations863.0ms (17.8%)

preprocess35.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	11	26
1	25	26
2	30	26
3	32	26
4	37	26
5	39	26
6	42	26
7	45	26
8	46	26
9	50	26
10	56	26
11	62	26
12	66	26
0	9	11
0	15	11
1	24	11
0	24	11