Metrics for sqrtexp (problem 3.4.4)

analyze208.0ms (2.8%)

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: 107.0ms

ival-mult: 34.0ms (31.7% of total)

ival-exp: 31.0ms (28.9% of total)

ival-sub: 20.0ms (18.7% of total)

ival-sqrt: 12.0ms (11.2% of total)

ival-div: 6.0ms (5.6% of total)

const: 3.0ms (2.8% of total)

backward-pass: 1.0ms (0.9% of total)

sample2.2s (30.1%)

Results

1.4s	5280×	1	valid
287.0ms	2976×	0	valid
189.0ms	2739×	0	unsamplable

Precisions

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

ival-exp: 779.0ms (51.7% of total)

ival-sub: 247.0ms (16.4% of total)

ival-mult: 136.0ms (9% of total)

ival-sqrt: 124.0ms (8.2% of total)

ival-div: 99.0ms (6.6% of total)

backward-pass: 94.0ms (6.2% of total)

const: 27.0ms (1.8% of total)

Bogosity

preprocess250.0ms (3.4%)

Algorithm

2×	egg-herbie

Rules

2108×	`-lowering-.f32`
2108×	`-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	125	27
4	234	20
5	435	18
6	954	18
7	3777	18
0	10	8
1	24	8
2	31	8
3	45	8
4	76	7
5	141	5
6	301	5
7	852	5
8	4984	5
0	8245	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)))))

explain215.0ms (2.9%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
164	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
164	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
1	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	0	-	-	`x`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`#s(literal 2 binary64)`
0	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	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`#s(literal 1 binary64)`
0	1	(50.00437546068447)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`

Results

146.0ms	318×	1	valid
18.0ms	194×	0	valid

Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-exp: 42.0ms (50.2% of total)

backward-pass: 13.0ms (15.5% of total)

ival-sub: 9.0ms (10.7% of total)

ival-mult: 7.0ms (8.4% of total)

ival-sqrt: 6.0ms (7.2% of total)

ival-div: 5.0ms (6% of total)

const: 1.0ms (1.2% 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)

simplify3.0ms (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%	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Results

14.0ms

256×

valid

Compiler

Compiled 15 to 6 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-exp: 2.0ms (34.9% of total)

ival-sqrt: 2.0ms (34.9% of total)

ival-add: 1.0ms (17.4% 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)

rewrite538.0ms (7.3%)

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	153	11
3	1168	11
0	8245	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) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))))
(/.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 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))))
(/.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 3 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (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)))))) (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 (expm1.f64 x) #s(literal 1/2 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 (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 3 binary64))) (expm1.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 0 binary64) (+.f64 #s(literal 1 binary64) (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 3 binary64))) (expm1.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 0 binary64) (+.f64 #s(literal 1 binary64) (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 (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64))))
(/.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 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
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(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (.f64 x #s(literal 2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (expm1.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(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))

simplify200.0ms (2.7%)

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	539	174
3	1189	171
4	2839	170
5	6888	170
0	8224	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 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 (.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)

eval51.0ms (0.7%)

Compiler: Compiled 6138 to 918 computations (85% saved)

prune41.0ms (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))))))))
▶	65.7%	(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)

simplify42.0ms (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: 1 (0.0ms)

Iter	Nodes	Cost
0	23	129
1	54	111
2	130	111
3	288	111
4	537	111
5	844	111
6	1181	111
7	1305	111
8	1306	111
0	1306	111

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)

localize117.0ms (1.6%)

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%	(.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%	(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	99.6%	(*.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

43.0ms	169×	0	valid
19.0ms	87×	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: 10.0ms (29.5% of total)

ival-mult: 9.0ms (26.5% of total)

ival-sqrt: 9.0ms (26.5% of total)

...c/correct-round.rkt:119:19: 6.0ms (17.7% of total)

const: 1.0ms (2.9% of total)

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

series13.0ms (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
1.0ms	x	@	-inf	(sqrt (+ 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))
1.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
1.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))

rewrite340.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3462×	`/-lowering-/.f32`
3462×	`/-lowering-/.f64`
3026×	`-lowering-.f32`
3026×	`-lowering-.f64`
2216×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	110
1	147	93
2	1427	93
0	8156	93

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 584

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

simplify286.0ms (3.9%)

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	1513
2	3415	1464
0	8714	1464

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

eval106.0ms (1.4%)

Compiler: Compiled 17635 to 2145 computations (87.8% saved)

prune87.0ms (1.2%)

Pruning

18 alts after pruning (12 fresh and 6 done)

	Pruned	Kept	Total
New	764	12	776
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	764	18	782

Accuracy

100.0%

Counts

782 → 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))))))))))
▶	63.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.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 binary64) (.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 x)))) x)))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))))
▶	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))
✓	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))))))))
✓	65.7%	(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)))
	1.5%	(sqrt.f64 (.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)))))
	2.3%	(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
▶	2.4%	(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))))
	3.4%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	2.4%	(sqrt.f64 x)
✓	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 439 to 308 computations (29.8% saved)

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

1700×	`fma-define`
1338×	`fma-lowering-fma.f32`
1338×	`fma-lowering-fma.f64`
754×	`-lowering-.f32`
754×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	304
1	95	272
2	224	259
3	615	251
4	1330	251
5	2152	251
6	2398	251
7	2414	251
8	2416	251
9	2429	251
10	2457	251
11	2464	251
0	2464	251

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))))
(+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))))
2
(* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))
x
(+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))
1
(/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))
(/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))
(+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2)))
1/4
(* (* x 1/6) (- (* x 1/6) 1/2))
(* x 1/6)
1/6
(- (* x 1/6) 1/2)
1/2
(* (+ 1/8 (* (* x (* x x)) 1/216)) x)
(+ 1/8 (* (* x (* x x)) 1/216))
1/8
(* (* x (* x x)) 1/216)
(* x (* x x))
(* x x)
1/216
(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
(/ 1 (sqrt (/ 1 (+ 2 x))))
1
(sqrt (/ 1 (+ 2 x)))
(/ 1 (+ 2 x))
(+ 2 x)
2
x
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* 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 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))))))
(+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))))))))
2
#s(literal 2 binary64)
(* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))))
x
(+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))
(+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64)))))))
1
#s(literal 1 binary64)
(/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))
(/.f64 x (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64))))))
(/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))
(+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2)))
(+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64))))
1/4
#s(literal 1/4 binary64)
(* (* x 1/6) (- (* x 1/6) 1/2))
(.f64 x (+.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal -1/12 binary64)))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(- (* x 1/6) 1/2)
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (+ 1/8 (* (* x (* x x)) 1/216)) x)
(.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))))
(+ 1/8 (* (* x (* x x)) 1/216))
(+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64))))
1/8
#s(literal 1/8 binary64)
(* (* x (* x x)) 1/216)
(.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64)))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
1/216
#s(literal 1/216 binary64)
(sqrt x)
(sqrt.f64 x)
x
(sqrt (* x (+ 1 (* 1/2 x))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 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)
(/ 1 (sqrt (/ 1 (+ 2 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ 2 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)))
(/ 1 (+ 2 x))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x 1/6)))
(.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(+ 1/2 (* x 1/6))
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 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)

localize185.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(.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	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
✓	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 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%	(sqrt.f64 x)
✓	accuracy	100.0%	(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
✓	accuracy	99.9%	(/.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)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))

Results

61.0ms	84×	0	valid
61.0ms	172×	0	invalid

Compiler

Compiled 345 to 38 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-div: 29.0ms (37.6% of total)

ival-mult: 20.0ms (25.9% of total)

ival-add: 10.0ms (13% of total)

...c/correct-round.rkt:119:19: 8.0ms (10.4% of total)

ival-sqrt: 8.0ms (10.4% of total)

ival-sub: 1.0ms (1.3% of total)

const: 1.0ms (1.3% of total)

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

series19.0ms (0.3%)

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (sqrt (+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))))>
#<alt (+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))))>
#<alt (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))>
#<alt (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))>
#<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 (/ 1 (sqrt (/ 1 (+ 2 x))))>
#<alt (sqrt (/ 1 (+ 2 x)))>
#<alt (/ 1 (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (* 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 (* x (+ 1/2 (* x 1/6)))>
#<alt (* x 1/6)>
#<alt (* x (* x x))>
#<alt (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))>
#<alt (* (* x (* x x)) 1/216)>
#<alt (+ 1/2 (* 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 (+ (* 1/2 (/ (* 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 (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 (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 (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* 1/2 (/ (* x (- 1/8 (* 1/64 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/16 (* -1/8 (/ (- 1/8 (* 1/64 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/8 (* 1/64 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 8 x))) (* 2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* 2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1 (/ (+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 8 (* -1 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/8 x) 1/4)))>
#<alt (+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))>
#<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 x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))>
#<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) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 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 (* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))>
#<alt (* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 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 (* 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))))>
#<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 (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 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))))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<alt (* 1/216 (pow x 3))>
#<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))))>

Calls

66 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))
2.0ms	x	@	0	(/ 1 (+ 2 x))
1.0ms	x	@	-inf	(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms	x	@	inf	(/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))
1.0ms	x	@	-inf	(sqrt (* x (+ 1 (* 1/2 x))))

rewrite402.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3574×	`-lowering-.f32`
3574×	`-lowering-.f64`
3370×	`/-lowering-/.f32`
3370×	`/-lowering-/.f64`
2148×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	235
1	236	127
2	2053	127
0	9428	127

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 706

Calls

Call 1

Inputs
(sqrt (+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))))
(+ 2 (* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))))
(* x (+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))))
(+ 1 (/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x))))
(sqrt x)
(sqrt (* x (+ 1 (* 1/2 x))))
(* x (+ 1 (* 1/2 x)))
(+ 1 (* 1/2 x))
(* 1/2 x)
(/ 1 (sqrt (/ 1 (+ 2 x))))
(sqrt (/ 1 (+ 2 x)))
(/ 1 (+ 2 x))
(+ 2 x)
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(* x 1/6)
(* x (* x x))
(/ 1 (/ (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))) (* (+ 1/8 (* (* x (* x x)) 1/216)) x)))
(* (* x (* x x)) 1/216)
(+ 1/2 (* x 1/6))

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 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 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))) (sqrt.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 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 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 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 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 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 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))) #s(literal 1/2 binary64))
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(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (/.f64 (.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 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))))) (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64)) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64)) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64))))))
(/.f64 (-.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 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (-.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 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))) #s(literal -1/4 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64))) (neg.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (-.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 (.f64 x x) #s(literal 1/36 binary64)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))) #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64)))) #s(literal -1 binary64))
(.f64 (+.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 x (+.f64 (.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))))))
(.f64 (-.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 1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/10077696 binary64))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/216 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))) (-.f64 (.f64 x (+.f64 (.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/10077696 binary64))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/216 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.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 1/16 binary64) (.f64 (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))) (-.f64 (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.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 x (+.f64 (.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))))))

simplify299.0ms (4%)

Algorithm

1×	egg-herbie

Rules

5034×	`-lowering-.f32`
5034×	`-lowering-.f64`
2658×	`+-lowering-+.f64`
2658×	`+-lowering-+.f32`
1336×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	2509
1	1428	2152
2	5043	2077
0	8089	2077

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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)))
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)))))
(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)
(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)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* 1/2 (/ (* x (- 1/8 (* 1/64 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/16 (* -1/8 (/ (- 1/8 (* 1/64 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/8 (* 1/64 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 8 x))) (* 2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* 2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1 (/ (+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 8 (* -1 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/8 x) 1/4)))
(+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))
(/ 1 x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)
(/ 1 x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))
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 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(* (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) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 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))))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 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)
(* 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))))
(* 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)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 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))))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
(* 1/216 (pow x 3))
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))))

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 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))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (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 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (/.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) (+ (* 1/4 (* (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 (.f64 x x) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (/.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)))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal -3/8 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 #s(literal 1/4 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 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 x (.f64 x (+.f64 (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (.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 #s(literal 1/4 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 #s(literal 2 binary64) (.f64 x #s(literal -3/8 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 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (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 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (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 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (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 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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)))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/32 binary64)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/32 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/128 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 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.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 1/8 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(* 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))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(* -1 (* x (* (sqrt -1) (sqrt -1/2))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) x) (sqrt.f64 #s(literal -1/2 binary64))))
(* -1 (* x (+ (* -1/2 (/ (sqrt -1) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (sqrt.f64 #s(literal -1/2 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/2 binary64))))))
(* -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)))))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 (+.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 #s(literal -1/2 binary64))) #s(literal -1/4 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))) x))))
(* -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)))))
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(.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 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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)
(* 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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 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))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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))))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))

eval123.0ms (1.7%)

Compiler: Compiled 24227 to 2995 computations (87.6% saved)

prune122.0ms (1.6%)

Pruning

22 alts after pruning (12 fresh and 10 done)

	Pruned	Kept	Total
New	991	7	998
Fresh	2	5	7
Picked	1	4	5
Done	0	6	6
Total	994	22	1016

Accuracy

100.0%

Counts

1016 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
	63.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
▶	0.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)))
	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))))))))))
▶	65.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
▶	69.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.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 binary64) (.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 x)))) x)))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))
✓	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))))))))
✓	65.7%	(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)))
	2.3%	(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)))))
	2.4%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)))))
✓	2.4%	(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))))
✓	2.4%	(sqrt.f64 x)
✓	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 441 to 318 computations (27.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
✓	cost-diff	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
✓	cost-diff	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)))
✓	cost-diff	(*.f64 x #s(literal -1/4 binary64))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
✓	cost-diff	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

12×	`+-lowering-+.f64`
12×	`/-lowering-/.f32`
12×	`/-lowering-/.f64`
12×	`+-lowering-+.f32`
8×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	89
1	36	86
2	38	86
0	38	86

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize83.0ms (1.1%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)))
✓	accuracy	100.0%	(/.f64 #s(literal -2 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))

Results

53.0ms

256×

invalid

Compiler

Compiled 99 to 23 computations (76.8% saved)

Precisions

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

ival-div: 9.0ms (32.4% of total)

ival-sqrt: 6.0ms (21.6% of total)

ival-add: 4.0ms (14.4% of total)

ival-mult: 4.0ms (14.4% of total)

ival-pow: 4.0ms (14.4% of total)

const: 1.0ms (3.6% of total)

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

series15.0ms (0.2%)

Counts

15 → 156

Calls

Call 1

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

Outputs
#<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 (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 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/8 x) 1/4)))>
#<alt (+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))>
#<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 (+ (* 1/2 (/ (* 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 (- 1/4 (* 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 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<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 (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/4))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))>
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* x (sqrt -1/2))>
#<alt (* x (+ (sqrt -1/2) (* -1/8 (/ x (sqrt -1/2)))))>
#<alt (* x (+ (sqrt -1/2) (* x (- (* -1/2 (/ (* x (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2))))) (sqrt -1/2))) (* 1/8 (/ 1 (sqrt -1/2)))))))>
#<alt (* x (+ (sqrt -1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/16 (* 1/8 (/ (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2)))) (pow (sqrt -1/2) 2))))) (sqrt -1/2))) (* -1/2 (/ (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2)))) (sqrt -1/2))))) (* 1/8 (/ 1 (sqrt -1/2)))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* 2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 8 x))) (* 2 (sqrt (/ 1 (pow x 5))))))))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -2 (sqrt (/ 1 (pow x 5)))) (* -1 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (+ 8 (* -1 x)))) (* 2 (sqrt x))) (pow x 3)))))))>
#<alt (/ (sqrt -2) x)>
#<alt (/ (+ (sqrt -2) (* 1/2 (/ x (sqrt -2)))) x)>
#<alt (/ (+ (sqrt -2) (* x (+ (* -1/8 (/ x (pow (sqrt -2) 3))) (* 1/2 (/ 1 (sqrt -2)))))) x)>
#<alt (/ (+ (sqrt -2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -2) 5))) (* 1/8 (/ 1 (pow (sqrt -2) 3))))) (* 1/2 (/ 1 (sqrt -2)))))) x)>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* -1/2 (sqrt (/ 1 (pow x 7)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))>
#<alt (/ -2 (pow x 2))>
#<alt (/ (- x 2) (pow x 2))>
#<alt (/ (- x 2) (pow x 2))>
#<alt (/ (- x 2) (pow x 2))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 2 (/ 1 x))) x)>
#<alt (/ (- 1 (* 2 (/ 1 x))) x)>
#<alt (/ (- 1 (* 2 (/ 1 x))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) 1) x))>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) 1) x))>
#<alt (* -1 (/ (- (* 2 (/ 1 x)) 1) x))>
#<alt (/ -2 x)>
#<alt (/ (- x 2) x)>
#<alt (/ (- x 2) x)>
#<alt (/ (- x 2) x)>
#<alt 1>
#<alt (- 1 (* 2 (/ 1 x)))>
#<alt (- 1 (* 2 (/ 1 x)))>
#<alt (- 1 (* 2 (/ 1 x)))>
#<alt 1>
#<alt (- 1 (* 2 (/ 1 x)))>
#<alt (- 1 (* 2 (/ 1 x)))>
#<alt (- 1 (* 2 (/ 1 x)))>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>

Calls

39 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(+ 2 x)
1.0ms	x	@	-inf	(/ 1 (sqrt (+ 1/2 (* x -1/4))))
1.0ms	x	@	inf	(/ 1 (sqrt (+ 1/2 (* x -1/4))))
1.0ms	x	@	inf	(sqrt (+ 1/2 (* x -1/4)))
1.0ms	x	@	-inf	(/ 1 (sqrt (/ (+ 1 (/ -2 x)) x)))

rewrite279.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3934×	`-lowering-.f32`
3934×	`-lowering-.f64`
3380×	`/-lowering-/.f32`
3380×	`/-lowering-/.f64`
1296×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	72
1	127	68
2	799	67
0	8231	67

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 613

Calls

Call 1

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

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

simplify250.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

4532×	`+-lowering-+.f64`
4532×	`+-lowering-+.f32`
3962×	`-lowering-.f32`
3962×	`-lowering-.f64`
1110×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	383	1594
1	1229	1406
2	4167	1376
0	8085	1376

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
(* 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))
(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)))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/8 x) 1/4)))
(+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))
(/ 1 x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)
(/ 1 x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))
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 (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 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 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(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 (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/4))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* x (sqrt -1/2))
(* x (+ (sqrt -1/2) (* -1/8 (/ x (sqrt -1/2)))))
(* x (+ (sqrt -1/2) (* x (- (* -1/2 (/ (* x (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2))))) (sqrt -1/2))) (* 1/8 (/ 1 (sqrt -1/2)))))))
(* x (+ (sqrt -1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/16 (* 1/8 (/ (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2)))) (pow (sqrt -1/2) 2))))) (sqrt -1/2))) (* -1/2 (/ (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2)))) (sqrt -1/2))))) (* 1/8 (/ 1 (sqrt -1/2)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* 2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 8 x))) (* 2 (sqrt (/ 1 (pow x 5))))))))
(* -1 (sqrt x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -2 (sqrt (/ 1 (pow x 5)))) (* -1 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (+ 8 (* -1 x)))) (* 2 (sqrt x))) (pow x 3)))))))
(/ (sqrt -2) x)
(/ (+ (sqrt -2) (* 1/2 (/ x (sqrt -2)))) x)
(/ (+ (sqrt -2) (* x (+ (* -1/8 (/ x (pow (sqrt -2) 3))) (* 1/2 (/ 1 (sqrt -2)))))) x)
(/ (+ (sqrt -2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -2) 5))) (* 1/8 (/ 1 (pow (sqrt -2) 3))))) (* 1/2 (/ 1 (sqrt -2)))))) x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* -1/2 (sqrt (/ 1 (pow x 7)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))
(/ -2 (pow x 2))
(/ (- x 2) (pow x 2))
(/ (- x 2) (pow x 2))
(/ (- x 2) (pow x 2))
(/ 1 x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/ 1 x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(/ -2 x)
(/ (- x 2) x)
(/ (- x 2) x)
(/ (- x 2) x)
1
(- 1 (* 2 (/ 1 x)))
(- 1 (* 2 (/ 1 x)))
(- 1 (* 2 (/ 1 x)))
1
(- 1 (* 2 (/ 1 x)))
(- 1 (* 2 (/ 1 x)))
(- 1 (* 2 (/ 1 x)))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)

Outputs
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 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 x (sqrt.f64 #s(literal 2 binary64))) #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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/16 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (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 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.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 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 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x 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 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.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))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* x (- (* 1/8 x) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x #s(literal 1/8 binary64)))))
(+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal -2 binary64)) x)) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal -2 binary64)) x)) (/.f64 #s(literal -8 binary64) (.f64 x (.f64 x x)))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x)) x)) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 x #s(literal 2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 x #s(literal 2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 x #s(literal 2 binary64))
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 x #s(literal 2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 x #s(literal 2 binary64))
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 x #s(literal 2 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 x (sqrt.f64 #s(literal 2 binary64))) #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 (+ (* 1/2 (/ (* x (- 1/4 (* 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 5/64 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -4 binary64)) (sqrt.f64 #s(literal -4 binary64))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 32 binary64) (/.f64 (.f64 x #s(literal 16 binary64)) #s(literal -4 binary64))))) (sqrt.f64 #s(literal -4 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -4 binary64)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -2 binary64))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -2 binary64)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -2 binary64)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64)))) (.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (.f64 x (.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (-.f64 (.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -1/1024 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt x) (sqrt -1/4))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/4 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(.f64 x (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(.f64 x (+.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1/4 binary64))))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(.f64 x (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/128 binary64)) (pow.f64 (sqrt.f64 #s(literal -1/4 binary64)) #s(literal 5 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1/4 binary64)))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/4 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* x (sqrt -1/2))
(*.f64 x (sqrt.f64 #s(literal -1/2 binary64)))
(* x (+ (sqrt -1/2) (* -1/8 (/ x (sqrt -1/2)))))
(.f64 x (+.f64 (sqrt.f64 #s(literal -1/2 binary64)) (/.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))))
(* x (+ (sqrt -1/2) (* x (- (* -1/2 (/ (* x (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2))))) (sqrt -1/2))) (* 1/8 (/ 1 (sqrt -1/2)))))))
(.f64 x (+.f64 (sqrt.f64 #s(literal -1/2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 x (/.f64 #s(literal -3/64 binary64) (sqrt.f64 #s(literal -1/2 binary64))))))))
(* x (+ (sqrt -1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/16 (* 1/8 (/ (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2)))) (pow (sqrt -1/2) 2))))) (sqrt -1/2))) (* -1/2 (/ (+ 1/8 (* 1/64 (/ 1 (pow (sqrt -1/2) 2)))) (sqrt -1/2))))) (* 1/8 (/ 1 (sqrt -1/2)))))))
(.f64 x (+.f64 (sqrt.f64 #s(literal -1/2 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 (.f64 #s(literal -5/256 binary64) x) (sqrt.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -3/64 binary64) (sqrt.f64 #s(literal -1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1/2 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))) (* 2 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 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 7))) (- 8 x))) (* 2 (sqrt (/ 1 (pow x 5))))))))
(.f64 x (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 8 binary64) x))))))
(* -1 (sqrt x))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))))
(.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 x)) (+ (* -2 (sqrt (/ 1 (pow x 5)))) (* -1 (sqrt (/ 1 (pow x 3))))))))
(.f64 (+.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (+ 8 (* -1 x)))) (* 2 (sqrt x))) (pow x 3)))))))
(.f64 (-.f64 #s(literal 0 binary64) 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 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 8 binary64) x))) (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (.f64 x (.f64 x x)))))
(/ (sqrt -2) x)
(/.f64 (sqrt.f64 #s(literal -2 binary64)) x)
(/ (+ (sqrt -2) (* 1/2 (/ x (sqrt -2)))) x)
(/.f64 (+.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -2 binary64)))) x)
(/ (+ (sqrt -2) (* x (+ (* -1/8 (/ x (pow (sqrt -2) 3))) (* 1/2 (/ 1 (sqrt -2)))))) x)
(/.f64 (+.f64 (sqrt.f64 #s(literal -2 binary64)) (.f64 x (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 x (sqrt.f64 #s(literal -2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -2 binary64)))))) x)
(/ (+ (sqrt -2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -2) 5))) (* 1/8 (/ 1 (pow (sqrt -2) 3))))) (* 1/2 (/ 1 (sqrt -2)))))) x)
(/.f64 (+.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)))))))) x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1/2 (sqrt (/ 1 (pow x 5))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* -1/2 (sqrt (/ 1 (pow x 7)))))))
(+.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) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))
(+.f64 (+.f64 (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 7 binary64)))))) (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ (- x 2) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- x 2) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- x 2) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- x 2) x)
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(/ (- x 2) x)
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(/ (- x 2) x)
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
1
#s(literal 1 binary64)
(- 1 (* 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(- 1 (* 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(- 1 (* 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
1
#s(literal 1 binary64)
(- 1 (* 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(- 1 (* 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(- 1 (* 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)

eval110.0ms (1.5%)

Compiler: Compiled 13621 to 2495 computations (81.7% saved)

prune108.0ms (1.5%)

Pruning

21 alts after pruning (11 fresh and 10 done)

	Pruned	Kept	Total
New	787	5	792
Fresh	1	6	7
Picked	3	2	5
Done	2	8	10
Total	793	21	814

Accuracy

100.0%

Counts

814 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	1.3%	(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -1/2 binary64))
	66.2%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
	1.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -1/2 binary64))))
	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))))))))))
	65.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
✓	69.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	1.2%	(sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.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 binary64) (.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 x)))) x)))))
	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))))
✓	64.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))
✓	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))))))))
✓	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)))
	2.3%	(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)))))
	2.4%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)))))
✓	2.4%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	2.4%	(sqrt.f64 x)
✓	70.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 616 to 317 computations (48.5% saved)

regimes31.0ms (0.4%)

Counts

31 → 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 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)))
(sqrt.f64 (.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) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -1/2 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))))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)))))
(sqrt.f64 (.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)))))
(/.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 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.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 binary64) (.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 x)))) x)))))
(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:

14.0ms

7.0ms

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

7.0ms

(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)

regimes9.0ms (0.1%)

Accuracy

Total -45.0b remaining (-237.3%)

Threshold costs -45b (-237.3%)

Counts

29 → 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 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)))
(sqrt.f64 (.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) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -1/2 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))))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)))))
(sqrt.f64 (.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)))))
(/.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 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 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)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.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 binary64) (.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 x)))) x)))))

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

Calls

1 calls:

8.0ms

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

2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	11	7

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 #s(literal 2 binary64))

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

soundness487.0ms (6.6%)

Rules

3346×	`-lowering-.f32`
3346×	`-lowering-.f64`
2108×	`-lowering-.f32`
2108×	`-lowering-.f64`
1870×	`+-lowering-+.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	52	221
1	162	175
2	539	174
3	1189	171
4	2839	170
5	6888	170
0	8224	170
0	10	8
1	24	8
2	31	8
3	45	8
4	76	7
5	141	5
6	301	5
7	852	5
8	4984	5
0	8245	5

Stop Event

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

Compiler

Compiled 23 to 20 computations (13% saved)

preprocess25.0ms (0.3%)

Compiler: Compiled 42 to 34 computations (19% saved)

analyze208.0ms (2.8%)

sample2.2s (30.1%)

preprocess250.0ms (3.4%)

explain215.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize23.0ms (0.3%)

series2.0ms (0%)

rewrite538.0ms (7.3%)

simplify200.0ms (2.7%)

eval51.0ms (0.7%)

prune41.0ms (0.6%)

simplify42.0ms (0.6%)

localize117.0ms (1.6%)

series13.0ms (0.2%)

rewrite340.0ms (4.6%)

simplify286.0ms (3.9%)

eval106.0ms (1.4%)

prune87.0ms (1.2%)

simplify78.0ms (1%)

localize185.0ms (2.5%)

series19.0ms (0.3%)

rewrite402.0ms (5.4%)

simplify299.0ms (4%)

eval123.0ms (1.7%)

prune122.0ms (1.6%)

simplify5.0ms (0.1%)

localize83.0ms (1.1%)

series15.0ms (0.2%)

rewrite279.0ms (3.8%)

simplify250.0ms (3.4%)

eval110.0ms (1.5%)

prune108.0ms (1.5%)

regimes31.0ms (0.4%)

regimes9.0ms (0.1%)

simplify8.0ms (0.1%)

soundness487.0ms (6.6%)

preprocess25.0ms (0.3%)

end0.0ms (0%)

Profiling