Metrics for sqrtexp (problem 3.4.4)

analyze269.0ms (3.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
50%	50%	50%	0%	0%	0%	0%	5
50%	50%	50%	0%	0%	0%	0%	6
53.1%	53.1%	46.9%	0%	0%	0%	0%	7
53.1%	53.1%	46.9%	0%	0%	0%	0%	8
53.9%	53.9%	46.1%	0%	0%	0%	0%	9
54.1%	54.1%	45.9%	0%	0%	0%	0%	10
54.2%	54.2%	45.8%	0%	0%	0%	0%	11
54.2%	54.2%	45.7%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-exp: 42.0ms (29.4% of total)

ival-sub: 32.0ms (22.4% of total)

ival-mult: 32.0ms (22.4% of total)

ival-sqrt: 21.0ms (14.7% of total)

ival-div: 9.0ms (6.3% of total)

const: 5.0ms (3.5% of total)

backward-pass: 1.0ms (0.7% of total)

sample2.3s (27.3%)

Results

1.4s	5226×	1	valid
247.0ms	2800×	0	unsamplable
234.0ms	3030×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-exp: 823.0ms (53.6% of total)

ival-sub: 226.0ms (14.7% of total)

ival-mult: 149.0ms (9.7% of total)

ival-sqrt: 126.0ms (8.2% of total)

ival-div: 103.0ms (6.7% of total)

backward-pass: 80.0ms (5.2% of total)

const: 29.0ms (1.9% of total)

Bogosity

preprocess247.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

2164×	`-lowering-.f32`
2164×	`-lowering-.f64`
1708×	`--lowering--.f32`
1708×	`--lowering--.f64`
1500×	`fnmsub-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	48	27
2	77	27
3	127	27
4	236	20
5	441	18
6	960	18
7	3778	18
0	10	8
1	24	8
2	31	8
3	46	8
4	77	7
5	140	5
6	300	5
7	853	5
8	4984	5
0	8232	5

Stop Event

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

Calls

Call 1

Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

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

Call 2

Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))

Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(sqrt (+ 1 (recip (exp x))))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
(neg (sqrt (+ 1 (recip (exp x)))))

explain180.0ms (2.1%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
164	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
163	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
4	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	-	-	`x`
0	-	-	`(exp.f64 x)`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`

Results

101.0ms	322×	1	valid
18.0ms	190×	0	valid

Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-exp: 47.0ms (56.9% of total)

ival-sub: 9.0ms (10.9% of total)

ival-mult: 7.0ms (8.5% of total)

backward-pass: 7.0ms (8.5% of total)

ival-sqrt: 6.0ms (7.3% of total)

ival-div: 5.0ms (6.1% of total)

const: 2.0ms (2.4% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`exp-lowering-exp.f32`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	8	13
0	8	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
1
(exp x)
x

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

localize23.0ms (0.3%)

Localize:

Found 3 expressions of interest:

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

Results

17.0ms

256×

valid

Compiler

Compiled 15 to 6 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sqrt: 5.0ms (53.7% of total)

ival-exp: 2.0ms (21.5% of total)

ival-add: 2.0ms (21.5% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>

Calls

9 calls:

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

rewrite559.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3504×	`/-lowering-/.f32`
3504×	`/-lowering-/.f64`
2980×	`-lowering-.f32`
2980×	`-lowering-.f64`
1782×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	23	11
2	154	11
3	1175	11
0	8280	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 241

Calls

Call 1

Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)

Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 2 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3/2 binary64)))) (sqrt.f64 (.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64))))) (sqrt.f64 (.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64))))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (exp.f64 (.f64 x #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64))))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64))))) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (exp.f64 (*.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -3 binary64)) (/.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 9 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (exp.f64 (*.f64 x #s(literal 3 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (exp.f64 (.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (hypot.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
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(exp.f64 x)
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))

simplify212.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

3346×	`-lowering-.f32`
3346×	`-lowering-.f64`
1870×	`+-lowering-+.f64`
1870×	`+-lowering-+.f32`
1432×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	221
1	162	175
2	540	174
3	1192	171
4	2849	170
5	6799	170
0	8138	170

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64))) (.f64 x (.f64 x #s(literal 7/192 binary64))))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

eval31.0ms (0.4%)

Compiler: Compiled 6114 to 918 computations (85% saved)

prune49.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	272	5	277
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	272	6	278

Accuracy

100.0%

Counts

278 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
▶	65.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
▶	64.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	64.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 88 to 71 computations (19.3% saved)

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	128	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))

Rules

884×	`fma-define`
764×	`fma-lowering-fma.f32`
764×	`fma-lowering-fma.f64`
476×	`sum3-define`
344×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	129
1	54	111
2	130	109
3	289	109
4	539	109
5	843	109
6	1178	109
7	1302	109
8	1303	109
0	1303	109

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt 2)
2
(sqrt (+ 2 x))
(+ 2 x)
2
x
(sqrt (+ 1 (+ x 1)))
(+ 1 (+ x 1))
1
(+ x 1)
x
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(+ 2 (* x (+ 1 (* 1/2 x))))
2
(* x (+ 1 (* 1/2 x)))
x
(+ 1 (* 1/2 x))
1
(* 1/2 x)
1/2
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
2
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
1
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (+ 2 x))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(sqrt (+ 1 (+ x 1)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(+ 1 (+ x 1))
(+.f64 #s(literal 2 binary64) x)
1
#s(literal 1 binary64)
(+ x 1)
(+.f64 x #s(literal 1 binary64))
x
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
x
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x 1/6)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)

localize103.0ms (1.2%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))

Results

44.0ms	171×	0	valid
23.0ms	85×	0	invalid

Compiler

Compiled 135 to 24 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-add: 11.0ms (32.3% of total)

ival-mult: 9.0ms (26.4% of total)

ival-sqrt: 9.0ms (26.4% of total)

...c/correct-round.rkt:119:19: 4.0ms (11.7% of total)

const: 1.0ms (2.9% of total)

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

series15.0ms (0.2%)

Counts

17 → 192

Calls

Call 1

Inputs
#<alt (sqrt 2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (+ 1 (+ x 1)))>
#<alt (+ 1 (+ x 1))>
#<alt (+ x 1)>
#<alt (sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (+ 1 (* 1/2 x))>
#<alt (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* 1/2 x)>
#<alt (* x 1/6)>
#<alt (* x (+ 1/2 (* x 1/6)))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>

Calls

48 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms	x	@	inf	(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
1.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
1.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
1.0ms	x	@	inf	(sqrt (+ 2 x))

rewrite334.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

3408×	`/-lowering-/.f32`
3408×	`/-lowering-/.f64`
3026×	`-lowering-.f32`
3026×	`-lowering-.f64`
2216×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	110
1	147	93
2	1434	91
0	8186	91

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 581

Calls

Call 1

Inputs
(sqrt 2)
(sqrt (+ 2 x))
(+ 2 x)
(sqrt (+ 1 (+ x 1)))
(+ 1 (+ x 1))
(+ x 1)
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* x (+ 1 (* 1/2 x)))
(+ 1 (* 1/2 x))
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* 1/2 x)
(* x 1/6)
(* x (+ 1/2 (* x 1/6)))

Outputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64))))) (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.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 #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 2 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 4 binary64))) (sqrt.f64 (-.f64 x #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (neg.f64 (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(.f64 (sqrt.f64 (+.f64 #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 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64)))))))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(+.f64 #s(literal 2 binary64) x)
(+.f64 x #s(literal 2 binary64))
(+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(+.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 4 binary64) (-.f64 x #s(literal 2 binary64))))
(fma.f64 x #s(literal 1 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 2 binary64))
(fma.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64))
(fma.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x)) (+.f64 #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 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 #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 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (+.f64 #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 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
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(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/6 binary64) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) x (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/6 binary64) (.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x)) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x)) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x #s(literal 1/2 binary64))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))))
(.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))

simplify291.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

5072×	`-lowering-.f32`
5072×	`-lowering-.f64`
3342×	`+-lowering-+.f64`
3342×	`+-lowering-+.f32`
2400×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	1816
1	926	1466
2	3421	1422
0	8720	1422

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (.f64 x (+.f64 (/.f64 (/.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 x x)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64)))) (sqrt.f64 #s(literal 1/6 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64)))) (sqrt.f64 #s(literal -1/6 binary64)))) x))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64)))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (.f64 x x))) x))))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))

eval107.0ms (1.3%)

Compiler: Compiled 17585 to 2135 computations (87.9% saved)

prune78.0ms (0.9%)

Pruning

18 alts after pruning (12 fresh and 6 done)

	Pruned	Kept	Total
New	761	12	773
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	761	18	779

Accuracy

100.0%

Counts

779 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
	2.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	65.8%	(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))))
▶	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	65.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	64.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	64.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
	2.1%	(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
▶	3.4%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
	21.2%	(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64))))))
	2.3%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
▶	3.9%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
▶	2.3%	(sqrt.f64 x)
✓	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 539 to 302 computations (44% saved)

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	128	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	128	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	128	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))

Rules

488×	`fma-define`
400×	`fma-lowering-fma.f32`
400×	`fma-lowering-fma.f64`
150×	`sum3-define`
134×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	159
1	74	142
2	154	137
3	309	136
4	513	136
5	588	136
0	588	136

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ x (+ (* x (* x 1/2)) 2)))
(+ x (+ (* x (* x 1/2)) 2))
x
(+ (* x (* x 1/2)) 2)
(* x (* x 1/2))
(* x 1/2)
1/2
2
(sqrt x)
x
(sqrt (* x (+ 1 (* 1/2 x))))
(* x (+ 1 (* 1/2 x)))
x
(+ 1 (* 1/2 x))
1
(* 1/2 x)
1/2
(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
(* (* x x) (+ 1/2 (* x 1/6)))
(* x x)
x
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(sqrt (+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))))
(+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6)))))
2
(* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))
x
(+ (+ 1 (* x 1/2)) (* x (* x 1/6)))
(+ 1 (* x 1/2))
1
(* x 1/2)
1/2
(* x (* x 1/6))
(* x 1/6)
1/6

Outputs
(sqrt (+ x (+ (* x (* x 1/2)) 2)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(+ x (+ (* x (* x 1/2)) 2))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
x
(+ (* x (* x 1/2)) 2)
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(* x (* x 1/2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x
(sqrt (* x (+ 1 (* 1/2 x))))
(sqrt.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
x
(+ 1 (* 1/2 x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (* x x) (+ 1/2 (* x 1/6)))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* x x)
(*.f64 x x)
x
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(sqrt (+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ (+ 1 (* x 1/2)) (* x (* x 1/6)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x 1/2))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* x (* x 1/6))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)

localize115.0ms (1.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	82.5%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))
✓	accuracy	100.0%	(+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))

Results

48.0ms	168×	0	invalid
28.0ms	88×	0	valid

Compiler

Compiled 177 to 27 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 16.0ms (41% of total)

ival-add: 10.0ms (25.6% of total)

ival-sqrt: 8.0ms (20.5% of total)

...c/correct-round.rkt:119:19: 4.0ms (10.2% of total)

const: 1.0ms (2.6% of total)

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

series10.0ms (0.1%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (sqrt (+ x (+ (* x (* x 1/2)) 2)))>
#<alt (+ x (+ (* x (* x 1/2)) 2))>
#<alt (+ (* x (* x 1/2)) 2)>
#<alt (* x (* x 1/2))>
#<alt (sqrt x)>
#<alt (sqrt (* x (+ 1 (* 1/2 x))))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (sqrt (* (* x x) (+ 1/2 (* x 1/6))))>
#<alt (* (* x x) (+ 1/2 (* x 1/6)))>
#<alt (* x x)>
#<alt (+ 1/2 (* x 1/6))>
#<alt (sqrt (+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))))>
#<alt (+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6)))))>
#<alt (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))>
#<alt (+ (+ 1 (* x 1/2)) (* x (* x 1/6)))>
#<alt (* x 1/2)>
#<alt (* x 1/6)>
#<alt (* x (* x 1/6))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* 1/2 (pow x 2)))>
#<alt (+ 2 (* 1/2 (pow x 2)))>
#<alt (+ 2 (* 1/2 (pow x 2)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<alt (* -1 (* x (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt -1) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (sqrt -1) (* x (pow (sqrt -1/2) 3)))) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (sqrt -1) (pow (sqrt -1/2) 3))) (* -1/16 (/ (sqrt -1) (* x (pow (sqrt -1/2) 5))))) x)) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
1.0ms	x	@	inf	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
0.0ms	x	@	0	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
0.0ms	x	@	-inf	(sqrt (* x (+ 1 (* 1/2 x))))
0.0ms	x	@	-inf	(sqrt x)

rewrite350.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3032×	`/-lowering-/.f32`
3032×	`/-lowering-/.f64`
2940×	`-lowering-.f32`
2940×	`-lowering-.f64`
2188×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	133
1	173	117
2	1357	111
0	8286	111

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 494

Calls

Call 1

Inputs
(sqrt (+ x (+ (* x (* x 1/2)) 2)))
(+ x (+ (* x (* x 1/2)) 2))
(+ (* x (* x 1/2)) 2)
(* x (* x 1/2))
(sqrt x)
(sqrt (* x (+ 1 (* 1/2 x))))
(* x (+ 1 (* 1/2 x)))
(+ 1 (* 1/2 x))
(* 1/2 x)
(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
(* (* x x) (+ 1/2 (* x 1/6)))
(* x x)
(+ 1/2 (* x 1/6))
(sqrt (+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))))
(+ 2 (* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6)))))
(* x (+ (+ 1 (* x 1/2)) (* x (* x 1/6))))
(+ (+ 1 (* x 1/2)) (* x (* x 1/6)))
(* x 1/2)
(* x 1/6)
(* x (* x 1/6))

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)))) (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)))))
(/.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (pow.f64 (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))))) (sqrt.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x))))))
(/.f64 (sqrt.f64 (neg.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (sqrt.f64 (neg.f64 (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 8 binary64))) (sqrt.f64 (+.f64 (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (.f64 x x))) (sqrt.f64 (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))))) (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x))))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (neg.f64 (pow.f64 (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)) x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)) x))))))
(.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)) x))))))
(.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal 1/4 binary64)))
(+.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)
(+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))
(+.f64 (+.f64 x #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)))
(-.f64 (/.f64 (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 4 binary64) (-.f64 (.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))
(fma.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 1 binary64) x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) x))
(fma.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) x)
(fma.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -2 binary64))) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x) (-.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #s(literal 4 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))))) (+.f64 (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))) (-.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))))) (neg.f64 (+.f64 (.f64 x x) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)))))
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(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)

simplify320.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

5070×	`-lowering-.f32`
5070×	`-lowering-.f64`
3832×	`+-lowering-+.f64`
3832×	`+-lowering-+.f32`
1442×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	2167
1	1180	1790
2	4317	1748
0	8173	1748

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
2
(+ 2 (* 1/2 (pow x 2)))
(+ 2 (* 1/2 (pow x 2)))
(+ 2 (* 1/2 (pow x 2)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(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)))
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* -1 (* x (* (sqrt -1) (sqrt -1/2))))
(* -1 (* x (+ (* -1/2 (/ (sqrt -1) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (sqrt -1) (* x (pow (sqrt -1/2) 3)))) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (sqrt -1) (pow (sqrt -1/2) 3))) (* -1/16 (/ (sqrt -1) (* x (pow (sqrt -1/2) 5))))) x)) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (.f64 (+.f64 (.f64 #s(literal -1/4 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (.f64 x (+.f64 (/.f64 (/.f64 #s(literal -3/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(.f64 x (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+ 2 (* 1/2 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+ 2 (* 1/2 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 2 binary64) (.f64 #s(literal 1/16 binary64) (/.f64 x #s(literal 1/6 binary64))))) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 x x))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64)) (.f64 x x))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 2 binary64) (.f64 x x))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))

eval90.0ms (1.1%)

Compiler: Compiled 18692 to 2080 computations (88.9% saved)

prune106.0ms (1.3%)

Pruning

19 alts after pruning (8 fresh and 11 done)

	Pruned	Kept	Total
New	760	4	764
Fresh	3	4	7
Picked	0	5	5
Done	0	6	6
Total	763	19	782

Accuracy

100.0%

Counts

782 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
▶	2.5%	(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
▶	2.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	65.8%	(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))
▶	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
▶	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	65.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	64.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	64.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	3.4%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
	2.1%	(sqrt.f64 (.f64 (.f64 x x) (*.f64 x #s(literal 1/6 binary64))))
	2.3%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	3.9%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
✓	2.3%	(sqrt.f64 x)
✓	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 436 to 266 computations (39% saved)

simplify165.0ms (2%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) x)
✓	cost-diff	128	(.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))
✓	cost-diff	128	(+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)))))))
✓	cost-diff	128	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
✓	cost-diff	0	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	64	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	64	(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
✓	cost-diff	256	(+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
✓	cost-diff	256	(+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
✓	cost-diff	256	(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))

Rules

2766×	`-lowering-.f32`
2766×	`-lowering-.f64`
1898×	`fma-lowering-fma.f32`
1898×	`fma-lowering-fma.f64`
1856×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	528
1	111	373
2	338	364
3	1341	363
4	5675	358
5	6616	358
0	8320	358

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))))
(+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6))))
2
(+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))
(* x (+ (* x 1/2) 1))
x
(+ (* x 1/2) 1)
(* x 1/2)
1/2
1
(* x (* (* x x) 1/6))
(* (* x x) 1/6)
(* x x)
1/6
(* x (sqrt 1/2))
x
(sqrt 1/2)
1/2
(* (pow (+ 1/2 (* x 1/6)) 1/2) x)
(pow (+ 1/2 (* x 1/6)) 1/2)
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
x
1/6
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
1
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
2
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(sqrt (+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))))
(+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))))
2
(* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))
(* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x)
(+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6)))))))
1
(* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1/2 (* x 1/6)))
x
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6)))))
(* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))
(/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))
(+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))
(* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))
(- (* x (+ 1/2 (* x 1/6))) 1)

Outputs
(sqrt (+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
2
#s(literal 2 binary64)
(+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ (* x 1/2) 1))
(.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
x
(+ (* x 1/2) 1)
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
(* x (* (* x x) 1/6))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (* x x) 1/6)
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* x x)
(*.f64 x x)
1/6
#s(literal 1/6 binary64)
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (pow (+ 1/2 (* x 1/6)) 1/2) x)
(.f64 x (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(pow (+ 1/2 (* x 1/6)) 1/2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
x
1/6
#s(literal 1/6 binary64)
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* x (+ 1/2 (* x 1/6)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(sqrt (+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))))
(+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))))
(+.f64 #s(literal 2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))))))))
2
#s(literal 2 binary64)
(* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
(+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))
1
#s(literal 1 binary64)
(* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))
(.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))
(* x (+ 1/2 (* x 1/6)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
x
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6)))))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))))))
(+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))
(* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))))
(- (* x (+ 1/2 (* x 1/6))) 1)
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))

localize219.0ms (2.6%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)))))
✓	accuracy	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	99.6%	(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.6%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/6 binary64))

Results

91.0ms	171×	0	valid
34.0ms	85×	0	invalid

Compiler

Compiled 565 to 40 computations (92.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-mult: 35.0ms (43.5% of total)

ival-sqrt: 15.0ms (18.6% of total)

ival-add: 13.0ms (16.2% of total)

ival-pow: 6.0ms (7.5% of total)

ival-div: 5.0ms (6.2% of total)

...c/correct-round.rkt:119:19: 4.0ms (5% of total)

ival-sub: 1.0ms (1.2% of total)

const: 1.0ms (1.2% of total)

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

series20.0ms (0.2%)

Counts

24 → 276

Calls

Call 1

Inputs
#<alt (sqrt (+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))))>
#<alt (+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6))))>
#<alt (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))>
#<alt (* x (+ (* x 1/2) 1))>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (pow (+ 1/2 (* x 1/6)) 1/2) x)>
#<alt (pow (+ 1/2 (* x 1/6)) 1/2)>
#<alt (+ 1/2 (* x 1/6))>
#<alt (* x 1/6)>
#<alt (/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))>
#<alt (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))>
#<alt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (sqrt (+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))))>
#<alt (+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))))>
#<alt (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))>
#<alt (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x)>
#<alt (* (* x x) 1/6)>
#<alt (* x (* (* x x) 1/6))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))>
#<alt (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))>
#<alt (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 6))>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))>
#<alt (/ 6 (pow x 3))>
#<alt (/ (- 6 (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))>
#<alt (/ 6 (pow x 3))>
#<alt (* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 3))))>
#<alt (* x (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))>
#<alt (* x (+ 1 (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 1/24 x)))))))>
#<alt (* 1/216 (pow x 7))>
#<alt (* (pow x 7) (+ 1/216 (* 1/24 (/ 1 x))))>
#<alt (* (pow x 7) (+ 1/216 (+ (/ 1/8 (pow x 2)) (* 1/24 (/ 1 x)))))>
#<alt (* (pow x 7) (+ 1/216 (+ (/ 1/8 (pow x 2)) (+ (* 1/24 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))>
#<alt (* 1/216 (pow x 7))>
#<alt (* (pow x 7) (+ 1/216 (* 1/24 (/ 1 x))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/8 (/ 1 x))) x)) 1/216)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (+ (/ 1/8 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1/216)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (* 1/8 x)))>
#<alt (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 1/24 x)))))>
#<alt (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* x (+ 1/24 (* 1/216 x)))))))>
#<alt (* 1/216 (pow x 6))>
#<alt (* (pow x 6) (+ 1/216 (* 1/24 (/ 1 x))))>
#<alt (* (pow x 6) (+ 1/216 (+ (/ 1/8 (pow x 2)) (* 1/24 (/ 1 x)))))>
#<alt (* (pow x 6) (+ 1/216 (+ (/ 1/8 (pow x 2)) (+ (* 1/24 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))>
#<alt (* 1/216 (pow x 6))>
#<alt (* (pow x 6) (+ 1/216 (* 1/24 (/ 1 x))))>
#<alt (* (pow x 6) (+ 1/216 (+ (/ 1/8 (pow x 2)) (* 1/24 (/ 1 x)))))>
#<alt (* (pow x 6) (+ 1/216 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/8 (/ 1 x))) x)) 1/24) x))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 x) 1/2))>
#<alt (* x (- (* x (+ 1/12 (* 1/6 x))) 1/2))>
#<alt (* x (- (* x (+ 1/12 (* x (+ 1/6 (* 1/36 x))))) 1/2))>
#<alt (* 1/36 (pow x 4))>
#<alt (* (pow x 4) (+ 1/36 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (- (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))) (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* 1/36 (pow x 4))>
#<alt (* (pow x 4) (+ 1/36 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/36 (* -1 (/ (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x)) 1/6) x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* -1/8 x))))))>
#<alt (/ 36 (pow x 4))>
#<alt (/ (- 36 (* 216 (/ 1 x))) (pow x 4))>
#<alt (/ (- (+ 36 (/ 1188 (pow x 2))) (* 216 (/ 1 x))) (pow x 4))>
#<alt (/ (- (+ 36 (/ 1188 (pow x 2))) (+ (* 216 (/ 1 x)) (* 5832 (/ 1 (pow x 3))))) (pow x 4))>
#<alt (/ 36 (pow x 4))>
#<alt (/ (- 36 (* 216 (/ 1 x))) (pow x 4))>
#<alt (/ (+ 36 (* -1 (/ (- 216 (* 1188 (/ 1 x))) x))) (pow x 4))>
#<alt (/ (+ 36 (* -1 (/ (+ 216 (* -1 (/ (- 1188 (* 5832 (/ 1 x))) x))) x))) (pow x 4))>

Calls

69 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
1.0ms	x	@	-inf	(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
1.0ms	x	@	inf	(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
1.0ms	x	@	-inf	(sqrt (+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))))
1.0ms	x	@	-inf	(* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))

rewrite361.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3026×	`fma-lowering-fma.f32`
3026×	`fma-lowering-fma.f64`
2444×	`-lowering-.f32`
2444×	`-lowering-.f64`
1976×	`prod-diff`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	272
1	255	202
2	2469	197
0	8268	197

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 754

Calls

Call 1

Inputs
(sqrt (+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))))
(+ 2 (+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6))))
(+ (* x (+ (* x 1/2) 1)) (* x (* (* x x) 1/6)))
(* x (+ (* x 1/2) 1))
(* x (sqrt 1/2))
(sqrt 1/2)
(* (pow (+ 1/2 (* x 1/6)) 1/2) x)
(pow (+ 1/2 (* x 1/6)) 1/2)
(+ 1/2 (* x 1/6))
(* x 1/6)
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(sqrt (+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))))
(+ 2 (* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))))
(* (* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x) (/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1)))))
(* (+ 1 (* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))) x)
(* (* x x) 1/6)
(* x (* (* x x) 1/6))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(* (* x (+ 1/2 (* x 1/6))) (* x (* (+ 1/2 (* x 1/6)) (* x (+ 1/2 (* x 1/6))))))
(* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))
(/ 1 (+ 1 (* (* x (+ 1/2 (* x 1/6))) (- (* x (+ 1/2 (* x 1/6))) 1))))

Outputs
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))) (sqrt.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))) (sqrt.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) (sqrt.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/36 binary64)) (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 x x) (.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/36 binary64)))) (sqrt.f64 (-.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 x x) (.f64 x #s(literal 1/6 binary64))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1 binary64))
(pow.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1/4 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))))
(.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1/2 binary64)))
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(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(+.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 2 binary64)))
(+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 x x) (*.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))
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simplify282.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

4926×	`-lowering-.f32`
4926×	`-lowering-.f64`
2288×	`+-lowering-+.f64`
2288×	`+-lowering-+.f32`
1364×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	504	3574
1	1687	3197
2	5664	3116
0	8093	3116

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt 1/6))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 6))
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(/ 6 (pow x 3))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/ 6 (pow x 3))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
x
(* x (+ 1 (* 1/8 (pow x 3))))
(* x (+ 1 (* (pow x 3) (+ 1/8 (* 1/8 x)))))
(* x (+ 1 (* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 1/24 x)))))))
(* 1/216 (pow x 7))
(* (pow x 7) (+ 1/216 (* 1/24 (/ 1 x))))
(* (pow x 7) (+ 1/216 (+ (/ 1/8 (pow x 2)) (* 1/24 (/ 1 x)))))
(* (pow x 7) (+ 1/216 (+ (/ 1/8 (pow x 2)) (+ (* 1/24 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))
(* 1/216 (pow x 7))
(* (pow x 7) (+ 1/216 (* 1/24 (/ 1 x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/8 (/ 1 x))) x)) 1/216)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (+ (/ 1/8 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1/216)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (* 1/8 x)))
(* (pow x 3) (+ 1/8 (* x (+ 1/8 (* 1/24 x)))))
(* (pow x 3) (+ 1/8 (* x (+ 1/8 (* x (+ 1/24 (* 1/216 x)))))))
(* 1/216 (pow x 6))
(* (pow x 6) (+ 1/216 (* 1/24 (/ 1 x))))
(* (pow x 6) (+ 1/216 (+ (/ 1/8 (pow x 2)) (* 1/24 (/ 1 x)))))
(* (pow x 6) (+ 1/216 (+ (/ 1/8 (pow x 2)) (+ (* 1/24 (/ 1 x)) (* 1/8 (/ 1 (pow x 3)))))))
(* 1/216 (pow x 6))
(* (pow x 6) (+ 1/216 (* 1/24 (/ 1 x))))
(* (pow x 6) (+ 1/216 (+ (/ 1/8 (pow x 2)) (* 1/24 (/ 1 x)))))
(* (pow x 6) (+ 1/216 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/8 (/ 1 x))) x)) 1/24) x))))
(* -1/2 x)
(* x (- (* 1/12 x) 1/2))
(* x (- (* x (+ 1/12 (* 1/6 x))) 1/2))
(* x (- (* x (+ 1/12 (* x (+ 1/6 (* 1/36 x))))) 1/2))
(* 1/36 (pow x 4))
(* (pow x 4) (+ 1/36 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))) (* 1/2 (/ 1 (pow x 3)))))
(* 1/36 (pow x 4))
(* (pow x 4) (+ 1/36 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/36 (* -1 (/ (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x)) 1/6) x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* -1/8 x))))))
(/ 36 (pow x 4))
(/ (- 36 (* 216 (/ 1 x))) (pow x 4))
(/ (- (+ 36 (/ 1188 (pow x 2))) (* 216 (/ 1 x))) (pow x 4))
(/ (- (+ 36 (/ 1188 (pow x 2))) (+ (* 216 (/ 1 x)) (* 5832 (/ 1 (pow x 3))))) (pow x 4))
(/ 36 (pow x 4))
(/ (- 36 (* 216 (/ 1 x))) (pow x 4))
(/ (+ 36 (* -1 (/ (- 216 (* 1188 (/ 1 x))) x))) (pow x 4))
(/ (+ 36 (* -1 (/ (+ 216 (* -1 (/ (- 1188 (* 5832 (/ 1 x))) x))) x))) (pow x 4))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
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(* (pow x 4) (+ 1/36 (* 1/6 (/ 1 x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal 1/6 binary64) x)) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(* (pow x 4) (- (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))) (* 1/2 (/ 1 (pow x 3)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/36 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 (/.f64 (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)) x) x))))
(* 1/36 (pow x 4))
(.f64 #s(literal 1/36 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* (pow x 4) (+ 1/36 (* 1/6 (/ 1 x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/36 (+ (/ 1/12 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal 1/6 binary64) x)) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(* (pow x 4) (+ 1/36 (* -1 (/ (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x)) 1/6) x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal 1/36 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* -1/8 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal -1/8 binary64)))))))
(/ 36 (pow x 4))
(/.f64 #s(literal 36 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ (- 36 (* 216 (/ 1 x))) (pow x 4))
(/.f64 (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -216 binary64) x)) (.f64 (.f64 x (*.f64 x x)) x))
(/ (- (+ 36 (/ 1188 (pow x 2))) (* 216 (/ 1 x))) (pow x 4))
(/.f64 (+.f64 (/.f64 #s(literal 1188 binary64) (.f64 x x)) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -216 binary64) x))) (.f64 (.f64 x (.f64 x x)) x))
(/ (- (+ 36 (/ 1188 (pow x 2))) (+ (* 216 (/ 1 x)) (* 5832 (/ 1 (pow x 3))))) (pow x 4))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1188 binary64) (.f64 x x)) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -216 binary64) x))) (/.f64 #s(literal -5832 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) x))
(/ 36 (pow x 4))
(/.f64 #s(literal 36 binary64) (.f64 (.f64 x (*.f64 x x)) x))
(/ (- 36 (* 216 (/ 1 x))) (pow x 4))
(/.f64 (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -216 binary64) x)) (.f64 (.f64 x (*.f64 x x)) x))
(/ (+ 36 (* -1 (/ (- 216 (* 1188 (/ 1 x))) x))) (pow x 4))
(/.f64 (-.f64 #s(literal 36 binary64) (/.f64 (-.f64 #s(literal 216 binary64) (/.f64 #s(literal 1188 binary64) x)) x)) (.f64 (.f64 x (*.f64 x x)) x))
(/ (+ 36 (* -1 (/ (+ 216 (* -1 (/ (- 1188 (* 5832 (/ 1 x))) x))) x))) (pow x 4))
(/.f64 (-.f64 #s(literal 36 binary64) (/.f64 (-.f64 #s(literal 216 binary64) (/.f64 (+.f64 #s(literal 1188 binary64) (/.f64 #s(literal -5832 binary64) x)) x)) x)) (.f64 (.f64 x (*.f64 x x)) x))

eval187.0ms (2.2%)

Compiler: Compiled 51222 to 3798 computations (92.6% saved)

prune133.0ms (1.6%)

Pruning

24 alts after pruning (13 fresh and 11 done)

	Pruned	Kept	Total
New	1294	12	1306
Fresh	2	1	3
Picked	4	1	5
Done	1	10	11
Total	1301	24	1325

Accuracy

100.0%

Counts

1325 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	0.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 18 binary64) x)) (.f64 x (.f64 x x)))))
	63.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
	65.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
	69.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	1.5%	(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
	2.5%	(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
✓	2.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	64.5%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
	64.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/12 binary64))))))))))
	64.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))
	65.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
	64.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) #s(literal 1 binary64))))
	71.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	65.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	64.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	64.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	3.4%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
	2.3%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	3.9%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
✓	2.3%	(sqrt.f64 x)
✓	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 1018 to 402 computations (60.5% saved)

regimes39.0ms (0.5%)

Counts

35 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x #s(literal 1/6 binary64))))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 18 binary64) x)) (.f64 x (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/12 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

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

Calls

3 calls:

11.0ms

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

9.0ms

8.0ms

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

Results

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes11.0ms (0.1%)

Counts

33 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x #s(literal 1/6 binary64))))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 18 binary64) x)) (.f64 x (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/12 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))))

Outputs

(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
71.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes11.0ms (0.1%)

Accuracy

Total -45.1b remaining (-238.4%)

Threshold costs -45.1b (-238.4%)

Counts

24 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x #s(literal 1/6 binary64))))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 18 binary64) x)) (.f64 x (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64))))))

Outputs
(sqrt.f64 #s(literal 2 binary64))

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
70.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-commutative_binary64`
4×	`unsub-neg_binary64`
4×	`sub-neg_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	33
1	32	33
2	36	33
3	39	33
4	42	33
5	45	33

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))

(sqrt.f64 #s(literal 2 binary64))

Outputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))))))))
(sqrt.f64 #s(literal 2 binary64))

soundness1.1s (12.8%)

Rules

4926×	`-lowering-.f32`
4926×	`-lowering-.f64`
3408×	`/-lowering-/.f32`
3408×	`/-lowering-/.f64`
3346×	`-lowering-.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	110
1	147	93
2	1434	91
0	8186	91
0	52	221
1	162	175
2	540	174
3	1192	171
4	2849	170
5	6799	170
0	8138	170
0	10	8
1	24	8
2	31	8
3	46	8
4	77	7
5	140	5
6	300	5
7	853	5
8	4984	5
0	8232	5
0	504	3574
1	1687	3197
2	5664	3116
0	8093	3116

Stop Event

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

Compiler

Compiled 98 to 66 computations (32.7% saved)

preprocess26.0ms (0.3%)

Compiler: Compiled 94 to 60 computations (36.2% saved)

analyze269.0ms (3.2%)

sample2.3s (27.3%)

preprocess247.0ms (2.9%)

explain180.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize23.0ms (0.3%)

series2.0ms (0%)

rewrite559.0ms (6.7%)

simplify212.0ms (2.5%)

eval31.0ms (0.4%)

prune49.0ms (0.6%)

simplify47.0ms (0.6%)

localize103.0ms (1.2%)

series15.0ms (0.2%)

rewrite334.0ms (4%)

simplify291.0ms (3.5%)

eval107.0ms (1.3%)

prune78.0ms (0.9%)

simplify24.0ms (0.3%)

localize115.0ms (1.4%)

series10.0ms (0.1%)

rewrite350.0ms (4.2%)

simplify320.0ms (3.8%)

eval90.0ms (1.1%)

prune106.0ms (1.3%)

simplify165.0ms (2%)

localize219.0ms (2.6%)

series20.0ms (0.2%)

rewrite361.0ms (4.3%)

simplify282.0ms (3.4%)

eval187.0ms (2.2%)

prune133.0ms (1.6%)

regimes39.0ms (0.5%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

simplify8.0ms (0.1%)

soundness1.1s (12.8%)

preprocess26.0ms (0.3%)

end0.0ms (0%)

Profiling