Metrics for sqrt times

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
0%	0%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

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

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

ival-mult: 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)

sample698.0ms (8.9%)

Results

511.0ms	8251×	0	valid
1.0ms	5×	1	valid
1.0ms	12×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 278.0ms

ival-sqrt: 127.0ms (45.6% of total)

ival-sub: 78.0ms (28% of total)

ival-mult: 59.0ms (21.2% of total)

const: 12.0ms (4.3% of total)

backward-pass: 3.0ms (1.1% of total)

Bogosity

preprocess17.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

132×	`sum3-define`
84×	`fma-define`
38×	`sub-neg`
36×	`fmsub-define`
22×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (sqrt (- x 1)) (sqrt x))

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

Call 2

Inputs
(* (sqrt (- x 1)) (sqrt x))
(* (sqrt (- (neg x) 1)) (sqrt (neg x)))
(neg (* (sqrt (- (neg x) 1)) (sqrt (neg x))))

Outputs
(* (sqrt (- x 1)) (sqrt x))
(* (sqrt (+ x -1)) (sqrt x))
(* (sqrt (- (neg x) 1)) (sqrt (neg x)))
(* (sqrt (- -1 x)) (sqrt (neg x)))
(neg (* (sqrt (- (neg x) 1)) (sqrt (neg x))))
(fnmsub (sqrt (- -1 x)) (sqrt (neg x)) 0)

explain148.0ms (1.9%)

FPErrors

Click to see full error table

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

Results

127.0ms

512×

valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sqrt: 7.0ms (44.3% of total)

ival-sub: 4.0ms (25.3% of total)

ival-mult: 4.0ms (25.3% of total)

const: 1.0ms (6.3% of total)

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

eval1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

4×	`sqrt-lowering-sqrt.f64`
4×	`+-lowering-+.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`
4×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	12	18
2	13	18
0	13	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (sqrt (- x 1)) (sqrt x))
(sqrt (- x 1))
(- x 1)
x
1
(sqrt x)

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

localize32.0ms (0.4%)

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%	(sqrt.f64 x)
✓	accuracy	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

24.0ms

256×

valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 4.0ms (51.8% of total)

ival-sub: 2.0ms (25.9% of total)

ival-mult: 2.0ms (25.9% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (* (sqrt (- x 1)) (sqrt x))>
#<alt (sqrt (- x 1))>
#<alt (- x 1)>
#<alt (sqrt x)>

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

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(sqrt x)
1.0ms	x	@	0	(* (sqrt (- x 1)) (sqrt x))
1.0ms	x	@	-inf	(sqrt (- x 1))
1.0ms	x	@	inf	(sqrt (- x 1))
0.0ms	x	@	-inf	(* (sqrt (- x 1)) (sqrt x))

rewrite470.0ms (6%)

Algorithm

1×	batch-egg-rewrite

Rules

3242×	`/-lowering-/.f32`
3242×	`/-lowering-/.f64`
2606×	`-lowering-.f32`
2606×	`-lowering-.f64`
1554×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	30	15
2	162	14
3	1441	14
0	8204	14

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 383

Calls

Call 1

Inputs
(* (sqrt (- x 1)) (sqrt x))
(sqrt (- x 1))
(- x 1)
(sqrt x)

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

simplify248.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

3384×	`-lowering-.f32`
3384×	`-lowering-.f64`
1818×	`fma-lowering-fma.f32`
1818×	`fma-lowering-fma.f64`
1688×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	443
1	473	384
2	1772	358
3	5484	352
0	8134	352

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval53.0ms (0.7%)

Compiler: Compiled 13668 to 1672 computations (87.8% saved)

prune84.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	425	6	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	426	6	432

Accuracy

100.0%

Counts

432 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.8%	(pow.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/4 binary64))
▶	99.4%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
▶	99.2%	(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
▶	98.6%	(+.f64 x #s(literal -1/2 binary64))
▶	60.4%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
▶	97.4%	x

Compiler

Compiled 98 to 68 computations (30.6% saved)

simplify213.0ms (2.7%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

2074×	`sum3-define`
1968×	`fnmsub-define`
1848×	`fmm-def`
1740×	`fnmadd-define`
1672×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	85
1	41	84
2	76	82
3	128	82
4	213	81
5	454	81
6	1169	81
7	2656	81
8	5677	81
9	7474	81
0	8024	81

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize124.0ms (1.6%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal -1 binary64)))
✓	accuracy	60.4%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal -1/8 binary64) x)
✓	accuracy	100.0%	(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	accuracy	100.0%	(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)

Results

70.0ms

256×

valid

Compiler

Compiled 91 to 22 computations (75.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-div: 8.0ms (31.3% of total)

ival-add: 7.0ms (27.4% of total)

ival-sub: 3.0ms (11.8% of total)

ival-mult: 3.0ms (11.8% of total)

ival-sqrt: 2.0ms (7.8% of total)

const: 1.0ms (3.9% of total)

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

series6.0ms (0.1%)

Counts

12 → 144

Calls

Call 1

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

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

Calls

36 calls:

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

rewrite477.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4190×	`/-lowering-/.f32`
4190×	`/-lowering-/.f64`
3912×	`-lowering-.f32`
3912×	`-lowering-.f64`
2376×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	141	68
2	1329	66
0	8692	66

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 599

Calls

Call 1

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

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

simplify334.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

3102×	`-lowering-.f32`
3102×	`-lowering-.f64`
1976×	`sum5-define`
1616×	`+-lowering-+.f64`
1616×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	901
1	363	846
2	1108	710
3	3634	687
4	7722	687
0	8710	687

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval150.0ms (1.9%)

Compiler: Compiled 19236 to 2230 computations (88.4% saved)

prune86.0ms (1.1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	737	6	743
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	739	10	749

Accuracy

100.0%

Counts

749 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	36.2%	(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
▶	26.2%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
▶	59.5%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
✓	99.4%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
▶	99.2%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	98.6%	(+.f64 x #s(literal -1/2 binary64))
▶	36.1%	(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))))
	39.8%	(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64))))
✓	60.4%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	97.4%	x

Compiler

Compiled 411 to 188 computations (54.3% saved)

simplify272.0ms (3.4%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))
✓	cost-diff	128	(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))))
✓	cost-diff	0	(-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
✓	cost-diff	128	(+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	128	(.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))
✓	cost-diff	1024	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	cost-diff	0	(+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
✓	cost-diff	1408	(/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))
✓	cost-diff	0	(-.f64 #s(literal 1/4 binary64) (*.f64 x x))
✓	cost-diff	0	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x)
✓	cost-diff	0	(-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (*.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	cost-diff	384	(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
✓	cost-diff	0	(/.f64 #s(literal 1/8 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
✓	cost-diff	0	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
2372×	`+-lowering-+.f64`
2372×	`+-lowering-+.f32`
1922×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	548
1	158	530
2	595	488
3	2980	474
0	8723	474

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize310.0ms (3.9%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
✓	accuracy	39.7%	(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	66.0%	(-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
✓	accuracy	30.7%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
✓	accuracy	60.1%	(/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))
✓	accuracy	100.0%	(-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (*.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	100.0%	(*.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
✓	accuracy	99.9%	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x)
✓	accuracy	39.7%	(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1/8 binary64) x)
✓	accuracy	100.0%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))

Results

204.0ms

256×

valid

Compiler

Compiled 698 to 46 computations (93.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-div: 24.0ms (35.4% of total)

ival-mult: 19.0ms (28% of total)

ival-add: 14.0ms (20.6% of total)

ival-sub: 9.0ms (13.3% of total)

const: 1.0ms (1.5% of total)

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

series16.0ms (0.2%)

Counts

25 → 300

Calls

Call 1

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

Outputs
#<alt (/ -1/8 x)>
#<alt (/ (- (* -1/2 x) 1/8) x)>
#<alt (/ (- (* x (- x 1/2)) 1/8) x)>
#<alt (/ (- (* x (- x 1/2)) 1/8) x)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (/ 1/8 x)>
#<alt (/ (+ 1/8 (* 1/2 x)) x)>
#<alt (/ (+ 1/8 (* 1/2 x)) x)>
#<alt (/ (+ 1/8 (* 1/2 x)) x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* 1/8 (/ 1 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 x)>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))>
#<alt (/ 1/32 x)>
#<alt (/ (+ 1/32 (* 1/8 x)) x)>
#<alt (/ (+ 1/32 (* x (+ 1/8 (* 3/8 x)))) x)>
#<alt (/ (+ 1/32 (* x (+ 1/8 (* x (+ 3/8 (* -1 (pow x 2))))))) x)>
#<alt (* -1 (pow x 3))>
#<alt (* (pow x 3) (- (* 3/8 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (* 3/8 (/ 1 (pow x 2)))) 1))>
#<alt (* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (+ (* 3/8 (/ 1 (pow x 2))) (* 1/32 (/ 1 (pow x 4))))) 1))>
#<alt (* -1 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1 (* 3/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ 3/8 (* 1/8 (/ 1 x))) (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- (+ 1 (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) (pow x 3)))) (* 3/8 (/ 1 (pow x 2))))))>
#<alt (* 1/4 x)>
#<alt (* x (+ 1/4 (* -1 (pow x 2))))>
#<alt (* x (+ 1/4 (* -1 (pow x 2))))>
#<alt (* x (+ 1/4 (* -1 (pow x 2))))>
#<alt (* -1 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* -1 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1 (pow x 2)))>
#<alt (+ 1/4 (* -1 (pow x 2)))>
#<alt (+ 1/4 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))>
#<alt (* -16 (pow x 2))>
#<alt (* (pow x 2) (- (* 32 x) 16))>
#<alt (* (pow x 2) (- (* x (+ 32 (* 64 x))) 16))>
#<alt (* (pow x 2) (- (* x (+ 32 (* x (+ 64 (* -640 x))))) 16))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 1/2 (/ 1 x))) x)>
#<alt (/ (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) x)>
#<alt (/ (+ 1 (+ (/ 3/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 5/16 (/ 1 (pow x 3)))))) x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 1/2 (/ 1 x))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/2 (* 3/8 (/ 1 x))) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 3/8 (/ 1 x)))) x)) 1) x))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))>
#<alt (/ (+ 1/16 (* x (+ 1/8 (* x (+ 1/2 x))))) (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* x (+ 1 (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1)))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))>
#<alt (/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))>
#<alt (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))>
#<alt (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))>
#<alt 1/4>
#<alt (+ 1/4 (* 1/2 x))>
#<alt (+ 1/4 (* x (+ 1/2 x)))>
#<alt (+ 1/4 (* x (+ 1/2 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt 1/4>
#<alt (+ 1/4 (* 1/2 x))>
#<alt (+ 1/4 (* x (+ 1/2 x)))>
#<alt (+ 1/4 (* x (+ 1/2 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt -1/4>
#<alt (- (* -1/2 x) 1/4)>
#<alt (- (* x (- (* -3 x) 1/2)) 1/4)>
#<alt (- (* x (- (* x (- (* 4 x) 3)) 1/2)) 1/4)>
#<alt (* 8 (pow x 4))>
#<alt (* (pow x 4) (- 8 (* 4 (/ 1 x))))>
#<alt (* (pow x 4) (- (+ 8 (/ 1 (pow x 2))) (* 4 (/ 1 x))))>
#<alt (* (pow x 4) (- (+ 8 (/ 1 (pow x 2))) (+ (* 4 (/ 1 x)) (* 5/2 (/ 1 (pow x 3))))))>
#<alt (* 8 (pow x 4))>
#<alt (* (pow x 4) (- 8 (* 4 (/ 1 x))))>
#<alt (* (pow x 4) (+ 8 (* -1 (/ (- 4 (/ 1 x)) x))))>
#<alt (* (pow x 4) (+ 8 (* -1 (/ (+ 4 (* -1 (/ (- 1 (* 5/2 (/ 1 x))) x))) x))))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))>
#<alt (/ -1/4096 (pow x 6))>
#<alt (/ (- (* -3/2048 x) 1/4096) (pow x 6))>
#<alt (/ (- (* x (- (* -9/1024 x) 3/2048)) 1/4096) (pow x 6))>
#<alt (/ (- (* x (- (* x (- (* -13/512 x) 9/1024)) 3/2048)) 1/4096) (pow x 6))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (- 1 (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 1 (* -1 (/ (+ 1/8 (* 3/32 (/ 1 x))) (pow x 3)))))>
#<alt (* (pow x 3) (- (+ 1 (* -1 (/ (+ 3/32 (* 9/128 (/ 1 x))) (pow x 4)))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (pow x 3)>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 (pow x 3))) 1)))>
#<alt (* -1 (* (pow x 3) (- (+ (/ 3/32 (pow x 4)) (* 1/8 (/ 1 (pow x 3)))) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (+ 3/32 (* 9/128 (/ 1 x))) x)) 1/8) (pow x 3))) 1)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<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 (/ -1/32 x)>
#<alt (/ (- (* -1/8 x) 1/32) x)>
#<alt (/ (- (* x (- (* -1/8 x) 1/8)) 1/32) x)>
#<alt (/ (- (* x (- (* -1/8 x) 1/8)) 1/32) x)>
#<alt (* -1/8 x)>
#<alt (* -1 (* x (+ 1/8 (* 1/8 (/ 1 x)))))>
#<alt (* x (- (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) x)) 1/8))>
#<alt (* x (- (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) x)) 1/8))>
#<alt (* -1/8 x)>
#<alt (* -1 (* x (+ 1/8 (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1/8 (+ (/ 1/32 (pow x 2)) (* 1/8 (/ 1 x))))))>
#<alt (* -1 (* x (+ 1/8 (+ (/ 1/32 (pow x 2)) (* 1/8 (/ 1 x))))))>
#<alt (/ 1/256 (pow x 4))>
#<alt (/ (+ 1/256 (* 1/64 x)) (pow x 4))>
#<alt (/ (+ 1/256 (* x (+ 1/64 (* 5/64 x)))) (pow x 4))>
#<alt (/ (+ 1/256 (* x (+ 1/64 (* x (+ 5/64 (* 1/8 x)))))) (pow x 4))>
#<alt 1/4>
#<alt (+ 1/4 (* 1/8 (/ 1 x)))>
#<alt (+ 1/4 (+ (/ 5/64 (pow x 2)) (* 1/8 (/ 1 x))))>
#<alt (+ 1/4 (+ (/ 5/64 (pow x 2)) (+ (* 1/8 (/ 1 x)) (* 1/64 (/ 1 (pow x 3))))))>
#<alt 1/4>
#<alt (+ 1/4 (* 1/8 (/ 1 x)))>
#<alt (+ 1/4 (+ (/ 5/64 (pow x 2)) (* 1/8 (/ 1 x))))>
#<alt (+ 1/4 (* -1 (/ (- (* -1 (/ (+ 5/64 (* 1/64 (/ 1 x))) x)) 1/8) x)))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ 1/8 x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ 1/8 x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (* 4 (pow x 2))>
#<alt (* (pow x 2) (+ 4 (* 16 (pow x 2))))>
#<alt (* (pow x 2) (+ 4 (* (pow x 2) (+ 16 (* -32 x)))))>
#<alt (* (pow x 2) (+ 4 (* (pow x 2) (+ 16 (* x (- (* 64 x) 32))))))>
#<alt (* 8 (pow x 3))>
#<alt (* (pow x 3) (+ 8 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 8 (* 2 (/ 1 (pow x 2)))) (/ 1 (pow x 3))))>
#<alt (* (pow x 3) (- (+ 8 (+ (* 2 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 3))))>
#<alt (* 8 (pow x 3))>
#<alt (* (pow x 3) (+ 8 (* 2 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 3)) (+ 8 (* 2 (/ 1 (pow x 2)))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1) (pow x 3))) (+ 8 (* 2 (/ 1 (pow x 2)))))))>
#<alt (* 256 (pow x 4))>
#<alt (* (pow x 4) (+ 256 (* -1024 x)))>
#<alt (* (pow x 4) (+ 256 (* x (- (* -1024 x) 1024))))>
#<alt (* (pow x 4) (+ 256 (* x (- (* x (- (* 12288 x) 1024)) 1024))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (* 1/2 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))) (pow x 2))>
#<alt (/ (- (+ 1 (* 1/16 (/ 1 (pow x 3)))) (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (* 1/2 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))) x))) (pow x 2))>
#<alt (/ 1/4096 (pow x 6))>
#<alt (/ (+ 1/4096 (* 3/2048 x)) (pow x 6))>
#<alt (/ (+ 1/4096 (* x (+ 3/2048 (* 9/1024 x)))) (pow x 6))>
#<alt (/ (+ 1/4096 (* x (+ 3/2048 (* x (+ 9/1024 (* 13/512 x)))))) (pow x 6))>
#<alt 1/8>
#<alt (+ 1/8 (* 3/32 (/ 1 x)))>
#<alt (+ 1/8 (+ (/ 9/128 (pow x 2)) (* 3/32 (/ 1 x))))>
#<alt (+ 1/8 (+ (/ 9/128 (pow x 2)) (+ (* 3/32 (/ 1 x)) (* 13/512 (/ 1 (pow x 3))))))>
#<alt 1/8>
#<alt (+ 1/8 (* 3/32 (/ 1 x)))>
#<alt (+ 1/8 (+ (/ 9/128 (pow x 2)) (* 3/32 (/ 1 x))))>
#<alt (+ 1/8 (* -1 (/ (- (* -1 (/ (+ 9/128 (* 13/512 (/ 1 x))) x)) 3/32) x)))>

Calls

75 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(- (* x (* x x)) (* (+ 1/2 (/ (+ 1/8 (/ 1/16 x)) x)) (* (+ 1/2 (/ (+ 1/8 (/ 1/16 x)) x)) (+ 1/2 (/ (+ 1/8 (/ 1/16 x)) x)))))
0.0ms	x	@	-inf	(/ (+ x (+ 1/2 (/ (+ 1/8 (/ 1/16 x)) x))) (- (* x x) (* (+ 1/2 (/ (+ 1/8 (/ 1/16 x)) x)) (+ 1/2 (/ (+ 1/8 (/ 1/16 x)) x)))))
0.0ms	x	@	-inf	(/ (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) 1)) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
0.0ms	x	@	inf	(/ (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) 1)) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
0.0ms	x	@	inf	(* (- 1/4 (* x x)) x)

rewrite402.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2800×	`-lowering-.f32`
2800×	`-lowering-.f64`
2078×	`/-lowering-/.f32`
2078×	`/-lowering-/.f64`
1288×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	331
1	398	279
2	4324	279
0	8360	279

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 675

Calls

Call 1

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

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

simplify311.0ms (4%)

Algorithm

1×	egg-herbie

Rules

4666×	`+-lowering-+.f64`
4666×	`+-lowering-+.f32`
4606×	`-lowering-.f32`
4606×	`-lowering-.f64`
1494×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	469	2566
1	1399	2290
2	4209	2132
0	8430	2132

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

Inputs
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(/ 1/8 x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 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 x)
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(/ 1/32 x)
(/ (+ 1/32 (* 1/8 x)) x)
(/ (+ 1/32 (* x (+ 1/8 (* 3/8 x)))) x)
(/ (+ 1/32 (* x (+ 1/8 (* x (+ 3/8 (* -1 (pow x 2))))))) x)
(* -1 (pow x 3))
(* (pow x 3) (- (* 3/8 (/ 1 (pow x 2))) 1))
(* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (* 3/8 (/ 1 (pow x 2)))) 1))
(* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (+ (* 3/8 (/ 1 (pow x 2))) (* 1/32 (/ 1 (pow x 4))))) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (* 3/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ 3/8 (* 1/8 (/ 1 x))) (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1 (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) (pow x 3)))) (* 3/8 (/ 1 (pow x 2))))))
(* 1/4 x)
(* x (+ 1/4 (* -1 (pow x 2))))
(* x (+ 1/4 (* -1 (pow x 2))))
(* x (+ 1/4 (* -1 (pow x 2))))
(* -1 (pow x 3))
(* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))
1/4
(+ 1/4 (* -1 (pow x 2)))
(+ 1/4 (* -1 (pow x 2)))
(+ 1/4 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(* -16 (pow x 2))
(* (pow x 2) (- (* 32 x) 16))
(* (pow x 2) (- (* x (+ 32 (* 64 x))) 16))
(* (pow x 2) (- (* x (+ 32 (* x (+ 64 (* -640 x))))) 16))
(/ 1 x)
(/ (+ 1 (* 1/2 (/ 1 x))) x)
(/ (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) x)
(/ (+ 1 (+ (/ 3/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 5/16 (/ 1 (pow x 3)))))) x)
(/ 1 x)
(/ (+ 1 (* 1/2 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/2 (* 3/8 (/ 1 x))) x)) 1) x))
(* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 3/8 (/ 1 x)))) x)) 1) x))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))
(/ (+ 1/16 (* x (+ 1/8 (* x (+ 1/2 x))))) (pow x 2))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))))
(* x (+ 1 (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))
(/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
1/4
(+ 1/4 (* 1/2 x))
(+ 1/4 (* x (+ 1/2 x)))
(+ 1/4 (* x (+ 1/2 x)))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
1/4
(+ 1/4 (* 1/2 x))
(+ 1/4 (* x (+ 1/2 x)))
(+ 1/4 (* x (+ 1/2 x)))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
-1/4
(- (* -1/2 x) 1/4)
(- (* x (- (* -3 x) 1/2)) 1/4)
(- (* x (- (* x (- (* 4 x) 3)) 1/2)) 1/4)
(* 8 (pow x 4))
(* (pow x 4) (- 8 (* 4 (/ 1 x))))
(* (pow x 4) (- (+ 8 (/ 1 (pow x 2))) (* 4 (/ 1 x))))
(* (pow x 4) (- (+ 8 (/ 1 (pow x 2))) (+ (* 4 (/ 1 x)) (* 5/2 (/ 1 (pow x 3))))))
(* 8 (pow x 4))
(* (pow x 4) (- 8 (* 4 (/ 1 x))))
(* (pow x 4) (+ 8 (* -1 (/ (- 4 (/ 1 x)) x))))
(* (pow x 4) (+ 8 (* -1 (/ (+ 4 (* -1 (/ (- 1 (* 5/2 (/ 1 x))) x))) x))))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(/ -1/4096 (pow x 6))
(/ (- (* -3/2048 x) 1/4096) (pow x 6))
(/ (- (* x (- (* -9/1024 x) 3/2048)) 1/4096) (pow x 6))
(/ (- (* x (- (* x (- (* -13/512 x) 9/1024)) 3/2048)) 1/4096) (pow x 6))
(pow x 3)
(* (pow x 3) (- 1 (* 1/8 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 1 (* -1 (/ (+ 1/8 (* 3/32 (/ 1 x))) (pow x 3)))))
(* (pow x 3) (- (+ 1 (* -1 (/ (+ 3/32 (* 9/128 (/ 1 x))) (pow x 4)))) (* 1/8 (/ 1 (pow x 3)))))
(pow x 3)
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 (pow x 3))) 1)))
(* -1 (* (pow x 3) (- (+ (/ 3/32 (pow x 4)) (* 1/8 (/ 1 (pow x 3)))) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (+ 3/32 (* 9/128 (/ 1 x))) x)) 1/8) (pow x 3))) 1)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(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)
(/ -1/32 x)
(/ (- (* -1/8 x) 1/32) x)
(/ (- (* x (- (* -1/8 x) 1/8)) 1/32) x)
(/ (- (* x (- (* -1/8 x) 1/8)) 1/32) x)
(* -1/8 x)
(* -1 (* x (+ 1/8 (* 1/8 (/ 1 x)))))
(* x (- (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) x)) 1/8))
(* x (- (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) x)) 1/8))
(* -1/8 x)
(* -1 (* x (+ 1/8 (* 1/8 (/ 1 x)))))
(* -1 (* x (+ 1/8 (+ (/ 1/32 (pow x 2)) (* 1/8 (/ 1 x))))))
(* -1 (* x (+ 1/8 (+ (/ 1/32 (pow x 2)) (* 1/8 (/ 1 x))))))
(/ 1/256 (pow x 4))
(/ (+ 1/256 (* 1/64 x)) (pow x 4))
(/ (+ 1/256 (* x (+ 1/64 (* 5/64 x)))) (pow x 4))
(/ (+ 1/256 (* x (+ 1/64 (* x (+ 5/64 (* 1/8 x)))))) (pow x 4))
1/4
(+ 1/4 (* 1/8 (/ 1 x)))
(+ 1/4 (+ (/ 5/64 (pow x 2)) (* 1/8 (/ 1 x))))
(+ 1/4 (+ (/ 5/64 (pow x 2)) (+ (* 1/8 (/ 1 x)) (* 1/64 (/ 1 (pow x 3))))))
1/4
(+ 1/4 (* 1/8 (/ 1 x)))
(+ 1/4 (+ (/ 5/64 (pow x 2)) (* 1/8 (/ 1 x))))
(+ 1/4 (* -1 (/ (- (* -1 (/ (+ 5/64 (* 1/64 (/ 1 x))) x)) 1/8) x)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* 16 (pow x 2))))
(* (pow x 2) (+ 4 (* (pow x 2) (+ 16 (* -32 x)))))
(* (pow x 2) (+ 4 (* (pow x 2) (+ 16 (* x (- (* 64 x) 32))))))
(* 8 (pow x 3))
(* (pow x 3) (+ 8 (* 2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 8 (* 2 (/ 1 (pow x 2)))) (/ 1 (pow x 3))))
(* (pow x 3) (- (+ 8 (+ (* 2 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 3))))
(* 8 (pow x 3))
(* (pow x 3) (+ 8 (* 2 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 3)) (+ 8 (* 2 (/ 1 (pow x 2)))))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1) (pow x 3))) (+ 8 (* 2 (/ 1 (pow x 2)))))))
(* 256 (pow x 4))
(* (pow x 4) (+ 256 (* -1024 x)))
(* (pow x 4) (+ 256 (* x (- (* -1024 x) 1024))))
(* (pow x 4) (+ 256 (* x (- (* x (- (* 12288 x) 1024)) 1024))))
(/ 1 (pow x 2))
(/ (- 1 (* 1/2 (/ 1 x))) (pow x 2))
(/ (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))) (pow x 2))
(/ (- (+ 1 (* 1/16 (/ 1 (pow x 3)))) (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (* 1/2 (/ 1 x))) (pow x 2))
(/ (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))) (pow x 2))
(/ (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))) x))) (pow x 2))
(/ 1/4096 (pow x 6))
(/ (+ 1/4096 (* 3/2048 x)) (pow x 6))
(/ (+ 1/4096 (* x (+ 3/2048 (* 9/1024 x)))) (pow x 6))
(/ (+ 1/4096 (* x (+ 3/2048 (* x (+ 9/1024 (* 13/512 x)))))) (pow x 6))
1/8
(+ 1/8 (* 3/32 (/ 1 x)))
(+ 1/8 (+ (/ 9/128 (pow x 2)) (* 3/32 (/ 1 x))))
(+ 1/8 (+ (/ 9/128 (pow x 2)) (+ (* 3/32 (/ 1 x)) (* 13/512 (/ 1 (pow x 3))))))
1/8
(+ 1/8 (* 3/32 (/ 1 x)))
(+ 1/8 (+ (/ 9/128 (pow x 2)) (* 3/32 (/ 1 x))))
(+ 1/8 (* -1 (/ (- (* -1 (/ (+ 9/128 (* 13/512 (/ 1 x))) x)) 3/32) x)))

Outputs
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* -1/2 x) 1/8) x)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64)))))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64)))))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(+.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(+.f64 (+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal -1/16 binary64) (*.f64 x x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (.f64 x x)))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64)))))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(*.f64 x (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x))))
(/ 1/32 x)
(/.f64 #s(literal 1/32 binary64) x)
(/ (+ 1/32 (* 1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 x #s(literal 1/8 binary64))) x)
(/ (+ 1/32 (* x (+ 1/8 (* 3/8 x)))) x)
(/.f64 (+.f64 #s(literal 1/32 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 3/8 binary64))))) x)
(/ (+ 1/32 (* x (+ 1/8 (* x (+ 3/8 (* -1 (pow x 2))))))) x)
(/.f64 (+.f64 #s(literal 1/32 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (-.f64 #s(literal 3/8 binary64) (*.f64 x x)))))) x)
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 3/8 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))
(* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (* 3/8 (/ 1 (pow x 2)))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))
(* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (+ (* 3/8 (/ 1 (pow x 2))) (* 1/32 (/ 1 (pow x 4))))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (+.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 3/8 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/8 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ 3/8 (* 1/8 (/ 1 x))) (pow x 2))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -3/8 binary64) (/.f64 #s(literal -1/8 binary64) x)) (.f64 x x))))
(* -1 (* (pow x 3) (- (+ 1 (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) (pow x 3)))) (* 3/8 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/32 binary64) x)) (.f64 x (.f64 x x))) (/.f64 #s(literal -3/8 binary64) (.f64 x x)))))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* x (+ 1/4 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* x (+ 1/4 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* x (+ 1/4 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1 (* 1/4 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1 (pow x 2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x x))
(+ 1/4 (* -1 (pow x 2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x x))
(+ 1/4 (* -1 (pow x 2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/4 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* -16 (pow x 2))
(.f64 x (.f64 x #s(literal -16 binary64)))
(* (pow x 2) (- (* 32 x) 16))
(.f64 x (.f64 x (+.f64 #s(literal -16 binary64) (*.f64 x #s(literal 32 binary64)))))
(* (pow x 2) (- (* x (+ 32 (* 64 x))) 16))
(.f64 (.f64 x x) (+.f64 #s(literal -16 binary64) (.f64 x (+.f64 #s(literal 32 binary64) (.f64 x #s(literal 64 binary64))))))
(* (pow x 2) (- (* x (+ 32 (* x (+ 64 (* -640 x))))) 16))
(.f64 (.f64 x x) (+.f64 #s(literal -16 binary64) (.f64 x (+.f64 #s(literal 32 binary64) (.f64 x (+.f64 #s(literal 64 binary64) (*.f64 x #s(literal -640 binary64))))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)
(/ (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 3/8 binary64) (*.f64 x x)))) x)
(/ (+ 1 (+ (/ 3/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 5/16 (/ 1 (pow x 3)))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 #s(literal 5/16 binary64) (.f64 x x)) x)) #s(literal 1 binary64))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (+ 1/2 (* 3/8 (/ 1 x))) x)) 1) x))
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(* -1 (* x (+ 1/8 (+ (/ 1/32 (pow x 2)) (* 1/8 (/ 1 x))))))
(+.f64 #s(literal -1/8 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/32 binary64) (.f64 x x)))))
(* -1 (* x (+ 1/8 (+ (/ 1/32 (pow x 2)) (* 1/8 (/ 1 x))))))
(+.f64 #s(literal -1/8 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/32 binary64) (.f64 x x)))))
(/ 1/256 (pow x 4))
(/.f64 #s(literal 1/256 binary64) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ 1/256 (* 1/64 x)) (pow x 4))
(/.f64 (+.f64 #s(literal 1/256 binary64) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 x x) (.f64 x x)))
(/ (+ 1/256 (* x (+ 1/64 (* 5/64 x)))) (pow x 4))
(/.f64 (+.f64 #s(literal 1/256 binary64) (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 x #s(literal 5/64 binary64))))) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ 1/256 (* x (+ 1/64 (* x (+ 5/64 (* 1/8 x)))))) (pow x 4))
(/.f64 (+.f64 #s(literal 1/256 binary64) (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/8 binary64)) #s(literal 5/64 binary64)))))) (.f64 (.f64 x x) (.f64 x x)))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* 1/8 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/4 binary64))
(+ 1/4 (+ (/ 5/64 (pow x 2)) (* 1/8 (/ 1 x))))
(+.f64 (/.f64 #s(literal 1/8 binary64) x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))
(+ 1/4 (+ (/ 5/64 (pow x 2)) (+ (* 1/8 (/ 1 x)) (* 1/64 (/ 1 (pow x 3))))))
(+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal 5/64 binary64) (.f64 x x)) (/.f64 #s(literal 1/64 binary64) (.f64 x (*.f64 x x)))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* 1/8 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/4 binary64))
(+ 1/4 (+ (/ 5/64 (pow x 2)) (* 1/8 (/ 1 x))))
(+.f64 (/.f64 #s(literal 1/8 binary64) x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))
(+ 1/4 (* -1 (/ (- (* -1 (/ (+ 5/64 (* 1/64 (/ 1 x))) x)) 1/8) x)))
(-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 #s(literal 5/64 binary64) (/.f64 #s(literal 1/64 binary64) x)) x)) x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 x x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* (pow x 2) (+ 4 (* 16 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 x (.f64 x #s(literal 16 binary64)))))
(* (pow x 2) (+ 4 (* (pow x 2) (+ 16 (* -32 x)))))
(.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 x (.f64 x (+.f64 #s(literal 16 binary64) (*.f64 x #s(literal -32 binary64)))))))
(* (pow x 2) (+ 4 (* (pow x 2) (+ 16 (* x (- (* 64 x) 32))))))
(.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 16 binary64) (.f64 x (+.f64 (.f64 x #s(literal 64 binary64)) #s(literal -32 binary64)))))))
(* 8 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 8 binary64)))
(* (pow x 3) (+ 8 (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(* (pow x 3) (- (+ 8 (* 2 (/ 1 (pow x 2)))) (/ 1 (pow x 3))))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))))))
(* (pow x 3) (- (+ 8 (+ (* 2 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 3))))
(.f64 (.f64 x x) (.f64 x (+.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) (.f64 x (.f64 x x))))))
(* 8 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 8 binary64)))
(* (pow x 3) (+ 8 (* 2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 3)) (+ 8 (* 2 (/ 1 (pow x 2)))))))
(+.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1) (pow x 3))) (+ 8 (* 2 (/ 1 (pow x 2)))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) (.f64 x (.f64 x x))) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(* 256 (pow x 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 256 binary64))
(* (pow x 4) (+ 256 (* -1024 x)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 256 binary64) (*.f64 x #s(literal -1024 binary64))))
(* (pow x 4) (+ 256 (* x (- (* -1024 x) 1024))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 256 binary64) (.f64 x (+.f64 #s(literal -1024 binary64) (.f64 x #s(literal -1024 binary64))))))
(* (pow x 4) (+ 256 (* x (- (* x (- (* 12288 x) 1024)) 1024))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 256 binary64) (.f64 x (+.f64 #s(literal -1024 binary64) (.f64 x (+.f64 #s(literal -1024 binary64) (*.f64 x #s(literal 12288 binary64))))))))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/2 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)) (*.f64 x x))
(/ (- (+ 1 (* 1/16 (/ 1 (pow x 3)))) (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (pow x 2))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) x) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (* 1/2 (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) (*.f64 x x))
(/ 1/4096 (pow x 6))
(/.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal 6 binary64)))
(/ (+ 1/4096 (* 3/2048 x)) (pow x 6))
(/.f64 (+.f64 #s(literal 1/4096 binary64) (*.f64 x #s(literal 3/2048 binary64))) (pow.f64 x #s(literal 6 binary64)))
(/ (+ 1/4096 (* x (+ 3/2048 (* 9/1024 x)))) (pow x 6))
(/.f64 (+.f64 #s(literal 1/4096 binary64) (.f64 x (+.f64 #s(literal 3/2048 binary64) (.f64 x #s(literal 9/1024 binary64))))) (pow.f64 x #s(literal 6 binary64)))
(/ (+ 1/4096 (* x (+ 3/2048 (* x (+ 9/1024 (* 13/512 x)))))) (pow x 6))
(/.f64 (+.f64 #s(literal 1/4096 binary64) (.f64 x (+.f64 #s(literal 3/2048 binary64) (.f64 x (+.f64 #s(literal 9/1024 binary64) (*.f64 x #s(literal 13/512 binary64))))))) (pow.f64 x #s(literal 6 binary64)))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 3/32 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/32 binary64) x))
(+ 1/8 (+ (/ 9/128 (pow x 2)) (* 3/32 (/ 1 x))))
(+.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 #s(literal 3/32 binary64) x) (/.f64 #s(literal 9/128 binary64) (*.f64 x x))))
(+ 1/8 (+ (/ 9/128 (pow x 2)) (+ (* 3/32 (/ 1 x)) (* 13/512 (/ 1 (pow x 3))))))
(+.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/32 binary64) x)) (+.f64 (/.f64 #s(literal 9/128 binary64) (.f64 x x)) (/.f64 #s(literal 13/512 binary64) (.f64 x (*.f64 x x)))))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 3/32 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 3/32 binary64) x))
(+ 1/8 (+ (/ 9/128 (pow x 2)) (* 3/32 (/ 1 x))))
(+.f64 #s(literal 1/8 binary64) (+.f64 (/.f64 #s(literal 3/32 binary64) x) (/.f64 #s(literal 9/128 binary64) (*.f64 x x))))
(+ 1/8 (* -1 (/ (- (* -1 (/ (+ 9/128 (* 13/512 (/ 1 x))) x)) 3/32) x)))
(-.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal -3/32 binary64) (/.f64 (+.f64 #s(literal 9/128 binary64) (/.f64 #s(literal 13/512 binary64) x)) x)) x))

eval476.0ms (6%)

Compiler: Compiled 94436 to 4176 computations (95.6% saved)

prune155.0ms (2%)

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	1640	6	1646
Fresh	0	1	1
Picked	2	3	5
Done	0	4	4
Total	1642	14	1656

Accuracy

100.0%

Counts

1656 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	36.2%	(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
✓	36.2%	(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
▶	26.2%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
	18.7%	(/.f64 (-.f64 (.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x x)))))) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
▶	26.2%	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
▶	26.2%	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x)) (/.f64 (/.f64 #s(literal -5/2 binary64) (.f64 x x)) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	59.5%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
✓	99.4%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
✓	99.2%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	98.6%	(+.f64 x #s(literal -1/2 binary64))
	36.2%	(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) (.f64 x x)))
▶	39.8%	(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64))))
✓	60.4%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	97.4%	x

Compiler

Compiled 633 to 348 computations (45% saved)

simplify217.0ms (2.8%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x x) (*.f64 x x))
✓	cost-diff	128	(+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	256	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x)) (/.f64 (/.f64 #s(literal -5/2 binary64) (.f64 x x)) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	cost-diff	384	(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x)) (/.f64 (/.f64 #s(literal -5/2 binary64) (.f64 x x)) x))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	cost-diff	128	(+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	128	(-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64)))))
✓	cost-diff	768	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	cost-diff	0	(.f64 (.f64 x x) (*.f64 x x))
✓	cost-diff	0	(.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x)))
✓	cost-diff	128	(+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	256	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	cost-diff	0	(-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (*.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64))))
✓	cost-diff	0	(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
✓	cost-diff	128	(/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))
✓	cost-diff	128	(-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (*.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x)))
✓	cost-diff	0	(+.f64 (*.f64 x x) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	384	(/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64)))

Rules

3024×	`-lowering-.f32`
3024×	`-lowering-.f64`
2362×	`+-lowering-+.f64`
2362×	`+-lowering-+.f32`
1756×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	602
1	191	578
2	685	548
3	3246	527
0	8526	527

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (/ (* (+ (* x x) -1) x) (+ x 1)))
(/ (* (+ (* x x) -1) x) (+ x 1))
(* (+ (* x x) -1) x)
(+ (* x x) -1)
(* x x)
x
-1
(+ x 1)
1
(/ (- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16))) (* (- -1/2 x) x))
(- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16)))
(- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x)))
(* x (- 1/4 (* x x)))
x
(- 1/4 (* x x))
1/4
(* x x)
(* 1/8 (- -1/2 x))
1/8
(- -1/2 x)
-1/2
(/ (- -1/2 x) (/ x 1/16))
(/ x 1/16)
1/16
(* (- -1/2 x) x)
(/ (* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)))
(* (* x x) (* x x))
(* x x)
x
(- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x))
8
(/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)
(- 4 (/ (+ 1 (/ -5/2 x)) x))
4
(/ (+ 1 (/ -5/2 x)) x)
(+ 1 (/ -5/2 x))
1
(/ -5/2 x)
-5/2
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(+ (* x x) (- 1/4 (* x -1/2)))
(- 1/4 (* x -1/2))
1/4
(* x -1/2)
-1/2
(/ x (+ 1/8 (/ 1/16 x)))
(+ 1/8 (/ 1/16 x))
1/8
(/ 1/16 x)
1/16
(/ (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2))))
(* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x))))
(+ -1/8 (* x (* x x)))
-1/8
(* x (* x x))
x
(* x x)
(/ x (+ 1/8 (/ 1/16 x)))
(+ 1/8 (/ 1/16 x))
1/8
(/ 1/16 x)
1/16
(+ 1/4 (* x (+ x 1/2)))
1/4
(* x (+ x 1/2))
(+ x 1/2)
1/2
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(+ (* x x) (- 1/4 (* x -1/2)))
(- 1/4 (* x -1/2))
(* x -1/2)
-1/2
(/ (* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x))))
(* (* x x) (* x x))
(* x x)
x
(+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x)))
(/ 1 (* x x))
1
(+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x))
(+ 8 (/ -4 x))
8
(/ -4 x)
-4
(/ (/ -5/2 (* x x)) x)
(/ -5/2 (* x x))
-5/2
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(+ (* x x) (- 1/4 (* x -1/2)))
(- 1/4 (* x -1/2))
1/4
(* x -1/2)
-1/2
(/ x (+ 1/8 (/ 1/16 x)))
(+ 1/8 (/ 1/16 x))
1/8
(/ 1/16 x)
1/16

Outputs
(sqrt (/ (* (+ (* x x) -1) x) (+ x 1)))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
(/ (* (+ (* x x) -1) x) (+ x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (+ (* x x) -1) x)
(.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))
(+ (* x x) -1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(* x x)
(*.f64 x x)
x
-1
#s(literal -1 binary64)
(+ x 1)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(/ (- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16))) (* (- -1/2 x) x))
(-.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal -1/2 binary64) x)) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) x))) (/.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1 binary64)) x))
(- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16)))
(+.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x x))))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/32 binary64) x)))
(- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x)))
(+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(* x (- 1/4 (* x x)))
(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x)))
x
(- 1/4 (* x x))
(-.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
(* 1/8 (- -1/2 x))
(-.f64 #s(literal -1/16 binary64) (*.f64 x #s(literal 1/8 binary64)))
1/8
#s(literal 1/8 binary64)
(- -1/2 x)
(-.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(/ (- -1/2 x) (/ x 1/16))
(+.f64 (/.f64 #s(literal -1/32 binary64) x) #s(literal -1/16 binary64))
(/ x 1/16)
(/.f64 x #s(literal 1/16 binary64))
1/16
#s(literal 1/16 binary64)
(* (- -1/2 x) x)
(*.f64 x (-.f64 #s(literal -1/2 binary64) x))
(/ (* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(.f64 (+.f64 #s(literal 8 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64)) x) #s(literal -4 binary64)) x)) (/.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 #s(literal -1/2 binary64) x)))))
(* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 8 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64)) x) #s(literal -4 binary64)) x)))
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
x
(- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x))
(+.f64 #s(literal 8 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64)) x) #s(literal -4 binary64)) x))
8
#s(literal 8 binary64)
(/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)
(/.f64 (+.f64 #s(literal 4 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x)
(- 4 (/ (+ 1 (/ -5/2 x)) x))
(+.f64 #s(literal 4 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x))
4
#s(literal 4 binary64)
(/ (+ 1 (/ -5/2 x)) x)
(/.f64 (+.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64)) x)
(+ 1 (/ -5/2 x))
(+.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(/ -5/2 x)
(/.f64 #s(literal -5/2 binary64) x)
-5/2
#s(literal -5/2 binary64)
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(+ (* x x) (- 1/4 (* x -1/2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 #s(literal -1/2 binary64) x)))
(- 1/4 (* x -1/2))
(+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)))
1/4
#s(literal 1/4 binary64)
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ x (+ 1/8 (/ 1/16 x)))
(/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(+ 1/8 (/ 1/16 x))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
1/8
#s(literal 1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
(/ (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) x)))) (.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 #s(literal -1 binary64) x)))
(- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2))))
(+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (-.f64 #s(literal -1/2 binary64) x))))
(* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x))))
(/.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(+ -1/8 (* x (* x x)))
(+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))
-1/8
#s(literal -1/8 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(/ x (+ 1/8 (/ 1/16 x)))
(/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(+ 1/8 (/ 1/16 x))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
1/8
#s(literal 1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
(+ 1/4 (* x (+ x 1/2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 #s(literal -1/2 binary64) x)))
1/4
#s(literal 1/4 binary64)
(* x (+ x 1/2))
(*.f64 x (+.f64 x #s(literal 1/2 binary64)))
(+ x 1/2)
(+.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(+ (* x x) (- 1/4 (* x -1/2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 #s(literal -1/2 binary64) x)))
(- 1/4 (* x -1/2))
(+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ (* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 (.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x))) (+.f64 (.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) x)))))
(* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x))) (+.f64 (*.f64 (/.f64 #s(literal -5/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(* (* x x) (* x x))
(.f64 x (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
x
(+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x)))
(+.f64 (+.f64 (/.f64 #s(literal -4 binary64) x) (/.f64 #s(literal -5/2 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/ 1 (* x x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x))
(+.f64 (/.f64 #s(literal -4 binary64) x) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -5/2 binary64) (.f64 x (.f64 x x)))))
(+ 8 (/ -4 x))
(+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x))
8
#s(literal 8 binary64)
(/ -4 x)
(/.f64 #s(literal -4 binary64) x)
-4
#s(literal -4 binary64)
(/ (/ -5/2 (* x x)) x)
(/.f64 #s(literal -5/2 binary64) (.f64 x (.f64 x x)))
(/ -5/2 (* x x))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
-5/2
#s(literal -5/2 binary64)
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 #s(literal -1/2 binary64) x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(+ (* x x) (- 1/4 (* x -1/2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 #s(literal -1/2 binary64) x)))
(- 1/4 (* x -1/2))
(+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)))
1/4
#s(literal 1/4 binary64)
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ x (+ 1/8 (/ 1/16 x)))
(/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(+ 1/8 (/ 1/16 x))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
1/8
#s(literal 1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)

localize527.0ms (6.7%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	98.7%	(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
✓	accuracy	30.7%	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x)) (/.f64 (/.f64 #s(literal -5/2 binary64) (.f64 x x)) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	66.0%	(-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64)))))
✓	accuracy	30.7%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
✓	accuracy	99.8%	(.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	30.7%	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
✓	accuracy	100.0%	(-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (*.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64))))
✓	accuracy	100.0%	(-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (*.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	99.9%	(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x)))
✓	accuracy	39.7%	(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x)
✓	accuracy	80.1%	(/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64)))
✓	accuracy	60.4%	(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64))))

Results

351.0ms

256×

valid

Compiler

Compiled 688 to 63 computations (90.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 137.0ms

ival-div: 55.0ms (40% of total)

ival-add: 34.0ms (24.7% of total)

ival-mult: 32.0ms (23.3% of total)

ival-sub: 12.0ms (8.7% of total)

ival-sqrt: 2.0ms (1.5% of total)

const: 2.0ms (1.5% of total)

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

series13.0ms (0.2%)

Counts

24 → 288

Calls

Call 1

Inputs
#<alt (/ (* (+ (* x x) -1) x) (+ x 1))>
#<alt (sqrt (/ (* (+ (* x x) -1) x) (+ x 1)))>
#<alt (* (+ (* x x) -1) x)>
#<alt (+ (* x x) -1)>
#<alt (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x)))>
#<alt (/ (- -1/2 x) (/ x 1/16))>
#<alt (/ (- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16))) (* (- -1/2 x) x))>
#<alt (- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16)))>
#<alt (/ (* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))>
#<alt (+ (* x x) (- 1/4 (* x -1/2)))>
#<alt (* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)))>
#<alt (* (* x x) (* x x))>
#<alt (/ (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))>
#<alt (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2))))>
#<alt (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x))))>
#<alt (* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x))))>
#<alt (/ (* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))>
#<alt (* x x)>
#<alt (* x (- 1/4 (* x x)))>
#<alt (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))>
#<alt (/ x (+ 1/8 (/ 1/16 x)))>
#<alt (* x (* x x))>
#<alt (/ -5/2 (* x x))>
#<alt (/ 1 (* x x))>

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

Calls

72 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)))
1.0ms	x	@	-inf	(sqrt (/ (* (+ (* x x) -1) x) (+ x 1)))
0.0ms	x	@	0	(/ (* (+ (* x x) -1) x) (+ x 1))
0.0ms	x	@	-inf	(/ (* (+ (* x x) -1) x) (+ x 1))
0.0ms	x	@	inf	(/ (* (+ (* x x) -1) x) (+ x 1))

rewrite439.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3354×	`-lowering-.f32`
3354×	`-lowering-.f64`
3162×	`/-lowering-/.f32`
3162×	`/-lowering-/.f64`
1400×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	319
1	503	289
2	5727	287
0	8447	287

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 576

Calls

Call 1

Inputs
(/ (* (+ (* x x) -1) x) (+ x 1))
(sqrt (/ (* (+ (* x x) -1) x) (+ x 1)))
(* (+ (* x x) -1) x)
(+ (* x x) -1)
(- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x)))
(/ (- -1/2 x) (/ x 1/16))
(/ (- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16))) (* (- -1/2 x) x))
(- (- (* x (- 1/4 (* x x))) (* 1/8 (- -1/2 x))) (/ (- -1/2 x) (/ x 1/16)))
(/ (* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(+ (* x x) (- 1/4 (* x -1/2)))
(* (* (* x x) (* x x)) (- 8 (/ (- 4 (/ (+ 1 (/ -5/2 x)) x)) x)))
(* (* x x) (* x x))
(/ (- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(- (* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x)))) (+ 1/4 (* x (+ x 1/2))))
(* (+ -1/8 (* x (* x x))) (/ x (+ 1/8 (/ 1/16 x))))
(* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x))))
(/ (* (* (* x x) (* x x)) (+ (/ 1 (* x x)) (+ (+ 8 (/ -4 x)) (/ (/ -5/2 (* x x)) x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x)))))
(* x x)
(* x (- 1/4 (* x x)))
(* (+ (* x x) (- 1/4 (* x -1/2))) (/ x (+ 1/8 (/ 1/16 x))))
(/ x (+ 1/8 (/ 1/16 x)))
(* x (* x x))
(/ -5/2 (* x x))
(/ 1 (* x x))

Outputs
(neg.f64 (/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) x) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) x) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (neg.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
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(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (-.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x x)))))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 x #s(literal -1/2 binary64))))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (-.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x x)))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/16 binary64) x))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (+.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 x #s(literal 1/2 binary64))))))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/64 binary64) (.f64 (/.f64 #s(literal 1/16 binary64) x) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x)))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(neg.f64 (/.f64 x (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/16 binary64) x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (neg.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/16 binary64) x)))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(*.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/16 binary64) x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) x)
(.f64 (/.f64 x (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/64 binary64) (.f64 (/.f64 #s(literal 1/16 binary64) x) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)))))
(.f64 (/.f64 x (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x)))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(neg.f64 (/.f64 #s(literal 5/2 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) #s(literal -5/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -5/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) #s(literal -5/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -5/2 binary64) x)))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/.f64 #s(literal -5/2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal -5/2 binary64) x) x)
(/.f64 #s(literal 5/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (/.f64 #s(literal -5/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (*.f64 x x) #s(literal -5/2 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) (.f64 x x)))
(.f64 #s(literal -5/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal -5/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -5/2 binary64))
(.f64 #s(literal 5/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 x #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 (.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))

simplify507.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

5498×	`-lowering-.f32`
5498×	`-lowering-.f64`
2620×	`+-lowering-+.f64`
2620×	`+-lowering-+.f32`
1654×	`neg-lowering-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	411	2411
1	1294	2141
2	4097	2022
0	8763	2022

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

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

Outputs
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- x 1))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* x (- x 1))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* x (- x 1))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x)) x)))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (pow x 2) 1))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x)))
(* x (- (pow x 2) 1))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x)))
(* x (- (pow x 2) 1))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(pow x 3)
(.f64 x (.f64 x x))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(+.f64 #s(literal -1 binary64) (*.f64 x x))
(- (pow x 2) 1)
(+.f64 #s(literal -1 binary64) (*.f64 x x))
(- (pow x 2) 1)
(+.f64 #s(literal -1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 3/8 x))
(+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 3/8 binary64)))
(+ 1/16 (* x (+ 3/8 (* -1 (pow x 2)))))
(+.f64 #s(literal 1/16 binary64) (.f64 x (-.f64 #s(literal 3/8 binary64) (.f64 x x))))
(+ 1/16 (* x (+ 3/8 (* -1 (pow x 2)))))
(+.f64 #s(literal 1/16 binary64) (.f64 x (-.f64 #s(literal 3/8 binary64) (.f64 x x))))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 3/8 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))
(* (pow x 3) (- (+ (/ 1/16 (pow x 3)) (* 3/8 (/ 1 (pow x 2)))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))))
(* (pow x 3) (- (+ (/ 1/16 (pow x 3)) (* 3/8 (/ 1 (pow x 2)))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 3/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ 3/8 (* 1/16 (/ 1 x))) (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3/8 binary64)) (.f64 x x))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ 3/8 (* 1/16 (/ 1 x))) (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3/8 binary64)) (.f64 x x))))
(/ -1/32 x)
(/.f64 #s(literal -1/32 binary64) x)
(/ (- (* -1/16 x) 1/32) x)
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(/ (- (* -1/16 x) 1/32) x)
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(/ (- (* -1/16 x) 1/32) x)
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
-1/16
#s(literal -1/16 binary64)
(* -1 (+ 1/16 (* 1/32 (/ 1 x))))
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(* -1 (+ 1/16 (* 1/32 (/ 1 x))))
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(* -1 (+ 1/16 (* 1/32 (/ 1 x))))
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
-1/16
#s(literal -1/16 binary64)
(* -1 (+ 1/16 (* 1/32 (/ 1 x))))
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(* -1 (+ 1/16 (* 1/32 (/ 1 x))))
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(* -1 (+ 1/16 (* 1/32 (/ 1 x))))
(+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/2 binary64))))) (*.f64 x x))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 x #s(literal -1/2 binary64)))))) (*.f64 x x))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 #s(literal -1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
(/ 1/32 x)
(/.f64 #s(literal 1/32 binary64) x)
(/ (+ 1/32 (* 1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/32 binary64) (*.f64 x #s(literal 1/8 binary64))) x)
(/ (+ 1/32 (* x (+ 1/8 (* 3/8 x)))) x)
(/.f64 (+.f64 #s(literal 1/32 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x #s(literal 3/8 binary64))))) x)
(/ (+ 1/32 (* x (+ 1/8 (* x (+ 3/8 (* -1 (pow x 2))))))) x)
(/.f64 (+.f64 #s(literal 1/32 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (-.f64 #s(literal 3/8 binary64) (*.f64 x x)))))) x)
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (* 3/8 (/ 1 (pow x 2))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))
(* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (* 3/8 (/ 1 (pow x 2)))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))))
(* (pow x 3) (- (+ (/ 1/8 (pow x 3)) (+ (* 3/8 (/ 1 (pow x 2))) (* 1/32 (/ 1 (pow x 4))))) 1))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 3/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1/32 binary64) (.f64 (.f64 x (*.f64 x x)) x))))))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (* 3/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ 3/8 (* 1/8 (/ 1 x))) (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 3/8 binary64)) (.f64 x x))))
(* -1 (* (pow x 3) (- (+ 1 (* -1 (/ (+ 1/8 (* 1/32 (/ 1 x))) (pow x 3)))) (* 3/8 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/32 binary64) x)) (.f64 x (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x)))))
(/ -5/8 x)
(/.f64 #s(literal -5/8 binary64) x)
(/ (- (* 1/4 x) 5/8) x)
(+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -5/8 binary64) x))
(/ (- (* x (+ 1/4 (* 3/2 x))) 5/8) x)
(+.f64 (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal -5/8 binary64) x))
(/ (- (* x (+ 1/4 (* x (+ 3/2 (* -4 x))))) 5/8) x)
(+.f64 (.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal 3/2 binary64) (*.f64 x #s(literal -4 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal -5/8 binary64) x))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 #s(literal -1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* 1/2 x))
(+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1/4 (* x (+ 1/2 x)))
(+.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 x #s(literal 1/2 binary64))))
(+ 1/4 (* x (+ 1/2 x)))
(+.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 x #s(literal 1/2 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))))
(* (pow x 2) (+ 1 (+ (/ 1/4 (pow x 2)) (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))))
(* -5/2 x)
(*.f64 x #s(literal -5/2 binary64))
(* x (- x 5/2))
(*.f64 x (+.f64 x #s(literal -5/2 binary64)))
(* x (- (* x (+ 1 (* -4 x))) 5/2))
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(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/ -5/2 (pow x 2))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/ -5/2 (pow x 2))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/ -5/2 (pow x 2))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/ -5/2 (pow x 2))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/ -5/2 (pow x 2))
(/.f64 #s(literal -5/2 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

eval169.0ms (2.1%)

Compiler: Compiled 59477 to 3075 computations (94.8% saved)

prune168.0ms (2.1%)

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	1372	7	1379
Fresh	1	1	2
Picked	5	0	5
Done	1	6	7
Total	1379	14	1393

Accuracy

100.0%

Counts

1393 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.2%	(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
	36.2%	(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
✓	36.2%	(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
	26.3%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
	36.2%	(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 x #s(literal -1/2 binary64)))))) (*.f64 x x))
	26.2%	(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))))))
	26.3%	(/.f64 (.f64 x (+.f64 #s(literal -5/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
	60.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
✓	99.4%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
✓	99.2%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	98.6%	(+.f64 x #s(literal -1/2 binary64))
	36.2%	(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) (.f64 x x)))
✓	60.4%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	97.4%	x

Compiler

Compiled 1006 to 361 computations (64.1% saved)

regimes19.0ms (0.2%)

Counts

26 → 1

Calls

Call 1

Inputs
x
(+.f64 x #s(literal -1/2 binary64))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 x #s(literal -1/2 binary64)))))) (*.f64 x x))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1/32 binary64) x))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (-.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 #s(literal 1/8 binary64) (-.f64 #s(literal -1/2 binary64) x))) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x #s(literal 1/16 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (.f64 x (+.f64 #s(literal -5/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))))))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 8 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -5/2 binary64) x)) x)) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -4 binary64) x)) (/.f64 (/.f64 #s(literal -5/2 binary64) (.f64 x x)) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
(/.f64 (-.f64 (.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x x)))))) x) (.f64 (-.f64 #s(literal -1/2 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (+.f64 #s(literal 8 binary64) (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 x #s(literal 1/2 binary64))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) (.f64 x x)))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64))))
(pow.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

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

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
8.0ms	x

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.6%	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
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
97.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

32×	`+-commutative_binary64`
24×	`sub-neg_binary64`
20×	`*-commutative_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	22	22
2	37	22
3	58	22
4	75	22
5	91	22
6	98	22
7	101	22
8	102	22

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness677.0ms (8.6%)

Rules

3384×	`-lowering-.f32`
3384×	`-lowering-.f64`
3102×	`-lowering-.f32`
3102×	`-lowering-.f64`
1976×	`sum5-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	443
1	473	384
2	1772	358
3	5484	352
0	8134	352
0	127	901
1	363	846
2	1108	710
3	3634	687
4	7722	687
0	8710	687

Stop Event

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

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess27.0ms (0.3%)

Compiler: Compiled 62 to 40 computations (35.5% saved)

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7

analyze2.0ms (0%)

sample698.0ms (8.9%)

preprocess17.0ms (0.2%)

explain148.0ms (1.9%)

eval1.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize32.0ms (0.4%)

series6.0ms (0.1%)

rewrite470.0ms (6%)

simplify248.0ms (3.2%)

eval53.0ms (0.7%)

prune84.0ms (1.1%)

simplify213.0ms (2.7%)

localize124.0ms (1.6%)

series6.0ms (0.1%)

rewrite477.0ms (6.1%)

simplify334.0ms (4.2%)

eval150.0ms (1.9%)

prune86.0ms (1.1%)

simplify272.0ms (3.4%)

localize310.0ms (3.9%)

series16.0ms (0.2%)

rewrite402.0ms (5.1%)

simplify311.0ms (4%)

eval476.0ms (6%)

prune155.0ms (2%)

simplify217.0ms (2.8%)

localize527.0ms (6.7%)

series13.0ms (0.2%)

rewrite439.0ms (5.6%)

simplify507.0ms (6.4%)

eval169.0ms (2.1%)

prune168.0ms (2.1%)

regimes19.0ms (0.2%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify17.0ms (0.2%)

soundness677.0ms (8.6%)

preprocess27.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7