Metrics for sqrt times

analyze5.0ms (0.1%)

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-sqrt: 1.0ms (88% of total)

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

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

const: 0.0ms (0% of total)

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

sample684.0ms (9.2%)

Results

489.0ms	8248×	0	valid
1.0ms	8×	1	valid
1.0ms	13×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 268.0ms

ival-sqrt: 137.0ms (51.2% of total)

ival-sub: 58.0ms (21.7% of total)

ival-mult: 57.0ms (21.3% of total)

const: 12.0ms (4.5% of total)

backward-pass: 4.0ms (1.5% of total)

Bogosity

preprocess81.0ms (1.1%)

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)

explain88.0ms (1.2%)

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

68.0ms

512×

valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sqrt: 7.0ms (46.9% of total)

ival-sub: 3.0ms (20.1% of total)

ival-mult: 3.0ms (20.1% of total)

const: 1.0ms (6.7% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.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)

localize31.0ms (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	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

22.0ms

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 (48.1% of total)

ival-sub: 2.0ms (24% of total)

ival-mult: 2.0ms (24% of total)

const: 0.0ms (0% of total)

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

series5.0ms (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
1.0ms	x	@	0	(* (sqrt (- x 1)) (sqrt x))
1.0ms	x	@	-inf	(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))

rewrite450.0ms (6.1%)

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	1452	14
0	8323	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 (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 (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 x) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x 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 (sqrt.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 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 (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 (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 x) (.f64 (.f64 x 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 (.f64 x 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))
(.f64 (sqrt.f64 (/.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))))) (sqrt.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x 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 x) (.f64 (.f64 x 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 x) (.f64 (.f64 x 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 (.f64 x 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 x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x 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 x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #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 x) (.f64 (.f64 x 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 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 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)))

simplify252.0ms (3.4%)

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	482	384
2	1842	358
3	5535	352
0	8190	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 x (.f64 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 (-.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))) (-.f64 #s(literal 0 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 x (-.f64 (neg.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 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (-.f64 (.f64 #s(literal -1/16 binary64) (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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))))
-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)

eval55.0ms (0.7%)

Compiler: Compiled 13660 to 1676 computations (87.7% saved)

prune51.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	426	5	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	427	5	432

Accuracy

100.0%

Counts

432 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(+.f64 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 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
▶	99.1%	(+.f64 x #s(literal -1/2 binary64))
▶	53.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
▶	97.8%	x

Compiler

Compiled 70 to 52 computations (25.7% saved)

simplify206.0ms (2.8%)

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

2316×	`fnmadd-define`
2278×	`sum3-define`
1678×	`fmsub-define`
1668×	`fnmsub-define`
1606×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	85
1	37	83
2	72	81
3	91	81
4	103	81
5	116	81
6	151	81
7	250	81
8	572	81
9	1464	81
10	2289	81
11	2818	81
12	3399	81
13	4931	81
14	7972	81
0	8122	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 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x) (+.f64 x #s(literal -1/2 binary64)))
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)

localize119.0ms (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	53.7%	(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 -1/8 binary64) (/.f64 #s(literal -1/16 binary64) 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 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)

Results

92.0ms

256×

valid

Compiler

Compiled 91 to 20 computations (78% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-add: 11.0ms (46.3% of total)

ival-div: 6.0ms (25.2% of total)

ival-mult: 4.0ms (16.8% of total)

ival-sqrt: 2.0ms (8.4% of total)

const: 1.0ms (4.2% of total)

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

series28.0ms (0.4%)

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 (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt -1/2>
#<alt (* -1 (+ 1/2 (* 1/8 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)>
#<alt (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)>
#<alt -1/2>
#<alt (* -1 (+ 1/2 (* 1/8 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)>
#<alt (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ -1/8 x)>
#<alt (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (/ -1/8 x)>
#<alt (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (/ -1/16 x)>
#<alt (/ (- (* -1/8 x) 1/16) x)>
#<alt (/ (- (* -1/8 x) 1/16) x)>
#<alt (/ (- (* -1/8 x) 1/16) x)>
#<alt -1/8>
#<alt (* -1 (+ 1/8 (* 1/16 (/ 1 x))))>
#<alt (* -1 (+ 1/8 (* 1/16 (/ 1 x))))>
#<alt (* -1 (+ 1/8 (* 1/16 (/ 1 x))))>
#<alt -1/8>
#<alt (* -1 (+ 1/8 (* 1/16 (/ 1 x))))>
#<alt (* -1 (+ 1/8 (* 1/16 (/ 1 x))))>
#<alt (* -1 (+ 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	@	inf	(* x (+ x -1))
0.0ms	x	@	-inf	(+ x (+ -1/2 (/ (+ -1/8 (/ -1/16 x)) x)))
0.0ms	x	@	0	(+ x (+ -1/2 (/ (+ -1/8 (/ -1/16 x)) x)))
0.0ms	x	@	0	(* (+ -1/2 (/ -1/8 x)) 1)
0.0ms	x	@	-inf	(/ (+ -1/8 (/ -1/16 x)) x)

rewrite443.0ms (6%)

Algorithm

1×	batch-egg-rewrite

Rules

4224×	`/-lowering-/.f32`
4224×	`/-lowering-/.f64`
4176×	`-lowering-.f32`
4176×	`-lowering-.f64`
2502×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	69
1	137	67
2	1348	65
0	8863	65

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 673

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

simplify384.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

3164×	`-lowering-.f32`
3164×	`-lowering-.f64`
1668×	`+-lowering-+.f64`
1668×	`+-lowering-+.f32`
1660×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	904
1	363	837
2	1092	705
3	3650	682
4	7817	682
0	8659	682

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

eval217.0ms (2.9%)

Compiler: Compiled 22491 to 2509 computations (88.8% saved)

prune99.0ms (1.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	814	3	817
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	815	7	822

Accuracy

100.0%

Counts

822 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.0%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
▶	35.0%	(/.f64 (+.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 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
▶	99.4%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	99.6%	(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
✓	99.1%	(+.f64 x #s(literal -1/2 binary64))
✓	53.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	97.8%	x

Compiler

Compiled 117 to 66 computations (43.6% saved)

simplify233.0ms (3.1%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
✓	cost-diff	0	(+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
✓	cost-diff	128	(*.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
✓	cost-diff	0	(+.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 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(/.f64 (+.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 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	cost-diff	128	(.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	128	(+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal -1/8 binary64) x)
✓	cost-diff	0	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))

Rules

2334×	`+-lowering-+.f64`
2334×	`+-lowering-+.f32`
2286×	`-lowering-.f32`
2286×	`-lowering-.f64`
1520×	`sum5-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	293
1	111	282
2	335	281
3	1523	275
4	7358	275
0	8049	275

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (/ -1/8 x) (+ x -1/2))
(/ -1/8 x)
-1/8
x
(+ x -1/2)
-1/2
(/ (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))
(+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))))
(* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x)))
(+ -1/8 (* x (* x x)))
-1/8
(* x (* x x))
x
(* x x)
(+ -1/8 (/ 1/16 x))
(/ 1/16 x)
1/16
(* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))
(+ (* x x) (- 1/4 (* x -1/2)))
(- 1/4 (* x -1/2))
1/4
(* x -1/2)
-1/2
(* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))
(- 1/64 (/ 1/256 (* x x)))
1/64
(/ 1/256 (* x x))
1/256
(/ 1 x)
1
(* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x)))
(/ (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))
(+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1))
(* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x))))
(- 1/4 (* x x))
1/4
(* x x)
x
(/ x (+ -1/8 (/ -1/16 x)))
(+ -1/8 (/ -1/16 x))
-1/8
(/ -1/16 x)
-1/16
(* (- -1/2 x) 1)
(- -1/2 x)
-1/2
1
(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))

Outputs
(+ (/ -1/8 x) (+ x -1/2))
(+.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 #s(literal -1/8 binary64) x)))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/8
#s(literal -1/8 binary64)
x
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))
(/.f64 (+.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 (.f64 (+.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)))) x)) (.f64 (+.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))))))
(+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 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 (.f64 (+.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)))) x))
(* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x)))
(.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)))
(+ -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)
(+ -1/8 (/ 1/16 x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
(* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))
(/.f64 (.f64 (+.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)))) x)
(+ (* 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)
(* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))
(/.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 #s(literal -1/256 binary64) (*.f64 x x))) x)
(- 1/64 (/ 1/256 (* x x)))
(+.f64 #s(literal 1/64 binary64) (/.f64 #s(literal -1/256 binary64) (*.f64 x x)))
1/64
#s(literal 1/64 binary64)
(/ 1/256 (* x x))
(/.f64 #s(literal 1/256 binary64) (*.f64 x x))
1/256
#s(literal 1/256 binary64)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x)))
(.f64 (+.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)))))
(/ (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (.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)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1))
(-.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))))
(* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) 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
(/ 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)
(* (- -1/2 x) 1)
(-.f64 #s(literal -1/2 binary64) x)
(- -1/2 x)
(-.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
1
#s(literal 1 binary64)
(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))
(/.f64 (*.f64 x (-.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))

localize185.0ms (2.5%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.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 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
✓	accuracy	39.0%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	98.9%	(/.f64 #s(literal 1/256 binary64) (*.f64 x x))
✓	accuracy	53.3%	(.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	39.0%	(/.f64 (+.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 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	100.0%	(/.f64 #s(literal -1/8 binary64) x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))

Results

115.0ms

256×

valid

Compiler

Compiled 338 to 40 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-div: 16.0ms (33.9% of total)

ival-mult: 15.0ms (31.8% of total)

ival-add: 10.0ms (21.2% of total)

ival-sub: 5.0ms (10.6% of total)

const: 1.0ms (2.1% of total)

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

series47.0ms (0.6%)

Counts

16 → 192

Calls

Call 1

Inputs
#<alt (+ (/ -1/8 x) (+ x -1/2))>
#<alt (/ -1/8 x)>
#<alt (+ x -1/2)>
#<alt (+ (* x x) (- 1/4 (* x -1/2)))>
#<alt (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))>
#<alt (/ (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))>
#<alt (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))))>
#<alt (* (- -1/2 x) 1)>
#<alt (/ (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))>
#<alt (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1))>
#<alt (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x))))>
#<alt (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))>
#<alt (/ 1/256 (* x x))>
#<alt (* x (* x x))>
#<alt (/ x (+ -1/8 (/ -1/16 x)))>
#<alt (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 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 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 -1/2>
#<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 1/4>
#<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 (/ -1/256 (pow x 3))>
#<alt (/ (- (* 1/64 (pow x 2)) 1/256) (pow x 3))>
#<alt (/ (- (* 1/64 (pow x 2)) 1/256) (pow x 3))>
#<alt (/ (- (* 1/64 (pow x 2)) 1/256) (pow x 3))>
#<alt (/ 1/64 x)>
#<alt (/ (- 1/64 (* 1/256 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/64 (* 1/256 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/64 (* 1/256 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/64 x)>
#<alt (* -1 (/ (- (* 1/256 (/ 1 (pow x 2))) 1/64) x))>
#<alt (* -1 (/ (- (* 1/256 (/ 1 (pow x 2))) 1/64) x))>
#<alt (* -1 (/ (- (* 1/256 (/ 1 (pow x 2))) 1/64) 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 (/ -1/1024 (pow x 3))>
#<alt (/ (- (* -1/512 x) 1/1024) (pow x 3))>
#<alt (/ (- (* x (- (* -1/128 x) 1/512)) 1/1024) (pow x 3))>
#<alt (/ (- (* x (- (* x (- (* 3/128 x) 1/128)) 1/512)) 1/1024) (pow x 3))>
#<alt (* -1/8 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/16 (/ 1 x)) 1/8))>
#<alt (* (pow x 3) (- (+ (/ 1/64 (pow x 2)) (* 1/16 (/ 1 x))) 1/8))>
#<alt (* (pow x 3) (- (+ (/ 1/64 (pow x 2)) (+ (* 1/16 (/ 1 x)) (* 3/128 (/ 1 (pow x 3))))) 1/8))>
#<alt (* -1/8 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/8 (* 1/16 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/8 (* -1 (/ (+ 1/16 (* 1/64 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/8 (* -1 (/ (+ 1/16 (+ (/ 3/128 (pow x 2)) (* 1/64 (/ 1 x)))) x)))))>
#<alt -1/2>
#<alt (- (* -1 x) 1/2)>
#<alt (- (* -1 x) 1/2)>
#<alt (- (* -1 x) 1/2)>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 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 -1/2>
#<alt (- (* -1 x) 1/2)>
#<alt (- (* x (- (* -4 x) 1)) 1/2)>
#<alt (- (* x (- (* x (- (* 8 x) 4)) 1)) 1/2)>
#<alt (* 8 (pow x 3))>
#<alt (* (pow x 3) (- 8 (* 4 (/ 1 x))))>
#<alt (* (pow x 3) (+ 8 (* -1 (/ (+ 4 (/ 1 x)) x))))>
#<alt (* (pow x 3) (- (+ 8 (* -1 (/ (+ 1 (* 1/2 (/ 1 x))) (pow x 2)))) (* 4 (/ 1 x))))>
#<alt (* 8 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))>
#<alt (* -1 (* (pow x 3) (- (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))) 8)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (+ 1 (* 1/2 (/ 1 x))) x)) 4) x)) 8)))>
#<alt (* -4 (pow x 2))>
#<alt (* (pow x 2) (- (* 8 x) 4))>
#<alt (* (pow x 2) (- (* 8 x) 4))>
#<alt (* (pow x 2) (- (* 8 x) 4))>
#<alt (* 8 (pow x 3))>
#<alt (* (pow x 3) (- 8 (* 4 (/ 1 x))))>
#<alt (* (pow x 3) (- 8 (* 4 (/ 1 x))))>
#<alt (* (pow x 3) (- 8 (* 4 (/ 1 x))))>
#<alt (* 8 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))>
#<alt (* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))>
#<alt (* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))>
#<alt (/ -1/1024 (pow x 3))>
#<alt (/ (- (* -1/512 x) 1/1024) (pow x 3))>
#<alt (/ (- (* x (- (* 1/128 (pow x 2)) 1/512)) 1/1024) (pow x 3))>
#<alt (/ (- (* x (- (* (pow x 2) (+ 1/128 (* 1/64 x))) 1/512)) 1/1024) (pow x 3))>
#<alt (* 1/64 x)>
#<alt (* x (+ 1/64 (* 1/128 (/ 1 x))))>
#<alt (* x (- (+ 1/64 (* 1/128 (/ 1 x))) (/ 1/512 (pow x 3))))>
#<alt (* x (+ 1/64 (+ (* -1 (/ (+ 1/512 (* 1/1024 (/ 1 x))) (pow x 3))) (* 1/128 (/ 1 x)))))>
#<alt (* 1/64 x)>
#<alt (* x (+ 1/64 (* 1/128 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/128 (* 1/512 (/ 1 (pow x 2)))) x)) 1/64)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/128 (* -1 (/ (+ 1/512 (* 1/1024 (/ 1 x))) (pow x 2)))) x)) 1/64)))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<alt (/ 1/256 (pow x 2))>
#<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 (* -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 (- (* 128 x) 64)))) 16))>
#<alt (* -8 x)>
#<alt (* x (- (* 4 (/ 1 x)) 8))>
#<alt (* x (- (* 4 (/ 1 x)) (+ 8 (/ 2 (pow x 2)))))>
#<alt (* x (- (+ (* 4 (/ 1 x)) (/ 1 (pow x 3))) (+ 8 (/ 2 (pow x 2)))))>
#<alt (* -8 x)>
#<alt (* -1 (* x (- 8 (* 4 (/ 1 x)))))>
#<alt (* -1 (* x (+ 8 (* -1 (/ (- 4 (* 2 (/ 1 x))) x)))))>
#<alt (* -1 (* x (+ 8 (* -1 (/ (+ 4 (* -1 (/ (- 2 (/ 1 x)) x))) x)))))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>
#<alt (* 8 (pow x 2))>

Calls

48 calls:

Time	Variable		Point	Expression
32.0ms	x	@	-inf	(+ (* x x) (- 1/4 (* x -1/2)))
2.0ms	x	@	inf	(* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))
1.0ms	x	@	inf	(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))
1.0ms	x	@	0	(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))
1.0ms	x	@	-inf	(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))

rewrite318.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3378×	`fma-lowering-fma.f32`
3378×	`fma-lowering-fma.f64`
2182×	`-lowering-.f32`
2182×	`-lowering-.f64`
2120×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	199
1	292	193
2	3336	193
0	8149	193

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 450

Calls

Call 1

Inputs
(+ (/ -1/8 x) (+ x -1/2))
(/ -1/8 x)
(+ x -1/2)
(+ (* x x) (- 1/4 (* x -1/2)))
(* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))
(/ (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))
(+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x))))
(* (- -1/2 x) 1)
(/ (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))
(+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1))
(* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x))))
(* (+ (* x x) (- 1/4 (* x -1/2))) (* (- 1/64 (/ 1/256 (* x x))) (/ 1 x)))
(/ 1/256 (* x x))
(* x (* x x))
(/ x (+ -1/8 (/ -1/16 x)))
(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))

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

simplify258.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

3402×	`-lowering-.f32`
3402×	`-lowering-.f64`
2174×	`+-lowering-+.f64`
2174×	`+-lowering-+.f32`
1826×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	285	1428
1	864	1308
2	2665	1168
3	7692	1153
0	8266	1153

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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 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)
-1/2
(- 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)))
1/4
(+ 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)))))
(/ -1/256 (pow x 3))
(/ (- (* 1/64 (pow x 2)) 1/256) (pow x 3))
(/ (- (* 1/64 (pow x 2)) 1/256) (pow x 3))
(/ (- (* 1/64 (pow x 2)) 1/256) (pow x 3))
(/ 1/64 x)
(/ (- 1/64 (* 1/256 (/ 1 (pow x 2)))) x)
(/ (- 1/64 (* 1/256 (/ 1 (pow x 2)))) x)
(/ (- 1/64 (* 1/256 (/ 1 (pow x 2)))) x)
(/ 1/64 x)
(* -1 (/ (- (* 1/256 (/ 1 (pow x 2))) 1/64) x))
(* -1 (/ (- (* 1/256 (/ 1 (pow x 2))) 1/64) x))
(* -1 (/ (- (* 1/256 (/ 1 (pow x 2))) 1/64) 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)))
(/ -1/1024 (pow x 3))
(/ (- (* -1/512 x) 1/1024) (pow x 3))
(/ (- (* x (- (* -1/128 x) 1/512)) 1/1024) (pow x 3))
(/ (- (* x (- (* x (- (* 3/128 x) 1/128)) 1/512)) 1/1024) (pow x 3))
(* -1/8 (pow x 3))
(* (pow x 3) (- (* 1/16 (/ 1 x)) 1/8))
(* (pow x 3) (- (+ (/ 1/64 (pow x 2)) (* 1/16 (/ 1 x))) 1/8))
(* (pow x 3) (- (+ (/ 1/64 (pow x 2)) (+ (* 1/16 (/ 1 x)) (* 3/128 (/ 1 (pow x 3))))) 1/8))
(* -1/8 (pow x 3))
(* -1 (* (pow x 3) (- 1/8 (* 1/16 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/8 (* -1 (/ (+ 1/16 (* 1/64 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/8 (* -1 (/ (+ 1/16 (+ (/ 3/128 (pow x 2)) (* 1/64 (/ 1 x)))) x)))))
-1/2
(- (* -1 x) 1/2)
(- (* -1 x) 1/2)
(- (* -1 x) 1/2)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* 1/2 (/ 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)))
-1/2
(- (* -1 x) 1/2)
(- (* x (- (* -4 x) 1)) 1/2)
(- (* x (- (* x (- (* 8 x) 4)) 1)) 1/2)
(* 8 (pow x 3))
(* (pow x 3) (- 8 (* 4 (/ 1 x))))
(* (pow x 3) (+ 8 (* -1 (/ (+ 4 (/ 1 x)) x))))
(* (pow x 3) (- (+ 8 (* -1 (/ (+ 1 (* 1/2 (/ 1 x))) (pow x 2)))) (* 4 (/ 1 x))))
(* 8 (pow x 3))
(* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))
(* -1 (* (pow x 3) (- (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))) 8)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (+ 1 (* 1/2 (/ 1 x))) x)) 4) x)) 8)))
(* -4 (pow x 2))
(* (pow x 2) (- (* 8 x) 4))
(* (pow x 2) (- (* 8 x) 4))
(* (pow x 2) (- (* 8 x) 4))
(* 8 (pow x 3))
(* (pow x 3) (- 8 (* 4 (/ 1 x))))
(* (pow x 3) (- 8 (* 4 (/ 1 x))))
(* (pow x 3) (- 8 (* 4 (/ 1 x))))
(* 8 (pow x 3))
(* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))
(* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))
(* -1 (* (pow x 3) (- (* 4 (/ 1 x)) 8)))
(/ -1/1024 (pow x 3))
(/ (- (* -1/512 x) 1/1024) (pow x 3))
(/ (- (* x (- (* 1/128 (pow x 2)) 1/512)) 1/1024) (pow x 3))
(/ (- (* x (- (* (pow x 2) (+ 1/128 (* 1/64 x))) 1/512)) 1/1024) (pow x 3))
(* 1/64 x)
(* x (+ 1/64 (* 1/128 (/ 1 x))))
(* x (- (+ 1/64 (* 1/128 (/ 1 x))) (/ 1/512 (pow x 3))))
(* x (+ 1/64 (+ (* -1 (/ (+ 1/512 (* 1/1024 (/ 1 x))) (pow x 3))) (* 1/128 (/ 1 x)))))
(* 1/64 x)
(* x (+ 1/64 (* 1/128 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 1/128 (* 1/512 (/ 1 (pow x 2)))) x)) 1/64)))
(* -1 (* x (- (* -1 (/ (+ 1/128 (* -1 (/ (+ 1/512 (* 1/1024 (/ 1 x))) (pow x 2)))) x)) 1/64)))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(/ 1/256 (pow x 2))
(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)
(* -16 (pow x 2))
(* (pow x 2) (- (* 32 x) 16))
(* (pow x 2) (- (* x (+ 32 (* -64 x))) 16))
(* (pow x 2) (- (* x (+ 32 (* x (- (* 128 x) 64)))) 16))
(* -8 x)
(* x (- (* 4 (/ 1 x)) 8))
(* x (- (* 4 (/ 1 x)) (+ 8 (/ 2 (pow x 2)))))
(* x (- (+ (* 4 (/ 1 x)) (/ 1 (pow x 3))) (+ 8 (/ 2 (pow x 2)))))
(* -8 x)
(* -1 (* x (- 8 (* 4 (/ 1 x)))))
(* -1 (* x (+ 8 (* -1 (/ (- 4 (* 2 (/ 1 x))) x)))))
(* -1 (* x (+ 8 (* -1 (/ (+ 4 (* -1 (/ (- 2 (/ 1 x)) x))) x)))))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))
(* 8 (pow x 2))

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

eval104.0ms (1.4%)

Compiler: Compiled 31189 to 2195 computations (93% saved)

prune76.0ms (1%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	700	7	707
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	702	12	714

Accuracy

100.0%

Counts

714 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.0%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (*.f64 x x) #s(literal 8 binary64)))
▶	35.0%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal -8 binary64)) (.f64 (+.f64 #s(literal -4 binary64) (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)) #s(literal 1 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
▶	35.0%	(/.f64 (+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
	35.0%	(/.f64 (+.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 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
▶	35.0%	(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64))))))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
	35.0%	(/.f64 (.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x x)))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
▶	35.0%	(/.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	99.4%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	99.6%	(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
✓	99.1%	(+.f64 x #s(literal -1/2 binary64))
✓	53.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	97.8%	x

Compiler

Compiled 537 to 334 computations (37.8% saved)

simplify351.0ms (4.7%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (*.f64 x x))))))))
✓	cost-diff	0	(/.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.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	0	(.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)))
✓	cost-diff	0	(+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64))))
✓	cost-diff	0	(/.f64 (+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.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	0	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
✓	cost-diff	0	(+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (*.f64 x x) #s(literal 8 binary64)))
✓	cost-diff	128	(*.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
✓	cost-diff	0	(+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64)))))))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64))))))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal -8 binary64)) (.f64 (+.f64 #s(literal -4 binary64) (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)) #s(literal 1 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
✓	cost-diff	128	(*.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
✓	cost-diff	128	(*.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))
✓	cost-diff	128	(.f64 (+.f64 #s(literal -4 binary64) (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)) #s(literal 1 binary64))

Rules

3748×	`+-lowering-+.f64`
3748×	`+-lowering-+.f32`
2540×	`-lowering-.f32`
2540×	`-lowering-.f64`
1890×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	639
1	206	610
2	640	600
3	2429	593
0	8238	593

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(/ (+ (* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))
(.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) (/.f64 (-.f64 (/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) (+.f64 #s(literal 4 binary64) (.f64 x #s(literal -8 binary64))))) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1/2 binary64) x)))
(+ (* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1))) (* (- -1/2 x) 1))
(+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) (+.f64 #s(literal 4 binary64) (*.f64 x #s(literal -8 binary64))))) (-.f64 #s(literal -1/2 binary64) x))
(* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1)))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) (+.f64 #s(literal 4 binary64) (*.f64 x #s(literal -8 binary64)))))
(- 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
(- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) (+.f64 #s(literal 4 binary64) (*.f64 x #s(literal -8 binary64))))
(* x -8)
(*.f64 x #s(literal -8 binary64))
-8
#s(literal -8 binary64)
(* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1)
(+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(+ -4 (/ (* -1 (+ (/ 1 x) -2)) x))
(+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x))
-4
#s(literal -4 binary64)
(/ (* -1 (+ (/ 1 x) -2)) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)
(* -1 (+ (/ 1 x) -2))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))
-1
#s(literal -1 binary64)
(+ (/ 1 x) -2)
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
-2
#s(literal -2 binary64)
(* (- -1/2 x) 1)
(-.f64 #s(literal -1/2 binary64) x)
(- -1/2 x)
(-.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))
(/.f64 (*.f64 x (-.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) 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)
(/ (+ -1/2 (* x (+ -1 (* x (+ -4 (* x 8)))))) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64))))))) (/.f64 (.f64 x (-.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(+ -1/2 (* x (+ -1 (* x (+ -4 (* x 8))))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64)))))))
-1/2
#s(literal -1/2 binary64)
(* x (+ -1 (* x (+ -4 (* x 8)))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64))))))
x
(+ -1 (* x (+ -4 (* x 8))))
(+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))
-1
#s(literal -1 binary64)
(* x (+ -4 (* x 8)))
(.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64))))
(+ -4 (* x 8))
(+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64)))
-4
#s(literal -4 binary64)
(* x 8)
(*.f64 x #s(literal 8 binary64))
8
#s(literal 8 binary64)
(* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))
(/.f64 (*.f64 x (-.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)
(/ 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)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1)) (* (* x x) 8))
(/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))) (.f64 x (.f64 x #s(literal 8 binary64))))
(+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1))
(-.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))))
(* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 x x))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) 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
(/ 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)
(* (- -1/2 x) 1)
(-.f64 #s(literal -1/2 binary64) x)
(- -1/2 x)
(-.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
1
#s(literal 1 binary64)
(* (* x x) 8)
(.f64 x (.f64 x #s(literal 8 binary64)))
8
#s(literal 8 binary64)
(/ (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (+ 1/128 (* x 1/64))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))
(/.f64 (+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64)))) (.f64 (+.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)))))
(+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (+ 1/128 (* x 1/64)))
(+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64))))
(* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x)))
(.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)))
(+ -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)
(+ -1/8 (/ 1/16 x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
(+ 1/128 (* x 1/64))
(+.f64 #s(literal 1/128 binary64) (*.f64 x #s(literal 1/64 binary64)))
1/128
#s(literal 1/128 binary64)
(* x 1/64)
(*.f64 x #s(literal 1/64 binary64))
1/64
#s(literal 1/64 binary64)
(* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x)))
(.f64 (+.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) (- 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 (+ 1/64 (* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x)))))))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))
(.f64 (+.f64 #s(literal 1/64 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x x)))))) (/.f64 x (.f64 (+.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 (+ 1/64 (* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x))))))))
(.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/128 binary64) (*.f64 x x)))))))
x
(+ 1/64 (* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x)))))))
(+.f64 #s(literal 1/64 binary64) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x x))))))
1/64
#s(literal 1/64 binary64)
(* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x))))))
(.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x x)))))
(* x x)
(*.f64 x x)
(+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x)))))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))
-1/8
#s(literal -1/8 binary64)
(+ (/ 1/16 x) (/ 3/128 (* x (* x x))))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x))))
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
(/ 3/128 (* x (* x x)))
(/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))
3/128
#s(literal 3/128 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x)))
(.f64 (+.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) (- 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)
(+ -1/8 (/ 1/16 x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))

localize455.0ms (6.1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (*.f64 x x))))))))
✓	accuracy	99.0%	(/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))
✓	accuracy	39.0%	(/.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	100.0%	(.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)))
✓	accuracy	100.0%	(+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	39.0%	(/.f64 (+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
✓	accuracy	100.0%	(+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))
✓	accuracy	99.8%	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
✓	accuracy	39.0%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (*.f64 x x) #s(literal 8 binary64)))
✓	accuracy	100.0%	(*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.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	99.9%	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal 8 binary64))))))
✓	accuracy	39.0%	(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64))))))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.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	100.0%	(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)
✓	accuracy	99.9%	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal -8 binary64)) (.f64 (+.f64 #s(literal -4 binary64) (/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)) #s(literal 1 binary64))))
✓	accuracy	39.0%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal -8 binary64)) (.f64 (+.f64 #s(literal -4 binary64) (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)) #s(literal 1 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))

Results

290.0ms

256×

valid

Compiler

Compiled 741 to 66 computations (91.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-div: 33.0ms (36% of total)

ival-mult: 33.0ms (36% of total)

ival-add: 19.0ms (20.7% of total)

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

const: 2.0ms (2.2% of total)

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

series14.0ms (0.2%)

Counts

24 → 288

Calls

Call 1

Inputs
#<alt (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1)>
#<alt (* -1 (+ (/ 1 x) -2))>
#<alt (* (- -1/2 x) 1)>
#<alt (/ (+ (* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))>
#<alt (/ (+ -1/2 (* x (+ -1 (* x (+ -4 (* x 8)))))) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))>
#<alt (+ -1/2 (* x (+ -1 (* x (+ -4 (* x 8))))))>
#<alt (* x (+ -1 (* x (+ -4 (* x 8)))))>
#<alt (+ -1 (* x (+ -4 (* x 8))))>
#<alt (/ (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1)) (* (* x x) 8))>
#<alt (+ (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x)))) (* (- -1/2 x) 1))>
#<alt (* (- 1/4 (* x x)) (/ x (+ -1/8 (/ -1/16 x))))>
#<alt (+ (* x x) (- 1/4 (* x -1/2)))>
#<alt (/ (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (+ 1/128 (* x 1/64))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))>
#<alt (+ (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x))) (+ 1/128 (* x 1/64)))>
#<alt (* (+ -1/8 (* x (* x x))) (+ -1/8 (/ 1/16 x)))>
#<alt (/ (* x (+ 1/64 (* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x)))))))) (* (+ (* x x) (- 1/4 (* x -1/2))) (+ -1/8 (/ 1/16 x))))>
#<alt (* x (+ 1/64 (* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x))))))))>
#<alt (+ 1/64 (* (* x x) (+ -1/8 (+ (/ 1/16 x) (/ 3/128 (* x (* x x)))))))>
#<alt (* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1)))>
#<alt (/ (* -1 (+ (/ 1 x) -2)) x)>
#<alt (/ x (+ -1/8 (/ -1/16 x)))>
#<alt (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x))))>
#<alt (* x (* x x))>
#<alt (/ 3/128 (* x (* x x)))>

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

Calls

72 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/ (* -1 (+ (/ 1 x) -2)) x)
0.0ms	x	@	0	(* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1)
0.0ms	x	@	0	(/ 3/128 (* x (* x x)))
0.0ms	x	@	0	(/ (+ (* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))
0.0ms	x	@	inf	(/ (+ (* (- 1/4 (* x x)) (- (* x -8) (* (+ -4 (/ (* -1 (+ (/ 1 x) -2)) x)) 1))) (* (- -1/2 x) 1)) (* (- -1/2 x) (/ x (+ -1/8 (/ -1/16 x)))))

rewrite581.0ms (7.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3256×	`-lowering-.f32`
3256×	`-lowering-.f64`
2666×	`/-lowering-/.f32`
2666×	`/-lowering-/.f64`
1482×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	337
1	513	316
2	5765	313
0	8089	313

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 522

Calls

Call 1

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

Outputs
(+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(+.f64 #s(literal -4 binary64) (*.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal 1 binary64)))
(+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal 1 binary64)) #s(literal -4 binary64))
(-.f64 (/.f64 #s(literal 16 binary64) (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x))) (/.f64 (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))) (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x))))
(fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) #s(literal -4 binary64))
(fma.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) x) #s(literal -4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64)))) (+.f64 #s(literal -64 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x)) (-.f64 #s(literal 16 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))))
(/.f64 (+.f64 #s(literal -64 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))) (+.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64)))))
(/.f64 (+.f64 #s(literal -64 binary64) (*.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))) (+.f64 (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))))
(/.f64 (-.f64 #s(literal 16 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))))) (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x)))
(/.f64 (neg.f64 (+.f64 #s(literal -64 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))))))) (neg.f64 (+.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 16 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))) (neg.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x))))
(/.f64 (-.f64 (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))) #s(literal 16 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -64 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))))))) (+.f64 #s(literal 16 binary64) (*.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))) (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x)))
(/.f64 (.f64 (+.f64 #s(literal -64 binary64) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)))))) #s(literal 1 binary64)) (+.f64 #s(literal 16 binary64) (*.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -4 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 16 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x) (/.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x))))) #s(literal 1 binary64)) (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x)))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(*.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) #s(literal 1 binary64))
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(/.f64 (.f64 (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (-.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 (-.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 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal -1/2 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(.f64 x (.f64 (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (-.f64 #s(literal -1/2 binary64) x)))
(*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.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 -1/2 binary64) x))
(.f64 (/.f64 (.f64 x (-.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 x (-.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))))
(.f64 (.f64 (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 1 binary64)) (-.f64 #s(literal -1/2 binary64) x))
(.f64 (/.f64 (.f64 x (-.f64 #s(literal -1/2 binary64) 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 (.f64 x (-.f64 #s(literal -1/2 binary64) 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 -3/128 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 3/128 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) #s(literal 3/128 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 3/128 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (/.f64 #s(literal 3/128 binary64) x)))
(/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 3/128 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))))
(/.f64 #s(literal -3/128 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (/.f64 #s(literal 3/128 binary64) x) (*.f64 x x))
(/.f64 (neg.f64 (/.f64 #s(literal 3/128 binary64) x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 3/128 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 3/128 binary64) x) x) x)
(pow.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 3/128 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x (*.f64 x x))))
(.f64 #s(literal 3/128 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 #s(literal -3/128 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 3/128 binary64))
(.f64 (/.f64 #s(literal 3/128 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))

simplify428.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

4700×	`-lowering-.f32`
4700×	`-lowering-.f64`
3998×	`+-lowering-+.f64`
3998×	`+-lowering-+.f32`
1406×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	2443
1	1160	2219
2	3676	2097
0	8489	2097

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

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

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

eval168.0ms (2.3%)

Compiler: Compiled 39822 to 2856 computations (92.8% saved)

prune105.0ms (1.4%)

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	987	7	994
Fresh	1	1	2
Picked	5	0	5
Done	0	5	5
Total	993	13	1006

Accuracy

100.0%

Counts

1006 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.0%	(/.f64 (+.f64 (-.f64 #s(literal -1/2 binary64) x) (.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
	34.9%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (*.f64 x x) #s(literal 8 binary64)))
	35.0%	(/.f64 (+.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 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/64 binary64) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
	35.0%	(/.f64 (+.f64 #s(literal 3/128 binary64) (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
	35.0%	(/.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))
	35.0%	(/.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))) (.f64 (+.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))))
	34.9%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x (-.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) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (-.f64 (.f64 x #s(literal -8 binary64)) #s(literal -4 binary64)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))))
✓	99.4%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	99.6%	(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
✓	99.1%	(+.f64 x #s(literal -1/2 binary64))
	38.6%	(.f64 (/.f64 (+.f64 (-.f64 #s(literal -1/2 binary64) x) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (-.f64 (.f64 x #s(literal -8 binary64)) #s(literal -4 binary64)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))) (-.f64 #s(literal -1/2 binary64) x)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
✓	53.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	97.8%	x

Compiler

Compiled 862 to 328 computations (61.9% saved)

regimes15.0ms (0.2%)

Counts

23 → 1

Calls

Call 1

Inputs
x
(+.f64 x #s(literal -1/2 binary64))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.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 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64))))))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (*.f64 x x) #s(literal 8 binary64)))
(/.f64 (+.f64 (-.f64 #s(literal -1/2 binary64) x) (.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (.f64 x #s(literal 8 binary64)))))) (.f64 (-.f64 #s(literal -1/2 binary64) x) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (*.f64 x x) #s(literal 8 binary64)))
(/.f64 (+.f64 #s(literal 3/128 binary64) (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1/2 binary64) 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) x) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (-.f64 (.f64 x #s(literal -8 binary64)) #s(literal -4 binary64)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))) (-.f64 #s(literal -1/2 binary64) x)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(/.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))) (.f64 (+.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))))
(/.f64 (+.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 1/128 binary64) (.f64 x #s(literal 1/64 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x (-.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) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (-.f64 (.f64 x #s(literal -8 binary64)) #s(literal -4 binary64)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 3/128 binary64) (.f64 x (.f64 x x)))))))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 3/128 binary64) (.f64 x x)))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal -8 binary64)) (.f64 (+.f64 #s(literal -4 binary64) (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) x)) #s(literal 1 binary64)))) (.f64 (-.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal -1/2 binary64) x) (/.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 #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)))) (/.f64 #s(literal 1/64 binary64) x))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.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 #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)))) (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/2 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 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:

7.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
6.0ms	x

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.4%	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:

2.0ms

Results

Accuracy	Segments	Branch
99.1%	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
97.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	17	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 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.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 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x #s(literal -1/2 binary64))
x

soundness819.0ms (11.1%)

Rules

4224×	`/-lowering-/.f32`
4224×	`/-lowering-/.f64`
4176×	`-lowering-.f32`
4176×	`-lowering-.f64`
3384×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	69
1	137	67
2	1348	65
0	8863	65
0	150	443
1	482	384
2	1842	358
3	5535	352
0	8190	352

Stop Event

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

Compiler

Compiled 37 to 22 computations (40.5% saved)

preprocess30.0ms (0.4%)

Compiler: Compiled 62 to 36 computations (41.9% 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

analyze5.0ms (0.1%)

sample684.0ms (9.2%)

preprocess81.0ms (1.1%)

explain88.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize31.0ms (0.4%)

series5.0ms (0.1%)

rewrite450.0ms (6.1%)

simplify252.0ms (3.4%)

eval55.0ms (0.7%)

prune51.0ms (0.7%)

simplify206.0ms (2.8%)

localize119.0ms (1.6%)

series28.0ms (0.4%)

rewrite443.0ms (6%)

simplify384.0ms (5.2%)

eval217.0ms (2.9%)

prune99.0ms (1.3%)

simplify233.0ms (3.1%)

localize185.0ms (2.5%)

series47.0ms (0.6%)

rewrite318.0ms (4.3%)

simplify258.0ms (3.5%)

eval104.0ms (1.4%)

prune76.0ms (1%)

simplify351.0ms (4.7%)

localize455.0ms (6.1%)

series14.0ms (0.2%)

rewrite581.0ms (7.8%)

simplify428.0ms (5.8%)

eval168.0ms (2.3%)

prune105.0ms (1.4%)

regimes15.0ms (0.2%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.1%)

soundness819.0ms (11.1%)

preprocess30.0ms (0.4%)

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