Metrics for Numeric.Log:$clog1p from log-domain-0.10.2.1, B

analyze2.0ms (0%)

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
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

const: 0.0ms (0% of total)

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

backward-pass: 0.0ms (0% of total)

sample749.0ms (7.4%)

Results

572.0ms	8255×	0	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 328.0ms

ival-add: 153.0ms (46.6% of total)

ival-sqrt: 90.0ms (27.4% of total)

ival-div: 72.0ms (21.9% of total)

const: 11.0ms (3.3% of total)

backward-pass: 3.0ms (0.9% of total)

Bogosity

preprocess37.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

568×	`fnmadd-define`
494×	`sum3-define`
408×	`fma-define`
326×	`fmsub-define`
304×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	29	25
2	58	24
3	140	24
4	329	24
5	650	24
6	1273	24
7	1681	24
8	1794	24
9	1908	24
10	1949	24
0	6	8
1	10	8
0	10	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ x (+ 1 (sqrt (+ x 1))))

Outputs
(/ x (+ 1 (sqrt (+ x 1))))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Call 2

Inputs
(/ x (+ 1 (sqrt (+ x 1))))
(/ (neg x) (+ 1 (sqrt (+ (neg x) 1))))
(neg (/ (neg x) (+ 1 (sqrt (+ (neg x) 1)))))

Outputs
(/ x (+ 1 (sqrt (+ x 1))))
(/ (neg x) (+ 1 (sqrt (+ (neg x) 1))))
(/ x (- -1 (sqrt (- 1 x))))
(neg (/ (neg x) (+ 1 (sqrt (+ (neg x) 1)))))
(/ x (+ 1 (sqrt (- 1 x))))

explain103.0ms (1%)

FPErrors

Click to see full error table

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

Results

48.0ms

512×

valid

Compiler

Compiled 59 to 20 computations (66.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sqrt: 9.0ms (46.3% of total)

ival-add: 6.0ms (30.9% of total)

ival-div: 4.0ms (20.6% of total)

const: 1.0ms (5.1% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Rules

8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
4×	`+-commutative`
2×	`sqrt-lowering-sqrt.f64`
2×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
1	10	23
0	10	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (+ 1 (sqrt (+ x 1))))
x
(+ 1 (sqrt (+ x 1)))
1
(sqrt (+ x 1))
(+ x 1)

Outputs
(/ x (+ 1 (sqrt (+ x 1))))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
x
(+ 1 (sqrt (+ x 1)))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(sqrt (+ x 1))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+ x 1)
(+.f64 x #s(literal 1 binary64))

localize29.0ms (0.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

21.0ms

256×

valid

Compiler

Compiled 25 to 7 computations (72% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (40.7% of total)

ival-div: 2.0ms (27.2% of total)

ival-sqrt: 2.0ms (27.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series34.0ms (0.3%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ x (+ 1 (sqrt (+ x 1))))>
#<alt (+ 1 (sqrt (+ x 1)))>
#<alt (sqrt (+ x 1))>
#<alt (+ x 1)>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))>
#<alt (sqrt x)>
#<alt (- (sqrt x) 1)>
#<alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)>
#<alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))>
#<alt (* -1 (sqrt x))>
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))>
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>

Calls

12 calls:

Time	Variable		Point	Expression
30.0ms	x	@	inf	(/ x (+ 1 (sqrt (+ x 1))))
2.0ms	x	@	-inf	(/ x (+ 1 (sqrt (+ x 1))))
0.0ms	x	@	-inf	(sqrt (+ x 1))
0.0ms	x	@	-inf	(+ 1 (sqrt (+ x 1)))
0.0ms	x	@	inf	(sqrt (+ x 1))

rewrite265.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1798×	`-lowering-.f32`
1798×	`-lowering-.f64`
1694×	`/-lowering-/.f32`
1694×	`/-lowering-/.f64`
1416×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	21
1	42	21
2	328	20
3	3669	20
0	8084	20

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 250

Calls

Call 1

Inputs
(/ x (+ 1 (sqrt (+ x 1))))
(+ 1 (sqrt (+ x 1)))
(sqrt (+ x 1))
(+ x 1)

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

simplify282.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

3228×	`-lowering-.f32`
3228×	`-lowering-.f64`
2086×	`+-lowering-+.f64`
2086×	`+-lowering-+.f32`
1856×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	538
1	520	434
2	1993	412
3	7762	412
0	8435	412

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -5/128 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(+.f64 (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64))))))
(* -1 (sqrt x))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) x) #s(literal -1 binary64)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))) x) x)))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))))
(+.f64 (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) #s(literal 1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))) (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))) (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))

eval85.0ms (0.8%)

Compiler: Compiled 5835 to 1090 computations (81.3% saved)

prune61.0ms (0.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	286	12	298
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	286	13	299

Accuracy

100.0%

Counts

299 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.7%	(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
▶	65.6%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
	65.1%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
▶	66.5%	(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
	65.6%	(/.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	40.2%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	65.6%	(/.f64 x #s(literal 2 binary64))
	35.7%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
▶	65.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
	64.3%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
▶	36.6%	(sqrt.f64 x)
	41.0%	(neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))

Compiler

Compiled 249 to 180 computations (27.7% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	cost-diff	(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64))
✓	cost-diff	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
✓	cost-diff	(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	cost-diff	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
✓	cost-diff	(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))

Rules

300×	`fma-define`
264×	`fma-lowering-fma.f32`
264×	`fma-lowering-fma.f64`
148×	`sum3-define`
128×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	129
1	38	113
2	97	113
3	187	113
4	304	113
5	416	113
6	449	113
0	449	113

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (+ (* 1/2 x) 2))
x
(+ (* 1/2 x) 2)
(* 1/2 x)
1/2
2
(/ x 2)
x
2
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))
x
(+ 1/2 (* x (+ -1/8 (* x 1/16))))
1/2
(* x (+ -1/8 (* x 1/16)))
(+ -1/8 (* x 1/16))
-1/8
(* x 1/16)
1/16
(/ x (+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2))
x
(+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2)
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))
(+ 1/2 (* x (+ -1/8 (* x 1/16))))
1/2
(* x (+ -1/8 (* x 1/16)))
(+ -1/8 (* x 1/16))
-1/8
(* x 1/16)
1/16
2
(sqrt x)
x

Outputs
(/ x (+ (* 1/2 x) 2))
(/.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
x
(+ (* 1/2 x) 2)
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
2
#s(literal 2 binary64)
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
x
(+ 1/2 (* x (+ -1/8 (* x 1/16))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
1/2
#s(literal 1/2 binary64)
(* x (+ -1/8 (* x 1/16)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
(+ -1/8 (* x 1/16))
(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
-1/8
#s(literal -1/8 binary64)
(* x 1/16)
(*.f64 x #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
(/ x (+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2))
(/.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
x
(+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2)
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(+ 1/2 (* x (+ -1/8 (* x 1/16))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
1/2
#s(literal 1/2 binary64)
(* x (+ -1/8 (* x 1/16)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
(+ -1/8 (* x 1/16))
(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
-1/8
#s(literal -1/8 binary64)
(* x 1/16)
(*.f64 x #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x

localize127.0ms (1.2%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/16 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	91.6%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/16 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))

Results

47.0ms	163×	0	valid
22.0ms	93×	0	invalid

Compiler

Compiled 135 to 18 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 9.0ms (39.3% of total)

ival-div: 6.0ms (26.2% of total)

ival-add: 5.0ms (21.8% of total)

ival-sqrt: 2.0ms (8.7% of total)

const: 1.0ms (4.4% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts

12 → 144

Calls

Call 1

Inputs
#<alt (/ x (+ (* 1/2 x) 2))>
#<alt (+ (* 1/2 x) 2)>
#<alt (* 1/2 x)>
#<alt (/ x 2)>
#<alt (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))>
#<alt (+ 1/2 (* x (+ -1/8 (* x 1/16))))>
#<alt (* x (+ -1/8 (* x 1/16)))>
#<alt (+ -1/8 (* x 1/16))>
#<alt (/ x (+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2))>
#<alt (+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2)>
#<alt (sqrt x)>
#<alt (* x 1/16)>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))>
#<alt (+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))>
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))>
#<alt (* 1/16 (pow x 2))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 2))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))>
#<alt (* -1/8 x)>
#<alt (* x (- (* 1/16 x) 1/8))>
#<alt (* x (- (* 1/16 x) 1/8))>
#<alt (* x (- (* 1/16 x) 1/8))>
#<alt (* 1/16 (pow x 2))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 2))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt -1/8>
#<alt (- (* 1/16 x) 1/8)>
#<alt (- (* 1/16 x) 1/8)>
#<alt (- (* 1/16 x) 1/8)>
#<alt (* 1/16 x)>
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 x)>
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))>
#<alt (/ 16 (pow x 2))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))>
#<alt (/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))>
#<alt (/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>

Calls

36 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+ -1/8 (* x 1/16))
1.0ms	x	@	inf	(/ x (+ (* 1/2 x) 2))
0.0ms	x	@	-inf	(sqrt x)
0.0ms	x	@	inf	(* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))
0.0ms	x	@	inf	(/ x (+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2))

rewrite317.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4612×	`-lowering-.f32`
4612×	`-lowering-.f64`
2856×	`/-lowering-/.f32`
2856×	`/-lowering-/.f64`
2084×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	112	69
2	952	69
0	8502	69

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 401

Calls

Call 1

Inputs
(/ x (+ (* 1/2 x) 2))
(+ (* 1/2 x) 2)
(* 1/2 x)
(/ x 2)
(* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))
(+ 1/2 (* x (+ -1/8 (* x 1/16))))
(* x (+ -1/8 (* x 1/16)))
(+ -1/8 (* x 1/16))
(/ x (+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2))
(+ (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))) 2)
(sqrt x)
(* x 1/16)

Outputs
(+.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (/.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 #s(literal 4 binary64) x)))
(+.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 #s(literal 4 binary64) x)) (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (/.f64 (*.f64 x x) #s(literal 4 binary64))))
(+.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) #s(literal -2 binary64)))
(+.f64 (.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)))) (.f64 (-.f64 #s(literal 4 binary64) x) (/.f64 x (+.f64 (/.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)))))
(+.f64 (.f64 (-.f64 #s(literal 4 binary64) x) (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)))) (.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (/.f64 x (+.f64 (/.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)))))
(+.f64 (.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (.f64 #s(literal -2 binary64) (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64)))) (/.f64 x (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64)))))
(neg.f64 (/.f64 x (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x)))
(/.f64 x (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
(/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 x #s(literal -2 binary64))) x))
(pow.f64 (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x) #s(literal -1 binary64))
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(/.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (pow.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 (.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64)) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64))) (.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 3 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64)))) (+.f64 (.f64 (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64)))) (.f64 (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64)))))))
(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64)) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64)))) (-.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (-.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))))))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))
(.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64))))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal -2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))
(.f64 (+.f64 #s(literal -8 binary64) (neg.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal -2 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) #s(literal 2 binary64))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 x #s(literal 1/16 binary64))
(*.f64 #s(literal 1/16 binary64) x)

simplify289.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

3102×	`+-lowering-+.f64`
3102×	`+-lowering-+.f32`
3084×	`-lowering-.f32`
3084×	`-lowering-.f64`
1386×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	908
1	459	813
2	1267	778
3	3464	756
0	8220	756

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
2
(- 2 (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
2
(- 2 (* 8 (/ 1 x)))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
2
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(* -1/8 x)
(* x (- (* 1/16 x) 1/8))
(* x (- (* 1/16 x) 1/8))
(* x (- (* 1/16 x) 1/8))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
-1/8
(- (* 1/16 x) 1/8)
(- (* 1/16 x) 1/8)
(- (* 1/16 x) 1/8)
(* 1/16 x)
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 x)
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(/ 16 (pow x 2))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))
(/ 16 (pow x 2))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))
(/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/32 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/32 binary64) (.f64 x #s(literal -1/128 binary64))))))))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(-.f64 #s(literal 2 binary64) (/.f64 #s(literal 8 binary64) x))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
(+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (/.f64 (-.f64 #s(literal 32 binary64) (/.f64 #s(literal 128 binary64) x)) x) x) (/.f64 #s(literal -8 binary64) x)))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(-.f64 #s(literal 2 binary64) (/.f64 #s(literal 8 binary64) x))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 32 binary64) (/.f64 #s(literal 128 binary64) x)) x)) x))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x x) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x x) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64)))))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64)))))
(* 1/16 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/16 binary64))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* 1/16 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/16 binary64))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* x (- (* 1/16 x) 1/8))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* x (- (* 1/16 x) 1/8))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* x (- (* 1/16 x) 1/8))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* 1/16 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/16 binary64))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* 1/16 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/16 binary64))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (-.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64))))
-1/8
#s(literal -1/8 binary64)
(- (* 1/16 x) 1/8)
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(- (* 1/16 x) 1/8)
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(- (* 1/16 x) 1/8)
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -5/128 binary64))))))))
(/ 16 (pow x 2))
(/.f64 #s(literal 16 binary64) (*.f64 x x))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) (*.f64 x x))
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -64 binary64) x)) x)) (*.f64 x x))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)))) x)) (.f64 x x))
(/ 16 (pow x 2))
(/.f64 #s(literal 16 binary64) (*.f64 x x))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) (*.f64 x x))
(/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -64 binary64) x)) x)) (*.f64 x x))
(/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)))) x)) (.f64 x x))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x x) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))) x)))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x x) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/16 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))) x)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))

eval93.0ms (0.9%)

Compiler: Compiled 19683 to 1694 computations (91.4% saved)

prune126.0ms (1.2%)

Pruning

23 alts after pruning (17 fresh and 6 done)

	Pruned	Kept	Total
New	766	11	777
Fresh	1	6	7
Picked	0	5	5
Done	0	1	1
Total	767	23	790

Accuracy

100.0%

Counts

790 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.7%	(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
	66.0%	(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
▶	66.5%	(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
▶	65.6%	(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	65.6%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
▶	65.1%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
✓	66.5%	(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	40.2%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	66.0%	(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
	65.3%	(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
✓	65.6%	(/.f64 x #s(literal 2 binary64))
	66.3%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
	65.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
	64.9%	(+.f64 (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal -2 binary64))))
▶	35.7%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
	65.3%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
	66.0%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
✓	65.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
	64.3%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	36.6%	(sqrt.f64 x)
	41.0%	(neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
▶	4.7%	#s(literal 2 binary64)

Compiler

Compiled 598 to 350 computations (41.5% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	cost-diff	0	(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	cost-diff	0	(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	cost-diff	128	(+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
✓	cost-diff	128	(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))

Rules

272×	`fma-define`
216×	`fma-lowering-fma.f32`
216×	`fma-lowering-fma.f64`
158×	`sum3-define`
136×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	133
1	60	119
2	127	119
3	291	119
4	426	119
5	471	119
0	471	119

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (+ (/ 1 (/ 2 x)) 2))
x
(+ (/ 1 (/ 2 x)) 2)
(/ 1 (/ 2 x))
1
(/ 2 x)
2
2
(/ x (+ (* x (+ 1/2 (* x -1/8))) 2))
x
(+ (* x (+ 1/2 (* x -1/8))) 2)
(* x (+ 1/2 (* x -1/8)))
(+ 1/2 (* x -1/8))
1/2
(* x -1/8)
-1/8
2
(/ x (+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16))))))
x
(+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16)))))
(+ (/ x 2) 2)
(/ x 2)
2
(* x (* x (+ -1/8 (* x 1/16))))
(* x (+ -1/8 (* x 1/16)))
(+ -1/8 (* x 1/16))
-1/8
(* x 1/16)
1/16
(+ (sqrt x) -1)
(sqrt x)
x
-1

Outputs
(/ x (+ (/ 1 (/ 2 x)) 2))
(/.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
x
(+ (/ 1 (/ 2 x)) 2)
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(/ 1 (/ 2 x))
(*.f64 x #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
2
#s(literal 2 binary64)
(/ x (+ (* x (+ 1/2 (* x -1/8))) 2))
(/.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))))
x
(+ (* x (+ 1/2 (* x -1/8))) 2)
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(* x (+ 1/2 (* x -1/8)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(+ 1/2 (* x -1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
1/2
#s(literal 1/2 binary64)
(* x -1/8)
(*.f64 x #s(literal -1/8 binary64))
-1/8
#s(literal -1/8 binary64)
2
#s(literal 2 binary64)
(/ x (+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16))))))
(/.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x))))
x
(+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16)))))
(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x)))
(+ (/ x 2) 2)
(+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* x (* x (+ -1/8 (* x 1/16))))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x))
(* x (+ -1/8 (* x 1/16)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
(+ -1/8 (* x 1/16))
(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
-1/8
#s(literal -1/8 binary64)
(* x 1/16)
(*.f64 x #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
(+ (sqrt x) -1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(sqrt x)
(sqrt.f64 x)
x
-1
#s(literal -1 binary64)

localize147.0ms (1.4%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/16 binary64))
✓	accuracy	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
✓	accuracy	91.6%	(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/8 binary64))
✓	accuracy	85.0%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))

Results

86.0ms	163×	0	valid
28.0ms	93×	0	invalid

Compiler

Compiled 145 to 27 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-div: 12.0ms (34.1% of total)

ival-add: 11.0ms (31.2% of total)

ival-mult: 9.0ms (25.6% of total)

ival-sqrt: 2.0ms (5.7% of total)

const: 1.0ms (2.8% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (/ x (+ (/ 1 (/ 2 x)) 2))>
#<alt (+ (/ 1 (/ 2 x)) 2)>
#<alt (/ 1 (/ 2 x))>
#<alt (/ 2 x)>
#<alt (/ x (+ (* x (+ 1/2 (* x -1/8))) 2))>
#<alt (+ (* x (+ 1/2 (* x -1/8))) 2)>
#<alt (* x (+ 1/2 (* x -1/8)))>
#<alt (+ 1/2 (* x -1/8))>
#<alt (/ x (+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16))))))>
#<alt (+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16)))))>
#<alt (+ (/ x 2) 2)>
#<alt (/ x 2)>
#<alt (+ (sqrt x) -1)>
#<alt (sqrt x)>
#<alt (* x -1/8)>
#<alt (* x (* x (+ -1/8 (* x 1/16))))>
#<alt (* x 1/16)>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))>
#<alt (+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -3/128 x))) 1/8))))>
#<alt (/ -8 x)>
#<alt (* -1 (/ (+ 8 (* 32 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 32 (* 256 (/ 1 x))) x)) 8) x)>
#<alt (/ (- (* -1 (/ (+ 256 (* 1536 (/ 1 x))) (pow x 2))) (+ 8 (* 32 (/ 1 x)))) x)>
#<alt (/ -8 x)>
#<alt (* -1 (/ (+ 8 (* 32 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 8 (+ (* 32 (/ 1 x)) (/ 256 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 8 (* -1 (/ (- (* -1 (/ (+ 256 (* 1536 (/ 1 x))) x)) 32) x))) x))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (* -1/8 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* -1/8 x)>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))>
#<alt (/ 16 (pow x 2))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))>
#<alt (/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))>
#<alt (/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (- (sqrt x) 1)>
#<alt (- (sqrt x) 1)>
#<alt (- (sqrt x) 1)>
#<alt (- (sqrt x) 1)>
#<alt (sqrt x)>
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (- (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>

Calls

51 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ x (+ (* x (+ 1/2 (* x -1/8))) 2))
0.0ms	x	@	-inf	(* x -1/8)
0.0ms	x	@	-inf	(/ x (+ (* x (+ 1/2 (* x -1/8))) 2))
0.0ms	x	@	0	(/ 2 x)
0.0ms	x	@	inf	(* x -1/8)

rewrite385.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3742×	`-lowering-.f32`
3742×	`-lowering-.f64`
3272×	`/-lowering-/.f32`
3272×	`/-lowering-/.f64`
1898×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	107
1	183	92
2	1477	92
0	8440	92

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 544

Calls

Call 1

Inputs
(/ x (+ (/ 1 (/ 2 x)) 2))
(+ (/ 1 (/ 2 x)) 2)
(/ 1 (/ 2 x))
(/ 2 x)
(/ x (+ (* x (+ 1/2 (* x -1/8))) 2))
(+ (* x (+ 1/2 (* x -1/8))) 2)
(* x (+ 1/2 (* x -1/8)))
(+ 1/2 (* x -1/8))
(/ x (+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16))))))
(+ (+ (/ x 2) 2) (* x (* x (+ -1/8 (* x 1/16)))))
(+ (/ x 2) 2)
(/ x 2)
(+ (sqrt x) -1)
(sqrt x)
(* x -1/8)
(* x (* x (+ -1/8 (* x 1/16))))
(* x 1/16)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))) (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(neg.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) x) #s(literal 1 binary64)))
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(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x))) (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))
(expm1.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 x (*.f64 (sqrt.f64 x) #s(literal -1 binary64)))))
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (+.f64 x #s(literal -1 binary64))) (neg.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 (-.f64 (.f64 x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 x #s(literal -1 binary64)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(pow.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (sqrt.f64 x) #s(literal -1 binary64)))))
(*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 x #s(literal -1/8 binary64))
(*.f64 #s(literal -1/8 binary64) x)
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x #s(literal 1/16 binary64))))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/16 binary64) (*.f64 x x)) x))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 x #s(literal 1/16 binary64)) (*.f64 x x)))
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(+.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(fma.f64 x (.f64 x #s(literal -1/8 binary64)) (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x))))
(fma.f64 x (.f64 x #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))))
(fma.f64 x (.f64 x #s(literal -1/8 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x))
(fma.f64 x (.f64 x #s(literal -1/8 binary64)) (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)))
(fma.f64 #s(literal -1/8 binary64) (.f64 x x) (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x))))
(fma.f64 #s(literal -1/8 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))))
(fma.f64 #s(literal -1/8 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x))
(fma.f64 #s(literal -1/8 binary64) (.f64 x x) (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) x (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x))))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) x (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) x (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) x (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x) (.f64 #s(literal -1/8 binary64) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x))))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64)) (.f64 #s(literal -1/8 binary64) (.f64 x x)))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x #s(literal 1/16 binary64)) (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64)))) (+.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -1/16 binary64) x)))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64))))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x #s(literal 1/16 binary64)) (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64))))) (neg.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 #s(literal -1/16 binary64) x))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (pow.f64 (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) x)) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/16 binary64) (*.f64 x x)) x)))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x))) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 x #s(literal 1/16 binary64)) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) #s(literal 3 binary64)) (.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64)))) (-.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) (.f64 #s(literal -1/8 binary64) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) #s(literal 3 binary64)) (.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x))) (-.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 x x))) (.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 x x))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) x)
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(*.f64 x #s(literal 1/16 binary64))
(*.f64 #s(literal 1/16 binary64) x)

simplify269.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

3478×	`-lowering-.f32`
3478×	`-lowering-.f64`
2456×	`+-lowering-+.f64`
2456×	`+-lowering-+.f32`
1292×	`distribute-lft-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	1182
1	589	1062
2	1610	1041
3	4192	1040
0	8612	1040

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
2
(- 2 (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
2
(- 2 (* 8 (/ 1 x)))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
2
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -3/128 x))) 1/8))))
(/ -8 x)
(* -1 (/ (+ 8 (* 32 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 32 (* 256 (/ 1 x))) x)) 8) x)
(/ (- (* -1 (/ (+ 256 (* 1536 (/ 1 x))) (pow x 2))) (+ 8 (* 32 (/ 1 x)))) x)
(/ -8 x)
(* -1 (/ (+ 8 (* 32 (/ 1 x))) x))
(* -1 (/ (+ 8 (+ (* 32 (/ 1 x)) (/ 256 (pow x 2)))) x))
(* -1 (/ (+ 8 (* -1 (/ (- (* -1 (/ (+ 256 (* 1536 (/ 1 x))) x)) 32) x))) x))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(/ 16 (pow x 2))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))
(/ 16 (pow x 2))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))
(/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))
2
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(- (sqrt x) 1)
(- (sqrt x) 1)
(- (sqrt x) 1)
(- (sqrt x) 1)
(sqrt x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/32 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/32 binary64) (.f64 x #s(literal -1/128 binary64))))))))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(-.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -32 binary64) x)) x))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
(+.f64 (/.f64 (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -128 binary64) x)) x) x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x)))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -32 binary64) x)) x))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -128 binary64) x)) x) #s(literal -8 binary64)) x))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -3/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -3/128 binary64))))))))
(/ -8 x)
(/.f64 #s(literal -8 binary64) x)
(* -1 (/ (+ 8 (* 32 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -32 binary64) x)) x)
(/ (- (* -1 (/ (+ 32 (* 256 (/ 1 x))) x)) 8) x)
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 #s(literal -32 binary64) (/.f64 #s(literal -256 binary64) x)) x)) x)
(/ (- (* -1 (/ (+ 256 (* 1536 (/ 1 x))) (pow x 2))) (+ 8 (* 32 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal -256 binary64) (/.f64 #s(literal 1536 binary64) x)) x) #s(literal -32 binary64)) x)) x)
(/ -8 x)
(/.f64 #s(literal -8 binary64) x)
(* -1 (/ (+ 8 (* 32 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -32 binary64) x)) x)
(* -1 (/ (+ 8 (+ (* 32 (/ 1 x)) (/ 256 (pow x 2)))) x))
(/.f64 (+.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -32 binary64) x)) (/.f64 #s(literal -256 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 8 (* -1 (/ (- (* -1 (/ (+ 256 (* 1536 (/ 1 x))) x)) 32) x))) x))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal -256 binary64) (/.f64 #s(literal 1536 binary64) x)) x) #s(literal -32 binary64)) x)) x)
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -5/128 binary64))))))))
(/ 16 (pow x 2))
(/.f64 #s(literal 16 binary64) (*.f64 x x))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) x) x)
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))
(/.f64 (-.f64 #s(literal 16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -32 binary64)) x)) (*.f64 x x))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)))) x)) (.f64 x x))
(/ 16 (pow x 2))
(/.f64 #s(literal 16 binary64) (*.f64 x x))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) x) x)
(/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -32 binary64)) x)) (*.f64 x x))
(/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)))) x)) (.f64 x x))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 x (.f64 x (*.f64 x (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(.f64 x (.f64 x (*.f64 x (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))) x))))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(- (sqrt x) 1)
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(- (sqrt x) 1)
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(- (sqrt x) 1)
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(- (sqrt x) 1)
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(sqrt x)
(sqrt.f64 x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/16 x) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(* (pow x 2) (- (* 1/16 x) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(* (pow x 2) (- (* 1/16 x) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))

eval131.0ms (1.3%)

Compiler: Compiled 18762 to 2022 computations (89.2% saved)

prune85.0ms (0.8%)

Pruning

24 alts after pruning (13 fresh and 11 done)

	Pruned	Kept	Total
New	746	2	748
Fresh	1	11	12
Picked	0	5	5
Done	0	6	6
Total	747	24	771

Accuracy

100.0%

Counts

771 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.7%	(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
	66.0%	(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
✓	66.5%	(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
✓	65.6%	(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	65.6%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
✓	65.1%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
✓	66.5%	(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	40.2%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	66.0%	(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
	65.3%	(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
✓	65.6%	(/.f64 x #s(literal 2 binary64))
▶	66.3%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
	65.0%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
▶	65.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	35.7%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
	65.3%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
▶	66.0%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
▶	65.6%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
✓	65.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
	64.3%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	36.6%	(sqrt.f64 x)
	41.0%	(neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
✓	4.7%	#s(literal 2 binary64)

Compiler

Compiled 475 to 324 computations (31.8% saved)

simplify260.0ms (2.6%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))
✓	cost-diff	128	(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	cost-diff	256	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
✓	cost-diff	0	(/.f64 (*.f64 x x) #s(literal 4 binary64))
✓	cost-diff	0	(+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))
✓	cost-diff	0	(/.f64 x (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))
✓	cost-diff	0	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))
✓	cost-diff	128	(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))

Rules

5028×	`-lowering-.f32`
5028×	`-lowering-.f64`
3452×	`+-lowering-+.f64`
3452×	`+-lowering-+.f32`
2094×	`fma-define`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	31	175
1	75	167
2	155	167
3	428	158
4	739	152
5	993	152
6	1128	152
7	1311	152
8	1734	152
9	2001	152
10	2826	151
11	4849	151
12	6298	151
0	8196	151

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (/ (+ (/ x 2) 2) x))
1
(/ (+ (/ x 2) 2) x)
(+ (/ x 2) 2)
(/ x 2)
x
2
(/ 1 (/ 2 x))
1
(/ 2 x)
2
x
(* (/ x (+ (/ (* x x) 4) -4)) (+ (/ x 2) -2))
(/ x (+ (/ (* x x) 4) -4))
x
(+ (/ (* x x) 4) -4)
(/ (* x x) 4)
(* x x)
4
-4
(+ (/ x 2) -2)
(/ x 2)
2
-2
(* (/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))) x)
(/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16))))))
1
(+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))
(+ 2 (/ x 2))
2
(/ x 2)
x
(* x (* x (+ -1/8 (* x 1/16))))
(* x (+ -1/8 (* x 1/16)))
(+ -1/8 (* x 1/16))
-1/8
(* x 1/16)
1/16
(/ x (+ 1 (sqrt x)))
x
(+ 1 (sqrt x))
1
(sqrt x)

Outputs
(/ 1 (/ (+ (/ x 2) 2) x))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(/ (+ (/ x 2) 2) x)
(+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(+ (/ x 2) 2)
(+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(/ 1 (/ 2 x))
(/.f64 x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(* (/ x (+ (/ (* x x) 4) -4)) (+ (/ x 2) -2))
(/.f64 (.f64 x (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64))) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))
(/ x (+ (/ (* x x) 4) -4))
(/.f64 x (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))
x
(+ (/ (* x x) 4) -4)
(+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))
(/ (* x x) 4)
(/.f64 (*.f64 x x) #s(literal 4 binary64))
(* x x)
(*.f64 x x)
4
#s(literal 4 binary64)
-4
#s(literal -4 binary64)
(+ (/ x 2) -2)
(+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
-2
#s(literal -2 binary64)
(* (/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))) x)
(/.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
(/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
1
#s(literal 1 binary64)
(+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64))))
(+ 2 (/ x 2))
(+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
(* x (* x (+ -1/8 (* x 1/16))))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(* x (+ -1/8 (* x 1/16)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
(+ -1/8 (* x 1/16))
(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
-1/8
#s(literal -1/8 binary64)
(* x 1/16)
(*.f64 x #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
(/ x (+ 1 (sqrt x)))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
x
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(sqrt x)
(sqrt.f64 x)

localize285.0ms (2.8%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	accuracy	92.1%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
✓	accuracy	100.0%	(+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
✓	accuracy	85.0%	(/.f64 x (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x)
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))

Results

161.0ms	163×	0	valid
72.0ms	93×	0	invalid

Compiler

Compiled 194 to 32 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-add: 78.0ms (50.8% of total)

ival-div: 39.0ms (25.4% of total)

ival-mult: 33.0ms (21.5% of total)

ival-sqrt: 2.0ms (1.3% of total)

const: 1.0ms (0.7% of total)

backward-pass: 0.0ms (0% of total)

series25.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (/ 1 (/ (+ (/ x 2) 2) x))>
#<alt (/ (+ (/ x 2) 2) x)>
#<alt (+ (/ x 2) 2)>
#<alt (/ x 2)>
#<alt (/ 1 (/ 2 x))>
#<alt (/ 2 x)>
#<alt (* (/ x (+ (/ (* x x) 4) -4)) (+ (/ x 2) -2))>
#<alt (/ x (+ (/ (* x x) 4) -4))>
#<alt (+ (/ (* x x) 4) -4)>
#<alt (/ (* x x) 4)>
#<alt (* (/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))) x)>
#<alt (/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16))))))>
#<alt (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))>
#<alt (+ 2 (/ x 2))>
#<alt (/ x (+ 1 (sqrt x)))>
#<alt (+ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (* x x)>
#<alt (+ (/ x 2) -2)>
#<alt (* x (* x (+ -1/8 (* x 1/16))))>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))>
#<alt (+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))>
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* 1/2 x)) x)>
#<alt (/ (+ 2 (* 1/2 x)) x)>
#<alt (/ (+ 2 (* 1/2 x)) x)>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ 1 x)))>
#<alt (+ 1/2 (* 2 (/ 1 x)))>
#<alt (+ 1/2 (* 2 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ 1 x)))>
#<alt (+ 1/2 (* 2 (/ 1 x)))>
#<alt (+ 1/2 (* 2 (/ 1 x)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))>
#<alt (- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))>
#<alt 2>
#<alt (- 2 (* 8 (/ 1 x)))>
#<alt (+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))>
#<alt (+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))>
#<alt (* -1/4 x)>
#<alt (* x (- (* -1/64 (pow x 2)) 1/4))>
#<alt (* x (- (* (pow x 2) (- (* -1/1024 (pow x 2)) 1/64)) 1/4))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -1/16384 (pow x 2)) 1/1024)) 1/64)) 1/4))>
#<alt (/ 4 x)>
#<alt (/ (+ 4 (* 64 (/ 1 (pow x 2)))) x)>
#<alt (/ (+ 4 (+ (* 64 (/ 1 (pow x 2))) (/ 1024 (pow x 4)))) x)>
#<alt (/ (+ 4 (+ (* 64 (/ 1 (pow x 2))) (+ (* 16384 (/ 1 (pow x 6))) (/ 1024 (pow x 4))))) x)>
#<alt (/ 4 x)>
#<alt (/ (+ 4 (* 64 (/ 1 (pow x 2)))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 64 (* 1024 (/ 1 (pow x 2)))) (pow x 2))) 4) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1024 (* 16384 (/ 1 (pow x 2)))) (pow x 4))) (+ 4 (* 64 (/ 1 (pow x 2))))) x))>
#<alt -4>
#<alt (- (* 1/4 (pow x 2)) 4)>
#<alt (- (* 1/4 (pow x 2)) 4)>
#<alt (- (* 1/4 (pow x 2)) 4)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))>
#<alt (/ 16 (pow x 2))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))>
#<alt (/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))>
#<alt (/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* x (- (* 1/16 x) 1/8)))>
#<alt (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 3))>
#<alt (/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (* -1 (/ (- (* -1 (/ (- 32 (* 64 (/ 1 x))) x)) 16) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (+ 64 (* 896 (/ 1 x))) x))) x)) 16) (pow x 3)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))>
#<alt 2>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (+ 2 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (/ x (+ 1 (sqrt x)))>
#<alt (/ x (+ 1 (sqrt x)))>
#<alt (/ x (+ 1 (sqrt x)))>
#<alt (/ x (+ 1 (sqrt x)))>
#<alt (sqrt x)>
#<alt (- (sqrt x) 1)>
#<alt (- (+ (sqrt x) (sqrt (/ 1 x))) 1)>
#<alt (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x))))>
#<alt (* -1 (sqrt x))>
#<alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) x)))>
#<alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ x (pow (sqrt -1) 4))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) x))) x)))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt -2>
#<alt (- (* 1/2 x) 2)>
#<alt (- (* 1/2 x) 2)>
#<alt (- (* 1/2 x) 2)>
#<alt (* 1/2 x)>
#<alt (* x (- 1/2 (* 2 (/ 1 x))))>
#<alt (* x (- 1/2 (* 2 (/ 1 x))))>
#<alt (* x (- 1/2 (* 2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 1/2)))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>

Calls

60 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	(/ (* x x) 4)
7.0ms	x	@	0	(/ (* x x) 4)
2.0ms	x	@	inf	(/ x (+ (/ (* x x) 4) -4))
0.0ms	x	@	0	(/ x (+ 1 (sqrt x)))
0.0ms	x	@	-inf	(/ x (+ 1 (sqrt x)))

rewrite417.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4744×	`-lowering-.f32`
4744×	`-lowering-.f64`
3164×	`/-lowering-/.f32`
3164×	`/-lowering-/.f64`
2114×	`--lowering--.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	130
1	218	112
2	2089	112
0	9452	112

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 643

Calls

Call 1

Inputs
(/ 1 (/ (+ (/ x 2) 2) x))
(/ (+ (/ x 2) 2) x)
(+ (/ x 2) 2)
(/ x 2)
(/ 1 (/ 2 x))
(/ 2 x)
(* (/ x (+ (/ (* x x) 4) -4)) (+ (/ x 2) -2))
(/ x (+ (/ (* x x) 4) -4))
(+ (/ (* x x) 4) -4)
(/ (* x x) 4)
(* (/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))) x)
(/ 1 (+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16))))))
(+ (+ 2 (/ x 2)) (* x (* x (+ -1/8 (* x 1/16)))))
(+ 2 (/ x 2))
(/ x (+ 1 (sqrt x)))
(+ 1 (sqrt x))
(sqrt x)
(* x x)
(+ (/ x 2) -2)
(* x (* x (+ -1/8 (* x 1/16))))

Outputs
(+.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))))
(+.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) x)) #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) #s(literal -2 binary64)) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))))
(fma.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64)) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) #s(literal -2 binary64) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))))
(fma.f64 #s(literal -2 binary64) (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 (.f64 (/.f64 x #s(literal 2 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 (.f64 #s(literal -2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))))
(fma.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) #s(literal 1 binary64)) (/.f64 x #s(literal 2 binary64)) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) #s(literal 1/2 binary64) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(fma.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) #s(literal 1/2 binary64)) x (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) x))
(/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
(/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 x (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64))) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64))) (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64))) (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64)))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) x) (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64)))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x) (.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) x)) (.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64)))))
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(pow.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(pow.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 #s(literal -2 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))) (sqrt.f64 #s(literal -2 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64)))
(.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64))
(+.f64 #s(literal -2 binary64) (/.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))
(-.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -2 binary64))
(fma.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal -2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #s(literal -2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64) #s(literal -2 binary64))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x) #s(literal -2 binary64))
(fma.f64 (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64)))) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))
(/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal -2 binary64) (/.f64 x #s(literal 2 binary64))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64)))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (+.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) (+.f64 #s(literal 4 binary64) x)))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (.f64 x #s(literal -1 binary64)))) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64))))))
(+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (*.f64 x #s(literal 1/16 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))) (.f64 (*.f64 x x) #s(literal -1/8 binary64)))
(+.f64 (.f64 (.f64 x #s(literal -1/8 binary64)) x) (.f64 (.f64 (*.f64 x x) #s(literal 1/16 binary64)) x))
(+.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (.f64 (.f64 x #s(literal 1/16 binary64)) (*.f64 x x)))
(+.f64 (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(fma.f64 x (.f64 x #s(literal -1/8 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/16 binary64))))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64)) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(fma.f64 #s(literal -1/8 binary64) (.f64 x x) (.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x) (.f64 #s(literal -1/8 binary64) (.f64 x x)))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) x (.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) x))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x #s(literal 1/16 binary64)) (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64)))) (-.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))) x)

simplify335.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

3066×	`-lowering-.f32`
3066×	`-lowering-.f64`
2358×	`fma-lowering-fma.f32`
2358×	`fma-lowering-fma.f64`
1864×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	1548
1	803	1354
2	2225	1330
3	6372	1327
0	8303	1327

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
2
(- 2 (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
2
(- 2 (* 8 (/ 1 x)))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
(/ 2 x)
(/ (+ 2 (* 1/2 x)) x)
(/ (+ 2 (* 1/2 x)) x)
(/ (+ 2 (* 1/2 x)) x)
1/2
(+ 1/2 (* 2 (/ 1 x)))
(+ 1/2 (* 2 (/ 1 x)))
(+ 1/2 (* 2 (/ 1 x)))
1/2
(+ 1/2 (* 2 (/ 1 x)))
(+ 1/2 (* 2 (/ 1 x)))
(+ 1/2 (* 2 (/ 1 x)))
2
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
2
(- 2 (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
2
(- 2 (* 8 (/ 1 x)))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
(* -1/4 x)
(* x (- (* -1/64 (pow x 2)) 1/4))
(* x (- (* (pow x 2) (- (* -1/1024 (pow x 2)) 1/64)) 1/4))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -1/16384 (pow x 2)) 1/1024)) 1/64)) 1/4))
(/ 4 x)
(/ (+ 4 (* 64 (/ 1 (pow x 2)))) x)
(/ (+ 4 (+ (* 64 (/ 1 (pow x 2))) (/ 1024 (pow x 4)))) x)
(/ (+ 4 (+ (* 64 (/ 1 (pow x 2))) (+ (* 16384 (/ 1 (pow x 6))) (/ 1024 (pow x 4))))) x)
(/ 4 x)
(/ (+ 4 (* 64 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 64 (* 1024 (/ 1 (pow x 2)))) (pow x 2))) 4) x))
(* -1 (/ (- (* -1 (/ (+ 1024 (* 16384 (/ 1 (pow x 2)))) (pow x 4))) (+ 4 (* 64 (/ 1 (pow x 2))))) x))
-4
(- (* 1/4 (pow x 2)) 4)
(- (* 1/4 (pow x 2)) 4)
(- (* 1/4 (pow x 2)) 4)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/4 (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(/ 16 (pow x 2))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))
(/ 16 (pow x 2))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))
(/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 3))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 3))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(* -1 (/ (- (* -1 (/ (- 32 (* 64 (/ 1 x))) x)) 16) (pow x 3)))
(* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (+ 64 (* 896 (/ 1 x))) x))) x)) 16) (pow x 3)))
2
(+ 2 (* 1/2 x))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))
2
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(/ x (+ 1 (sqrt x)))
(/ x (+ 1 (sqrt x)))
(/ x (+ 1 (sqrt x)))
(/ x (+ 1 (sqrt x)))
(sqrt x)
(- (sqrt x) 1)
(- (+ (sqrt x) (sqrt (/ 1 x))) 1)
(- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ x (pow (sqrt -1) 4))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) x))) x)))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-2
(- (* 1/2 x) 2)
(- (* 1/2 x) 2)
(- (* 1/2 x) 2)
(* 1/2 x)
(* x (- 1/2 (* 2 (/ 1 x))))
(* x (- 1/2 (* 2 (/ 1 x))))
(* x (- 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/32 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/32 binary64) (.f64 x #s(literal -1/128 binary64))))))))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x)) (/.f64 (/.f64 #s(literal -128 binary64) x) (*.f64 x x)))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 128 binary64) x) #s(literal -32 binary64)) x)) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* 1/2 x)) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(/ (+ 2 (* 1/2 x)) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(/ (+ 2 (* 1/2 x)) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ 1/2 (* 2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ 1/2 (* 2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ 1/2 (* 2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(+ 1/2 (* 2 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/32 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/32 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/32 (* -1/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/32 binary64) (.f64 x #s(literal -1/128 binary64))))))))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x))
(- (+ 2 (/ 32 (pow x 2))) (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x))
(- (+ 2 (/ 32 (pow x 2))) (+ (* 8 (/ 1 x)) (* 128 (/ 1 (pow x 3)))))
(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x)) (/.f64 (/.f64 #s(literal -128 binary64) x) (*.f64 x x)))
2
#s(literal 2 binary64)
(- 2 (* 8 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -8 binary64) x))
(+ 2 (* -1 (/ (- 8 (* 32 (/ 1 x))) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal -8 binary64)) x))
(+ 2 (* -1 (/ (+ 8 (* -1 (/ (- 32 (* 128 (/ 1 x))) x))) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 128 binary64) x) #s(literal -32 binary64)) x)) x))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* x (- (* -1/64 (pow x 2)) 1/4))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal -1/64 binary64)))))
(* x (- (* (pow x 2) (- (* -1/1024 (pow x 2)) 1/64)) 1/4))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/64 binary64) (.f64 (*.f64 x x) #s(literal -1/1024 binary64))))))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -1/16384 (pow x 2)) 1/1024)) 1/64)) 1/4))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/1024 binary64) (.f64 (*.f64 x x) #s(literal -1/16384 binary64))))))))
(/ 4 x)
(/.f64 #s(literal 4 binary64) x)
(/ (+ 4 (* 64 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 4 binary64) (/.f64 #s(literal 64 binary64) (*.f64 x x))) x)
(/ (+ 4 (+ (* 64 (/ 1 (pow x 2))) (/ 1024 (pow x 4)))) x)
(/.f64 (+.f64 #s(literal 4 binary64) (+.f64 (/.f64 #s(literal 64 binary64) (.f64 x x)) (/.f64 #s(literal 1024 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(/ (+ 4 (+ (* 64 (/ 1 (pow x 2))) (+ (* 16384 (/ 1 (pow x 6))) (/ 1024 (pow x 4))))) x)
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 64 binary64) (.f64 x x)) (/.f64 #s(literal 1024 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 16384 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 4 binary64))) x)
(/ 4 x)
(/.f64 #s(literal 4 binary64) x)
(/ (+ 4 (* 64 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 4 binary64) (/.f64 #s(literal 64 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 64 (* 1024 (/ 1 (pow x 2)))) (pow x 2))) 4) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -64 binary64) (/.f64 #s(literal -1024 binary64) (.f64 x x))) (.f64 x x)) #s(literal -4 binary64)) x))
(* -1 (/ (- (* -1 (/ (+ 1024 (* 16384 (/ 1 (pow x 2)))) (pow x 4))) (+ 4 (* 64 (/ 1 (pow x 2))))) x))
(/.f64 (+.f64 (+.f64 #s(literal 4 binary64) (/.f64 #s(literal 64 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal 1024 binary64) (/.f64 #s(literal 16384 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))) x)
-4
#s(literal -4 binary64)
(- (* 1/4 (pow x 2)) 4)
(+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -4 binary64))
(- (* 1/4 (pow x 2)) 4)
(+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -4 binary64))
(- (* 1/4 (pow x 2)) 4)
(+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* (pow x 2) (- 1/4 (* 4 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -5/128 binary64))))))))
(/ 16 (pow x 2))
(/.f64 #s(literal 16 binary64) (*.f64 x x))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) x) x)
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -64 binary64) x)) x)) (*.f64 x x))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (-.f64 #s(literal 32 binary64) (/.f64 (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)) x)) x)) (*.f64 x x))
(/ 16 (pow x 2))
(/.f64 #s(literal 16 binary64) (*.f64 x x))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) x) x)
(/ (+ 16 (* -1 (/ (- (* 64 (/ 1 x)) 32) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -64 binary64) x)) x)) (*.f64 x x))
(/ (+ 16 (* -1 (/ (- (+ (* 64 (/ 1 x)) (/ 896 (pow x 2))) 32) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 16 binary64) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 64 binary64) x) #s(literal -32 binary64)) (/.f64 #s(literal 896 binary64) (.f64 x x))) x)) (.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -5/128 binary64)))))))
(/ 16 (pow x 3))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) (.f64 x (.f64 x x)))
(/ (- (+ 16 (* 32 (/ 1 x))) (/ 64 (pow x 2))) (pow x 3))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -64 binary64) x)) x)) (.f64 x (.f64 x x)))
(/ (+ 16 (+ (* -1 (/ (+ 64 (* 896 (/ 1 x))) (pow x 2))) (* 32 (/ 1 x)))) (pow x 3))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (-.f64 #s(literal 32 binary64) (/.f64 (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)) x)) x)) (.f64 x (.f64 x x)))
(/ 16 (pow x 3))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 (/.f64 #s(literal 32 binary64) x) #s(literal 16 binary64)) (.f64 x (.f64 x x)))
(* -1 (/ (- (* -1 (/ (- 32 (* 64 (/ 1 x))) x)) 16) (pow x 3)))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 #s(literal -64 binary64) x)) x)) (.f64 x (.f64 x x)))
(* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (+ 64 (* 896 (/ 1 x))) x))) x)) 16) (pow x 3)))
(/.f64 (-.f64 #s(literal -16 binary64) (/.f64 (-.f64 #s(literal 32 binary64) (/.f64 (+.f64 #s(literal 64 binary64) (/.f64 #s(literal 896 binary64) x)) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (* 2 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (/.f64 #s(literal 2 binary64) (.f64 x (*.f64 x x)))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(.f64 (-.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)) (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2))) 1/8) x)) 1/16)))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/16 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))) x))))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(+ 2 (* 1/2 x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(* x (+ 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))
(/ x (+ 1 (sqrt x)))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ x (+ 1 (sqrt x)))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ x (+ 1 (sqrt x)))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ x (+ 1 (sqrt x)))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(- (+ (sqrt x) (sqrt (/ 1 x))) 1)
(+.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x))))
(+.f64 (+.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) x))
(* -1 (sqrt x))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) x)))
(-.f64 (/.f64 (-.f64 (sqrt.f64 x) x) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ x (pow (sqrt -1) 4))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) x))) x)))
(-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (sqrt.f64 (.f64 x (.f64 x x))) x)) x)))
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-2
#s(literal -2 binary64)
(- (* 1/2 x) 2)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(- (* 1/2 x) 2)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(- (* 1/2 x) 2)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (- 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* x (- 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* x (- 1/2 (* 2 (/ 1 x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* -1 (* x (- (* 2 (/ 1 x)) 1/2)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -2 binary64))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/16 x) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(* (pow x 2) (- (* 1/16 x) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(* (pow x 2) (- (* 1/16 x) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* 1/16 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/16 binary64)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))

eval158.0ms (1.6%)

Compiler: Compiled 17408 to 2198 computations (87.4% saved)

prune373.0ms (3.7%)

Pruning

33 alts after pruning (18 fresh and 15 done)

	Pruned	Kept	Total
New	945	12	957
Fresh	2	6	8
Picked	1	4	5
Done	0	11	11
Total	948	33	981

Accuracy

100.0%

Counts

981 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	38.2%	(/.f64 (-.f64 (.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
	65.9%	(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
	65.6%	(/.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
	56.7%	(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
✓	66.5%	(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
✓	65.6%	(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	65.6%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
✓	65.1%	(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
✓	66.5%	(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	40.2%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	66.0%	(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
	65.3%	(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
✓	65.6%	(/.f64 x #s(literal 2 binary64))
✓	66.3%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
	65.0%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
✓	65.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
	66.3%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
	66.3%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
✓	35.7%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
	66.0%	(*.f64 (/.f64 x (+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) x)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
	65.3%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
	65.4%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64)))))))
	5.9%	(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (*.f64 #s(literal 1/2 binary64) x))
	66.0%	(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
	66.0%	(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
	64.6%	(.f64 (/.f64 x (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
✓	65.6%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
	66.0%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
✓	65.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	36.6%	(sqrt.f64 x)
	41.0%	(neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
✓	4.7%	#s(literal 2 binary64)

Compiler

Compiled 1175 to 491 computations (58.2% saved)

regimes28.0ms (0.3%)

Counts

38 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(*.f64 (/.f64 x (+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) x)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
(/.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 x (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal -2 binary64))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))

Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Calls

2 calls:

14.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
11.0ms	x

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes35.0ms (0.3%)

Counts

36 → 2

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(*.f64 (/.f64 x (+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) x)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
(/.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 x (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal -2 binary64))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))

Outputs

(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 x (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
99.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes13.0ms (0.1%)

Counts

35 → 2

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(*.f64 (/.f64 x (+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) x)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
(/.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 x (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal -2 binary64))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Outputs

(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 x (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes13.0ms (0.1%)

Counts

33 → 2

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(*.f64 (/.f64 x (+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) x)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
(/.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 x (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal -2 binary64))))
(sqrt.f64 x)

Outputs
(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(sqrt.f64 x)

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes15.0ms (0.2%)

Counts

32 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x))
(/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) x))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 2 binary64)))
(/.f64 x (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) x) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 x x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(*.f64 (/.f64 x (+.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) x)) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 x (.f64 (-.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x)
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64))) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))
(/.f64 x (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 4 binary64)) x))))
(/.f64 (.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 x (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 x (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)))) (/.f64 x (.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (.f64 (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) (+.f64 (/.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64))))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -4 binary64)) x)))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 x (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal -4 binary64))) (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal -2 binary64))))

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

Calls

1 calls:

14.0ms

Results

Accuracy	Segments	Branch
66.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
66.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))

Outputs
(/.f64 x #s(literal 2 binary64))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
65.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

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

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
4.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch18.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	1.650643989105335e-10	0.07987076420712955

Results

8.0ms

144×

valid

Compiler

Compiled 274 to 198 computations (27.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (50.4% of total)

ival-div: 1.0ms (25.2% of total)

ival-sqrt: 1.0ms (25.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch16.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.07987076420712955	573586633517.2264

Results

9.0ms

160×

valid

Compiler

Compiled 263 to 189 computations (28.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (45.7% of total)

ival-div: 1.0ms (22.8% of total)

ival-sqrt: 1.0ms (22.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch21.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.07987076420712955	573586633517.2264

Results

14.0ms

160×

valid

Compiler

Compiled 243 to 169 computations (30.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (45.6% of total)

ival-div: 1.0ms (22.8% of total)

ival-sqrt: 1.0ms (22.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

28×	`unsub-neg_binary64`
28×	`+-commutative_binary64`
22×	`neg-mul-1_binary64`
16×	`*-commutative_binary64`
16×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	103
1	58	103
2	66	103
3	78	102
4	102	102
5	117	102
6	127	102
7	137	102
8	145	102

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 3458764513820541/2305843009213693952 binary64)) (/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal 3 binary64)) (/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal 8106479329266893/2251799813685248 binary64)) (/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 3458764513820541/2305843009213693952 binary64)) (/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal 3458764513820541/2305843009213693952 binary64)) (/.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal 3 binary64)) (/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal 3 binary64)) (/.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal 8106479329266893/2251799813685248 binary64)) (/.f64 x (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
(if (<=.f64 x #s(literal 8106479329266893/2251799813685248 binary64)) (/.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
(/.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)

soundness4.4s (43.5%)

Rules

4612×	`-lowering-.f32`
4612×	`-lowering-.f64`
3228×	`-lowering-.f32`
3228×	`-lowering-.f64`
3102×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	908
1	459	813
2	1267	778
3	3464	756
0	8220	756
0	270	1548
1	803	1354
2	2225	1330
3	6372	1327
0	8303	1327
0	17	79
1	112	69
2	952	69
0	8502	69
0	161	538
1	520	434
2	1993	412
3	7762	412
0	8435	412
0	6	21
1	42	21
2	328	20
3	3669	20
0	8084	20

Stop Event

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

Compiler

Compiled 270 to 160 computations (40.7% saved)

preprocess46.0ms (0.4%)

Compiler: Compiled 224 to 88 computations (60.7% saved)

analyze2.0ms (0%)

sample749.0ms (7.4%)

preprocess37.0ms (0.4%)

explain103.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize29.0ms (0.3%)

series34.0ms (0.3%)

rewrite265.0ms (2.6%)

simplify282.0ms (2.8%)

eval85.0ms (0.8%)

prune61.0ms (0.6%)

simplify20.0ms (0.2%)

localize127.0ms (1.2%)

series8.0ms (0.1%)

rewrite317.0ms (3.1%)

simplify289.0ms (2.8%)

eval93.0ms (0.9%)

prune126.0ms (1.2%)

simplify17.0ms (0.2%)

localize147.0ms (1.4%)

series8.0ms (0.1%)

rewrite385.0ms (3.8%)

simplify269.0ms (2.6%)

eval131.0ms (1.3%)

prune85.0ms (0.8%)

simplify260.0ms (2.6%)

localize285.0ms (2.8%)

series25.0ms (0.2%)

rewrite417.0ms (4.1%)

simplify335.0ms (3.3%)

eval158.0ms (1.6%)

prune373.0ms (3.7%)

regimes28.0ms (0.3%)

regimes35.0ms (0.3%)

regimes13.0ms (0.1%)

regimes13.0ms (0.1%)

regimes15.0ms (0.2%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch18.0ms (0.2%)

bsearch16.0ms (0.2%)

bsearch21.0ms (0.2%)

simplify17.0ms (0.2%)

soundness4.4s (43.5%)

preprocess46.0ms (0.4%)

end0.0ms (0%)

Profiling