Metrics for sqrtexp (problem 3.4.4)

analyze191.0ms (2.5%)

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: 99.0ms

ival-mult: 34.0ms (34.2% of total)

ival-exp: 24.0ms (24.2% of total)

ival-sub: 20.0ms (20.1% of total)

ival-sqrt: 11.0ms (11.1% of total)

ival-div: 6.0ms (6% of total)

const: 3.0ms (3% of total)

backward-pass: 1.0ms (1% of total)

sample2.3s (30.3%)

Results

1.5s	5226×	1	valid
226.0ms	3030×	0	valid
198.0ms	2741×	0	unsamplable

Precisions

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

ival-exp: 789.0ms (53.3% of total)

ival-sub: 205.0ms (13.9% of total)

ival-mult: 155.0ms (10.5% of total)

ival-sqrt: 126.0ms (8.5% of total)

ival-div: 99.0ms (6.7% of total)

backward-pass: 78.0ms (5.3% of total)

const: 27.0ms (1.8% of total)

Bogosity

preprocess241.0ms (3.2%)

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)))))

explain192.0ms (2.5%)

FPErrors

Click to see full error table

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

Results

112.0ms	330×	1	valid
22.0ms	182×	0	valid

Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-exp: 46.0ms (52.5% of total)

ival-sub: 12.0ms (13.7% of total)

ival-mult: 10.0ms (11.4% of total)

backward-pass: 7.0ms (8% of total)

ival-sqrt: 6.0ms (6.9% of total)

ival-div: 5.0ms (5.7% of total)

const: 2.0ms (2.3% 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%	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	accuracy	100.0%	(exp.f64 x)

Results

16.0ms

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 (34.4% of total)

ival-add: 2.0ms (34.4% of total)

ival-sqrt: 2.0ms (34.4% 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)

rewrite292.0ms (3.9%)

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

simplify216.0ms (2.9%)

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)

eval31.0ms (0.4%)

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

prune263.0ms (3.5%)

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
▶	66.2%	(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))))))))
▶	67.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
▶	65.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	66.2%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.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)))))))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	71.9%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 108 to 85 computations (21.3% saved)

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	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 1 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	128	(+.f64 #s(literal 1 binary64) (+.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))))))))
✓	cost-diff	128	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.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)))))))))
✓	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 #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

942×	`fma-define`
764×	`fma-lowering-fma.f32`
764×	`fma-lowering-fma.f64`
496×	`sum3-define`
350×	`sum4-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	196
1	54	163
2	141	163
3	317	163
4	620	163
5	1026	163
6	1347	163
7	1384	163
8	1385	163
0	1385	163

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize121.0ms (1.6%)

Localize:

Found 15 expressions of interest:

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

45.0ms	174×	0	valid
21.0ms	81×	0	invalid
2.0ms	1×	5	exit

Compiler

Compiled 202 to 24 computations (88.1% saved)

Precisions

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

ival-mult: 11.0ms (31.3% of total)

ival-add: 10.0ms (28.5% of total)

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

...c/correct-round.rkt:119:19: 4.0ms (11.4% of total)

const: 1.0ms (2.8% of total)

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

series15.0ms (0.2%)

Counts

17 → 192

Calls

Call 1

Inputs
#<alt (sqrt 2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (+ 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 (sqrt (+ 1 (+ 1 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))>
#<alt (+ 1 (+ 1 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 1 (* x (+ 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 (+ (* 1/2 (/ (* 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 (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 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* 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)) (/ 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) (/ 1 (pow x 2)))) x)) 1/6)))>
#<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
3.0ms	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 (* x (+ 1/2 (* x 1/6)))))))
1.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))

rewrite398.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3210×	`/-lowering-/.f32`
3210×	`/-lowering-/.f64`
2704×	`-lowering-.f32`
2704×	`-lowering-.f64`
2344×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	140
1	148	114
2	1470	114
0	8128	114

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 539

Calls

Call 1

Inputs
(sqrt 2)
(sqrt (+ 2 x))
(+ 2 x)
(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))))
(sqrt (+ 1 (+ 1 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(+ 1 (+ 1 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 1 (* x (+ 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 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64))))) (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) x)) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 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 x x) #s(literal 4 binary64))) (sqrt.f64 (-.f64 x #s(literal 2 binary64))))
(/.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) x))))
(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 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x))))
(*.f64 (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 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))
(-.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))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (-.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (.f64 (-.f64 #s(literal 2 binary64) x) (.f64 x x))) (.f64 (-.f64 #s(literal 2 binary64) x) (-.f64 #s(literal 2 binary64) x)))
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(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.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 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (pow.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.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 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) x)

simplify265.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

4804×	`-lowering-.f32`
4804×	`-lowering-.f64`
3964×	`+-lowering-+.f64`
3964×	`+-lowering-+.f32`
1794×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	2116
1	961	1772
2	3592	1709
0	8404	1709

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 (+ (* 1/2 (/ (* 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)))))
(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)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* 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 (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) (/ 1 (pow x 2)))) x)) 1/6)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))

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

eval119.0ms (1.6%)

Compiler: Compiled 27495 to 2429 computations (91.2% saved)

prune87.0ms (1.1%)

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	898	10	908
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	899	15	914

Accuracy

100.0%

Counts

914 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.4%	(/.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))))))))))
	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	3.7%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.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))))))) (+.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))))))))) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))))
▶	67.6%	(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
	34.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))))))))
▶	66.2%	(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)))))))))
✓	66.2%	(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))))))))
✓	65.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	66.2%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.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)))))))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 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)))))))
	3.4%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	2.2%	(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
▶	2.4%	(sqrt.f64 x)
✓	71.9%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 454 to 268 computations (41% saved)

simplify125.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

1882×	`fma-define`
1374×	`fma-lowering-fma.f32`
1374×	`fma-lowering-fma.f64`
754×	`-lowering-.f32`
754×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	289
1	90	258
2	212	249
3	516	242
4	951	242
5	1723	242
6	2251	242
7	2381	242
8	2395	242
9	2395	242
10	2410	242
0	2410	242

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize181.0ms (2.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 x (.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	87.3%	(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Results

64.0ms	166×	0	invalid
44.0ms	89×	0	valid
9.0ms	1×	5	exit

Compiler

Compiled 319 to 36 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 24.0ms (36.2% of total)

ival-add: 21.0ms (31.7% of total)

ival-sqrt: 9.0ms (13.6% of total)

...c/correct-round.rkt:119:19: 8.0ms (12.1% of total)

ival-div: 2.0ms (3% of total)

ival-sub: 1.0ms (1.5% of total)

const: 1.0ms (1.5% of total)

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

series17.0ms (0.2%)

Counts

21 → 252

Calls

Call 1

Inputs
#<alt (sqrt (+ (+ 2 x) (* 1/2 (* x x))))>
#<alt (+ (+ 2 x) (* 1/2 (* x x)))>
#<alt (+ 2 x)>
#<alt (* 1/2 (* x x))>
#<alt (sqrt x)>
#<alt (sqrt (* x (* x (* x 1/6))))>
#<alt (* x (* x (* x 1/6)))>
#<alt (* x (* x 1/6))>
#<alt (* x 1/6)>
#<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 (sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))))))))>
#<alt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2)))))))>
#<alt (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))))))>
#<alt (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2)))))>
#<alt (* x x)>
#<alt (* (* x (* x x)) 1/216)>
#<alt (* x (* x x))>
#<alt (* (* x 1/6) (- (* x 1/6) 1/2))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 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 (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (sqrt 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 (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 (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/216 (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 (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 (* -1/12 x)>
#<alt (* x (- (* 1/36 x) 1/12))>
#<alt (* x (- (* 1/36 x) 1/12))>
#<alt (* x (- (* 1/36 x) 1/12))>
#<alt (* 1/36 (pow x 2))>
#<alt (* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))>
#<alt (* 1/36 (pow x 2))>
#<alt (* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))>

Calls

63 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(* (* x (* x x)) 1/216)
1.0ms	x	@	-inf	(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms	x	@	0	(sqrt (* x (* x (* x 1/6))))
0.0ms	x	@	inf	(* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))))))
0.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2))))))))

rewrite350.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3724×	`-lowering-.f32`
3724×	`-lowering-.f64`
2278×	`/-lowering-/.f32`
2278×	`/-lowering-/.f64`
2022×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	181
1	210	134
2	1951	132
0	8241	132

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 445

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x))))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))) (sqrt.f64 (neg.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (sqrt.f64 (neg.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))))
(/.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (-.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))))))
(.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) #s(literal 1/4 binary64)))
(+.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
(+.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 2 binary64))
(+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) x)
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(fma.f64 x #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 1 binary64) x (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (-.f64 x #s(literal 2 binary64))))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (-.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 #s(literal 2 binary64) x))
(fma.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(/.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))))
(/.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))) (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)) (.f64 #s(literal 2 binary64) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))))
(/.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) (.f64 (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))) (-.f64 #s(literal 2 binary64) (.f64 (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (-.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(pow.f64 (/.f64 (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) x)))) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) x) (.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) #s(literal -1 binary64))
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(fma.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 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 #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)))) #s(literal 1 binary64))
(/.f64 #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 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #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)))) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
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(pow.f64 (*.f64 x x) #s(literal 1 binary64))
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(*.f64 x x)
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(.f64 #s(literal 1 binary64) (.f64 x x))
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(exp.f64 (.f64 #s(literal 3 binary64) (log.f64 (.f64 x #s(literal 1/6 binary64)))))
(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 3 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal 3/2 binary64))
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(pow.f64 (exp.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64)))) #s(literal 3 binary64))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64)))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/216 binary64)))
(.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
(.f64 #s(literal 1/216 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 x x) #s(literal 1/216 binary64)) x)
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 3/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 3/2 binary64)))
(.f64 (.f64 #s(literal 1/216 binary64) x) (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (+.f64 (.f64 (neg.f64 (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/12 binary64) x (.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (fma.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/6 binary64) (*.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/6 binary64)) (*.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (fma.f64 #s(literal -1/6 binary64) (.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (fma.f64 (neg.f64 x) #s(literal 1/12 binary64) (.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (neg.f64 (*.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 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 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64)))
(fma.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1/12 binary64)) (+.f64 (.f64 (neg.f64 (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/6 binary64))) (neg.f64 (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/36 binary64) (neg.f64 (.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/36 binary64) (.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/36 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)) (neg.f64 (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) (+.f64 (.f64 (neg.f64 (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/12 binary64))))
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(fma.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x #s(literal 1/6 binary64)) (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (+.f64 (.f64 (neg.f64 (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1/6 binary64) (neg.f64 (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1/6 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(fma.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 (neg.f64 (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/12 binary64))))
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(fma.f64 #s(literal 1/36 binary64) (.f64 x x) (neg.f64 (.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) x (neg.f64 (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) x (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) x (.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64) (+.f64 (.f64 (neg.f64 (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/12 binary64))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))) (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))) #s(literal -1/8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (+.f64 (.f64 (.f64 x #s(literal 1/12 binary64)) (.f64 x #s(literal 1/12 binary64))) (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 (.f64 x #s(literal 1/12 binary64)) (.f64 x #s(literal 1/12 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64))))
(/.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))) #s(literal -1/8 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 x #s(literal 1/6 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))) #s(literal -1/8 binary64)) (.f64 x #s(literal 1/6 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 x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64)) (.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1/12 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 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 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (*.f64 x #s(literal 1/6 binary64)))
(.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1/12 binary64)) x)
(.f64 (.f64 (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64))

simplify253.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

4938×	`-lowering-.f32`
4938×	`-lowering-.f64`
2920×	`+-lowering-+.f64`
2920×	`+-lowering-+.f32`
2560×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	2173
1	943	1935
2	3543	1835
0	8467	1835

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
2
(+ 2 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))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(sqrt 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))))
(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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/216 (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))
(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)
(* -1/12 x)
(* x (- (* 1/36 x) 1/12))
(* x (- (* 1/36 x) 1/12))
(* x (- (* 1/36 x) 1/12))
(* 1/36 (pow x 2))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(* 1/36 (pow x 2))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/36 (* 1/12 (/ 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 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (.f64 (+.f64 (.f64 #s(literal -1/4 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) x))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) x) (+.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)))) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (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))))) #s(literal 1 binary64)))
(* -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 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) #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 x #s(literal 2 binary64)))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))))
(* 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 x #s(literal 2 binary64))))
(* (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 x #s(literal 2 binary64))))
(* (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))))))
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)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
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(.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 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (.f64 x x))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 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))))))
(* 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 x (*.f64 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 x (.f64 x (*.f64 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 x #s(literal 2 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 (* 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)))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 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))
(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))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* x (- (* 1/36 x) 1/12))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/36 binary64))))
(* x (- (* 1/36 x) 1/12))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/36 binary64))))
(* x (- (* 1/36 x) 1/12))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/36 binary64))))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/36 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/36 binary64) (/.f64 #s(literal -1/12 binary64) x)))

eval95.0ms (1.3%)

Compiler: Compiled 18927 to 2158 computations (88.6% saved)

prune83.0ms (1.1%)

Pruning

15 alts after pruning (6 fresh and 9 done)

	Pruned	Kept	Total
New	757	2	759
Fresh	1	4	5
Picked	1	4	5
Done	0	5	5
Total	759	15	774

Accuracy

100.0%

Counts

774 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
▶	1.6%	(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
▶	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	67.6%	(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
	34.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))))))))
✓	66.2%	(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)))))))))
▶	66.2%	(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 x #s(literal -1/12 binary64))))))))
✓	66.2%	(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))))))))
✓	65.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	66.2%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.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)))))))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 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)))))))
▶	3.4%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	2.4%	(sqrt.f64 x)
✓	71.9%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 354 to 232 computations (34.5% saved)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.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	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(+.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 x #s(literal -1/12 binary64)))))
✓	cost-diff	(.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 x #s(literal -1/12 binary64))))))
✓	cost-diff	(+.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 x #s(literal -1/12 binary64)))))))
✓	cost-diff	(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 x #s(literal -1/12 binary64))))))))

Rules

1952×	`fma-define`
1376×	`fma-lowering-fma.f32`
1376×	`fma-lowering-fma.f64`
696×	`-lowering-.f32`
696×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	294
1	82	253
2	194	253
3	522	253
4	981	253
5	1818	253
6	2352	253
7	2482	253
8	2496	253
9	2496	253
10	2505	253
0	2505	253

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))))
(+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12))))))
2
(* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))
x
(+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12))))
1
(/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))
(* (+ 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
(+ 1/4 (* x -1/12))
1/4
(* x -1/12)
-1/12
(* x (sqrt 1/2))
x
(sqrt 1/2)
1/2
(* (pow (* x 1/6) 1/2) x)
(pow (* x 1/6) 1/2)
(* x 1/6)
x
1/6
1/2
(sqrt (* x (* x (+ 1/2 (* x 1/6)))))
(* x (* x (+ 1/2 (* x 1/6))))
x
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
1
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
2
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6

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

localize171.0ms (2.3%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (.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	85.6%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	99.9%	(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(/.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 x #s(literal -1/12 binary64))))
✓	accuracy	100.0%	(.f64 x (.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))
✓	accuracy	99.8%	(*.f64 x #s(literal -1/12 binary64))

Results

62.0ms	170×	0	invalid
38.0ms	85×	0	valid
9.0ms	1×	5	exit

Compiler

Compiled 321 to 37 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 23.0ms (36% of total)

...c/correct-round.rkt:119:19: 12.0ms (18.8% of total)

ival-add: 9.0ms (14.1% of total)

ival-sqrt: 7.0ms (11% of total)

ival-pow: 6.0ms (9.4% of total)

ival-div: 5.0ms (7.8% of total)

const: 1.0ms (1.6% of total)

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

series14.0ms (0.2%)

Counts

21 → 240

Calls

Call 1

Inputs
#<alt (sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))))>
#<alt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12))))))>
#<alt (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))>
#<alt (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12))))>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (pow (* x 1/6) 1/2) x)>
#<alt (pow (* x 1/6) 1/2)>
#<alt (* x 1/6)>
#<alt (sqrt (* x (* x (+ 1/2 (* x 1/6)))))>
#<alt (* x (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
#<alt (+ 1/2 (* x 1/6))>
#<alt (/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))>
#<alt (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))>
#<alt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x -1/12)>
#<alt (* (* x (* x x)) 1/216)>
#<alt (* x (* x x))>
#<alt (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))>

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 (* (pow x 2) (sqrt -1/18))>
#<alt (* (pow x 2) (- (sqrt -1/18) (* 1/12 (/ 1 (* x (sqrt -1/18))))))>
#<alt (* (pow x 2) (- (+ (sqrt -1/18) (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* (pow x 2) (sqrt -1/18))))) (/ 1/12 (* x (sqrt -1/18)))))>
#<alt (* (pow x 2) (- (+ (sqrt -1/18) (+ (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* (pow x 2) (sqrt -1/18)))) (* -1/2 (/ (+ 2 (* 1/12 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (pow (sqrt -1/18) 2)))) (* (pow x 3) (sqrt -1/18)))))) (/ 1/12 (* x (sqrt -1/18)))))>
#<alt (* (pow x 2) (sqrt -1/18))>
#<alt (* (pow x 2) (- (sqrt -1/18) (* 1/12 (/ 1 (* x (sqrt -1/18))))))>
#<alt (* (pow x 2) (+ (sqrt -1/18) (* -1 (/ (+ (* 1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* x (sqrt -1/18)))) (* 1/12 (/ 1 (sqrt -1/18)))) x))))>
#<alt (* (pow x 2) (+ (sqrt -1/18) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (sqrt -1/18))) (* -1/2 (/ (- 2 (* -1/12 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (pow (sqrt -1/18) 2)))) (* x (sqrt -1/18))))) x)) (* 1/12 (/ 1 (sqrt -1/18)))) x))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* -1/18 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* -1/18 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1/18))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/18 x)))))))>
#<alt (* -1/18 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* -1/18 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))>
#<alt (* (pow x 4) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1/18))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/18 x))))))>
#<alt (* -1/18 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))>
#<alt (* (pow x 3) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* -1/18 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (* -1 (/ (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) x)) 1/6) x)))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<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 (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 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 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 6))>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))>
#<alt (/ 6 (pow x 3))>
#<alt (/ (- 6 (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))>
#<alt (/ 6 (pow x 3))>
#<alt (* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 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 (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 (* x (+ 1/6 (* 1/18 x)))))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* x (+ 1/18 (* 1/27 x)))))))>
#<alt (* -1/18 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))>
#<alt (* (pow x 3) (- (* -1 (/ (+ 1/2 (* 3 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* -1/18 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))>
#<alt (* -1 (* (pow x 3) (+ 1/18 (* -1 (/ (- (* -1 (/ (+ 1/2 (* 3 (/ 1 x))) x)) 1/6) x)))))>

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(sqrt (* x (* x (+ 1/2 (* x 1/6)))))
1.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))))
1.0ms	x	@	-inf	(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
1.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))))
1.0ms	x	@	inf	(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))

rewrite356.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3872×	`-lowering-.f32`
3872×	`-lowering-.f64`
3232×	`/-lowering-/.f32`
3232×	`/-lowering-/.f64`
2292×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	212
1	208	178
2	1729	176
0	8937	176

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 485

Calls

Call 1

Inputs
(sqrt (+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))))
(+ 2 (* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12))))))
(* x (+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))))
(+ 1 (/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12))))
(* x (sqrt 1/2))
(sqrt 1/2)
(* (pow (* x 1/6) 1/2) x)
(pow (* x 1/6) 1/2)
(* x 1/6)
(sqrt (* x (* x (+ 1/2 (* x 1/6)))))
(* x (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x -1/12)
(* (* x (* x x)) 1/216)
(* x (* x x))
(/ (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (+ 1/4 (* x -1/12)))

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))))))) (sqrt.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))) #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64))))))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 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 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 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 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64))))))))) #s(literal 1/2 binary64))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))))) #s(literal -1 binary64)))
(.f64 (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/12 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/1728 binary64)))) (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x #s(literal -1/12 binary64)) (-.f64 (.f64 x #s(literal -1/12 binary64)) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 x (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/12 binary64) x)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/1728 binary64)))) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x #s(literal -1/12 binary64)) (-.f64 (*.f64 x #s(literal -1/12 binary64)) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/1728 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x #s(literal -1/12 binary64)) (-.f64 (*.f64 x #s(literal -1/12 binary64)) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/1728 binary64)))) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x #s(literal -1/12 binary64)) (-.f64 (*.f64 x #s(literal -1/12 binary64)) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/12 binary64) x)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/1728 binary64)))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x #s(literal -1/12 binary64)) (-.f64 (.f64 x #s(literal -1/12 binary64)) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/12 binary64) x)))))
(.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))) #s(literal -1 binary64)) (/.f64 (neg.f64 x) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))
(.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))
(.f64 (/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))) #s(literal -1 binary64)) (/.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/12 binary64)))))

simplify300.0ms (4%)

Algorithm

1×	egg-herbie

Rules

5332×	`-lowering-.f32`
5332×	`-lowering-.f64`
2890×	`+-lowering-+.f64`
2890×	`+-lowering-+.f32`
1514×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	473	2604
1	1524	2330
2	5226	2290
0	8320	2290

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* 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))))))
(* (pow x 2) (sqrt -1/18))
(* (pow x 2) (- (sqrt -1/18) (* 1/12 (/ 1 (* x (sqrt -1/18))))))
(* (pow x 2) (- (+ (sqrt -1/18) (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* (pow x 2) (sqrt -1/18))))) (/ 1/12 (* x (sqrt -1/18)))))
(* (pow x 2) (- (+ (sqrt -1/18) (+ (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* (pow x 2) (sqrt -1/18)))) (* -1/2 (/ (+ 2 (* 1/12 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (pow (sqrt -1/18) 2)))) (* (pow x 3) (sqrt -1/18)))))) (/ 1/12 (* x (sqrt -1/18)))))
(* (pow x 2) (sqrt -1/18))
(* (pow x 2) (- (sqrt -1/18) (* 1/12 (/ 1 (* x (sqrt -1/18))))))
(* (pow x 2) (+ (sqrt -1/18) (* -1 (/ (+ (* 1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* x (sqrt -1/18)))) (* 1/12 (/ 1 (sqrt -1/18)))) x))))
(* (pow x 2) (+ (sqrt -1/18) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (sqrt -1/18))) (* -1/2 (/ (- 2 (* -1/12 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (pow (sqrt -1/18) 2)))) (* x (sqrt -1/18))))) x)) (* 1/12 (/ 1 (sqrt -1/18)))) x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* -1/18 (pow x 4))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(* (pow x 4) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(* -1/18 (pow x 4))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1/18))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/18 x)))))))
(* -1/18 (pow x 4))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(* (pow x 4) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(* -1/18 (pow x 4))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1/18))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/18 x))))))
(* -1/18 (pow x 3))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(* (pow x 3) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(* -1/18 (pow x 3))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/18 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1 (* (pow x 3) (+ 1/18 (* -1 (/ (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) x)) 1/6) x)))))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* 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)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 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))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 6))
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(/ 6 (pow x 3))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/ 6 (pow x 3))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 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))
(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 (* x (+ 1/6 (* 1/18 x)))))
(* x (+ 1/2 (* x (+ 1/6 (* x (+ 1/18 (* 1/27 x)))))))
(* -1/18 (pow x 3))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(* (pow x 3) (- (* -1 (/ (+ 1/2 (* 3 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(* -1/18 (pow x 3))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/18 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(* -1 (* (pow x 3) (+ 1/18 (* -1 (/ (- (* -1 (/ (+ 1/2 (* 3 (/ 1 x))) x)) 1/6) x)))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* 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))))))))
(* (pow x 2) (sqrt -1/18))
(.f64 (.f64 x x) (sqrt.f64 #s(literal -1/18 binary64)))
(* (pow x 2) (- (sqrt -1/18) (* 1/12 (/ 1 (* x (sqrt -1/18))))))
(.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(literal -1/18 binary64)) (/.f64 (/.f64 #s(literal -1/12 binary64) x) (sqrt.f64 #s(literal -1/18 binary64)))))
(* (pow x 2) (- (+ (sqrt -1/18) (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* (pow x 2) (sqrt -1/18))))) (/ 1/12 (* x (sqrt -1/18)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal -1/18 binary64))) (*.f64 x x)) (+.f64 (sqrt.f64 #s(literal -1/18 binary64)) (/.f64 (/.f64 #s(literal -1/12 binary64) x) (sqrt.f64 #s(literal -1/18 binary64))))))
(* (pow x 2) (- (+ (sqrt -1/18) (+ (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* (pow x 2) (sqrt -1/18)))) (* -1/2 (/ (+ 2 (* 1/12 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (pow (sqrt -1/18) 2)))) (* (pow x 3) (sqrt -1/18)))))) (/ 1/12 (* x (sqrt -1/18)))))
(.f64 (.f64 x x) (+.f64 (+.f64 (sqrt.f64 #s(literal -1/18 binary64)) (/.f64 (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal -1/18 binary64))) (.f64 x x))) (+.f64 (/.f64 (/.f64 #s(literal -23/32 binary64) (sqrt.f64 #s(literal -1/18 binary64))) (.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1/12 binary64) x) (sqrt.f64 #s(literal -1/18 binary64))))))
(* (pow x 2) (sqrt -1/18))
(.f64 (.f64 x x) (sqrt.f64 #s(literal -1/18 binary64)))
(* (pow x 2) (- (sqrt -1/18) (* 1/12 (/ 1 (* x (sqrt -1/18))))))
(.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(literal -1/18 binary64)) (/.f64 (/.f64 #s(literal -1/12 binary64) x) (sqrt.f64 #s(literal -1/18 binary64)))))
(* (pow x 2) (+ (sqrt -1/18) (* -1 (/ (+ (* 1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (* x (sqrt -1/18)))) (* 1/12 (/ 1 (sqrt -1/18)))) x))))
(.f64 (.f64 x x) (-.f64 (sqrt.f64 #s(literal -1/18 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal -1/18 binary64))) x) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -1/18 binary64)))) x)))
(* (pow x 2) (+ (sqrt -1/18) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (sqrt -1/18))) (* -1/2 (/ (- 2 (* -1/12 (/ (+ 1/2 (* 1/144 (/ 1 (pow (sqrt -1/18) 2)))) (pow (sqrt -1/18) 2)))) (* x (sqrt -1/18))))) x)) (* 1/12 (/ 1 (sqrt -1/18)))) x))))
(.f64 (.f64 x x) (-.f64 (sqrt.f64 #s(literal -1/18 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -1/18 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal -1/18 binary64))) (/.f64 (/.f64 #s(literal -23/32 binary64) (sqrt.f64 #s(literal -1/18 binary64))) x)) 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)))))))
(* -1/18 (pow x 4))
(.f64 #s(literal -1/18 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x) #s(literal -1/18 binary64)))
(* -1/18 (pow x 4))
(.f64 #s(literal -1/18 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1/18))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1/6 binary64) (/.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 (* x (+ 1/6 (* 1/18 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/18 binary64))))))))
(* -1/18 (pow x 4))
(.f64 #s(literal -1/18 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x) #s(literal -1/18 binary64)))
(* -1/18 (pow x 4))
(.f64 #s(literal -1/18 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* -1 (* (pow x 4) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1/18))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/18 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/18 binary64)))))))
(* -1/18 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/18 binary64)))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 3) (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x) #s(literal -1/18 binary64)))
(* -1/18 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/18 binary64)))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* -1 (* (pow x 3) (+ 1/18 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* -1 (* (pow x 3) (+ 1/18 (* -1 (/ (- (* -1 (/ (+ 1/2 (* 2 (/ 1 x))) x)) 1/6) x)))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 1/18 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))))
(* 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 (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 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))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 x #s(literal 1/12 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/144 binary64)) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (/.f64 (.f64 x #s(literal 1/3456 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal 1/2 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) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 x (.f64 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 (.f64 (sqrt.f64 #s(literal 1/6 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)))) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal -3/16 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal -3/16 binary64)) (+.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 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 #s(literal 1/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
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(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x) (/.f64 #s(literal -18 binary64) (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
(/ 6 (pow x 3))
(/.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) x)
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (.f64 x (.f64 x x)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(/.f64 (-.f64 #s(literal -6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
(/.f64 (-.f64 #s(literal -6 binary64) (/.f64 (-.f64 #s(literal -18 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.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 x (*.f64 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 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x 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 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 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 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x x)) x)
(* 1/216 (pow x 3))
(.f64 (.f64 #s(literal 1/216 binary64) (*.f64 x 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))
(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 (* x (+ 1/6 (* 1/18 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/18 binary64))))))
(* x (+ 1/2 (* x (+ 1/6 (* x (+ 1/18 (* 1/27 x)))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 x #s(literal 1/27 binary64))))))))
(* -1/18 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/18 binary64)))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/18))
(.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/18 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 3) (- (* -1 (/ (+ 1/2 (* 3 (/ 1 x))) (pow x 2))) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3 binary64) x)) x)) x) #s(literal -1/18 binary64)))
(* -1/18 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/18 binary64)))
(* -1 (* (pow x 3) (+ 1/18 (* 1/6 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)))
(* -1 (* (pow x 3) (+ 1/18 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal -1/18 binary64) (/.f64 #s(literal -1/6 binary64) x)) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* -1 (* (pow x 3) (+ 1/18 (* -1 (/ (- (* -1 (/ (+ 1/2 (* 3 (/ 1 x))) x)) 1/6) x)))))
(.f64 (-.f64 #s(literal 1/18 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3 binary64) x)) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))

eval106.0ms (1.4%)

Compiler: Compiled 25105 to 2975 computations (88.1% saved)

prune97.0ms (1.3%)

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	833	8	841
Fresh	1	0	1
Picked	3	2	5
Done	3	6	9
Total	840	16	856

Accuracy

100.0%

Counts

856 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	0.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (.f64 x (.f64 x x)))))
	65.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
	67.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
	70.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	2.6%	(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
	1.6%	(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
✓	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	67.6%	(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
	66.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 1/18 binary64) (*.f64 x #s(literal 1/27 binary64))))))))))))
	67.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/18 binary64))))))))))
✓	65.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 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)))))))
✓	3.4%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	2.4%	(sqrt.f64 x)
✓	71.9%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 542 to 265 computations (51.1% saved)

regimes24.0ms (0.3%)

Counts

27 → 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)))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(sqrt.f64 (.f64 x (.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 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 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)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (.f64 x (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.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)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/18 binary64))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 1/18 binary64) (*.f64 x #s(literal 1/27 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 x #s(literal -1/12 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 (-.f64 #s(literal 1 binary64) (.f64 (+.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))))))) (+.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))))))))) (-.f64 #s(literal 0 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 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

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

Calls

3 calls:

8.0ms

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

7.0ms

6.0ms

(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)

regimes10.0ms (0.1%)

Accuracy

Total -46.0b remaining (-256.1%)

Threshold costs -46b (-256.1%)

Counts

25 → 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)))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(sqrt.f64 (.f64 x (.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 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 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)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (.f64 x (.f64 x x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.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)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/18 binary64))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x (+.f64 #s(literal 1/18 binary64) (*.f64 x #s(literal 1/27 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 x #s(literal -1/12 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 (-.f64 #s(literal 1 binary64) (.f64 (+.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))))))) (+.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))))))))) (-.f64 #s(literal 0 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 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))))))))

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
71.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (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))

soundness481.0ms (6.4%)

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)

preprocess23.0ms (0.3%)

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

analyze191.0ms (2.5%)

sample2.3s (30.3%)

preprocess241.0ms (3.2%)

explain192.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize23.0ms (0.3%)

series2.0ms (0%)

rewrite292.0ms (3.9%)

simplify216.0ms (2.9%)

eval31.0ms (0.4%)

prune263.0ms (3.5%)

simplify47.0ms (0.6%)

localize121.0ms (1.6%)

series15.0ms (0.2%)

rewrite398.0ms (5.3%)

simplify265.0ms (3.5%)

eval119.0ms (1.6%)

prune87.0ms (1.1%)

simplify125.0ms (1.7%)

localize181.0ms (2.4%)

series17.0ms (0.2%)

rewrite350.0ms (4.6%)

simplify253.0ms (3.3%)

eval95.0ms (1.3%)

prune83.0ms (1.1%)

simplify72.0ms (1%)

localize171.0ms (2.3%)

series14.0ms (0.2%)

rewrite356.0ms (4.7%)

simplify300.0ms (4%)

eval106.0ms (1.4%)

prune97.0ms (1.3%)

regimes24.0ms (0.3%)

regimes10.0ms (0.1%)

simplify7.0ms (0.1%)

soundness481.0ms (6.4%)

preprocess23.0ms (0.3%)

end0.0ms (0%)

Profiling