Metrics for sqrtexp (problem 3.4.4)

analyze423.0ms (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: 209.0ms

ival-sub: 64.0ms (30.7% of total)

ival-exp: 59.0ms (28.3% of total)

ival-mult: 34.0ms (16.3% of total)

ival-sqrt: 28.0ms (13.4% of total)

ival-div: 17.0ms (8.1% of total)

const: 6.0ms (2.9% of total)

backward-pass: 1.0ms (0.5% of total)

sample4.1s (24%)

Results

2.4s	5298×	1	valid
455.0ms	2958×	0	valid
384.0ms	2685×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 2.6s

ival-exp: 1.2s (44.4% of total)

ival-sub: 405.0ms (15.6% of total)

ival-mult: 345.0ms (13.3% of total)

ival-sqrt: 267.0ms (10.3% of total)

ival-div: 227.0ms (8.7% of total)

backward-pass: 151.0ms (5.8% of total)

const: 51.0ms (2% of total)

Bogosity

preprocess523.0ms (3.1%)

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)))))

explain668.0ms (3.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
158	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
158	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
3	-	-	`(/.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

451.0ms	312×	1	valid
108.0ms	200×	0	valid

Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 392.0ms

ival-mult: 265.0ms (67.6% of total)

ival-exp: 64.0ms (16.3% of total)

ival-sub: 20.0ms (5.1% of total)

backward-pass: 15.0ms (3.8% of total)

ival-sqrt: 14.0ms (3.6% of total)

ival-div: 12.0ms (3.1% of total)

const: 3.0ms (0.8% of total)

eval1.0ms (0%)

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

prune2.0ms (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)

simplify7.0ms (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

localize47.0ms (0.3%)

Localize:

Found 3 expressions of interest:

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

Results

33.0ms

256×

valid

Compiler

Compiled 15 to 6 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-exp: 4.0ms (32% of total)

ival-sqrt: 4.0ms (32% of total)

ival-add: 3.0ms (24% of total)

const: 1.0ms (8% of total)

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

series4.0ms (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)))
1.0ms	x	@	inf	(sqrt (+ 1 (exp x)))
1.0ms	x	@	-inf	(sqrt (+ 1 (exp x)))
0.0ms	x	@	0	(+ 1 (exp x))
0.0ms	x	@	0	(exp x)

rewrite784.0ms (4.6%)

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))

simplify519.0ms (3.1%)

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)

eval85.0ms (0.5%)

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

prune82.0ms (0.5%)

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
▶	62.0%	(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))))))))
▶	63.7%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
▶	61.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	63.7%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	68.8%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 100 to 79 computations (21% saved)

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

904×	`fma-define`
764×	`fma-lowering-fma.f32`
764×	`fma-lowering-fma.f64`
488×	`sum3-define`
340×	`sum4-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	163
1	54	137
2	141	137
3	303	137
4	547	137
5	800	137
6	1197	137
7	1352	137
8	1353	137
0	1353	137

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

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

localize284.0ms (1.7%)

Localize:

Found 15 expressions of interest:

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

131.0ms	162×	0	valid
58.0ms	94×	0	invalid

Compiler

Compiled 169 to 24 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-add: 34.0ms (39.6% of total)

ival-sqrt: 22.0ms (25.6% of total)

ival-mult: 21.0ms (24.5% of total)

...c/correct-round.rkt:119:19: 7.0ms (8.2% of total)

const: 1.0ms (1.2% of total)

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

series41.0ms (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 (+ 1 (+ 1 (* x (+ 1 (* 1/2 x))))))>
#<alt (+ 1 (+ 1 (* x (+ 1 (* 1/2 x)))))>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* 1/2 x)>
#<alt (* x 1/6)>
#<alt (* x (+ 1/2 (* x 1/6)))>

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

Calls

48 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(* x 1/6)
3.0ms	x	@	inf	(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
2.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
2.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
2.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))

rewrite881.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3434×	`/-lowering-/.f32`
3434×	`/-lowering-/.f64`
3080×	`-lowering-.f32`
3080×	`-lowering-.f64`
2312×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	128
1	148	105
2	1470	105
0	8455	105

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 607

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

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

simplify675.0ms (4%)

Algorithm

1×	egg-herbie

Rules

5116×	`-lowering-.f32`
5116×	`-lowering-.f64`
3430×	`+-lowering-+.f64`
3430×	`+-lowering-+.f32`
2408×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	1998
1	934	1614
2	3475	1554
0	8862	1554

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 (+ (* -1/4 (/ (* 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)))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 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)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))

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

eval317.0ms (1.9%)

Compiler: Compiled 24751 to 2462 computations (90.1% saved)

prune221.0ms (1.3%)

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	905	13	918
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	907	17	924

Accuracy

100.0%

Counts

924 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.2%	(/.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))))))))))
	60.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
	2.7%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	62.0%	(sqrt.f64 (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (.f64 (-.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 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))
▶	61.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
▶	63.7%	(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
	62.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))))
	62.0%	(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)))))))))
▶	62.0%	(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 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))))))))))
✓	62.0%	(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))))))))
✓	61.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
	1.9%	(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
▶	2.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
	3.2%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	2.0%	(sqrt.f64 x)
✓	68.8%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 647 to 334 computations (48.4% saved)

simplify215.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2112×	`fma-define`
1430×	`fma-lowering-fma.f32`
1430×	`fma-lowering-fma.f64`
794×	`-lowering-.f32`
794×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	297
1	98	264
2	245	254
3	657	246
4	1382	246
5	2177	246
6	2431	246
7	2586	246
8	2586	246
9	2611	246
0	2611	246

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize429.0ms (2.5%)

Localize:

Found 17 expressions of interest:

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

Results

187.0ms	180×	0	invalid
84.0ms	76×	0	valid

Compiler

Compiled 343 to 38 computations (88.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-mult: 51.0ms (36.1% of total)

ival-div: 26.0ms (18.4% of total)

ival-add: 25.0ms (17.7% of total)

ival-sqrt: 21.0ms (14.9% of total)

...c/correct-round.rkt:119:19: 13.0ms (9.2% of total)

ival-sub: 3.0ms (2.1% of total)

const: 2.0ms (1.4% of total)

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

series33.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

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

Calls

60 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(* (* x (* x x)) 1/216)
2.0ms	x	@	-inf	(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms	x	@	inf	(* x (+ 1 (* (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (/ 1 (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2)))))))
1.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 1 (* (* (+ 1/8 (* (* x (* x x)) 1/216)) x) (/ 1 (+ 1/4 (* (* x 1/6) (- (* x 1/6) 1/2)))))))))
1.0ms	x	@	-inf	(sqrt x)

rewrite832.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3378×	`-lowering-.f32`
3378×	`-lowering-.f64`
2208×	`fma-lowering-fma.f32`
2208×	`fma-lowering-fma.f64`
1788×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	164
1	234	121
2	2128	119
0	8185	119

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 498

Calls

Call 1

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

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

simplify721.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

4944×	`-lowering-.f32`
4944×	`-lowering-.f64`
3872×	`+-lowering-+.f64`
3872×	`+-lowering-+.f32`
1284×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	359	2212
1	1229	1930
2	4515	1843
0	8277	1843

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
2
(+ 2 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 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/8 x) 1/4)))
(+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))
(/ 1 x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)
(/ 1 x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))
(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)))))
(* 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)
(* 1/216 (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)

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x (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 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (/.f64 (/.f64 #s(literal -3/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (.f64 x x))))))
(* -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 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (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)) 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 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 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 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
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 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/16 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) x) (.f64 x x)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 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)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -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) x) (.f64 x x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* x (- (* 1/8 x) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x #s(literal 1/8 binary64)))))
(+ 1/2 (* x (- (* x (+ 1/8 (* -1/16 x))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (* 2 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal -2 binary64)) x)) x)
(/ (- (+ 1 (/ 4 (pow x 2))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal -2 binary64)) x) (/.f64 #s(literal -8 binary64) (.f64 x (.f64 x x))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 2 (/ 1 x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 x)) 2) x)) 1) x))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 x)) 4) x)) 2) x)) 1) x))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x)) x)) (-.f64 #s(literal 0 binary64) x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 5/96 binary64) x)))))
(* (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 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1/32 (* (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))))))
(.f64 (.f64 x x) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) (.f64 (/.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))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))))
(* (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)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (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))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))))))))
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(.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64)))
(* 1/216 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/216 binary64)))
(* 1/216 (pow x 3))
(.f64 x (.f64 (*.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))

eval255.0ms (1.5%)

Compiler: Compiled 18065 to 2085 computations (88.5% saved)

prune207.0ms (1.2%)

Pruning

17 alts after pruning (10 fresh and 7 done)

	Pruned	Kept	Total
New	818	7	825
Fresh	5	3	8
Picked	2	3	5
Done	0	4	4
Total	825	17	842

Accuracy

100.0%

Counts

842 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.8%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
	60.9%	(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
	61.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
▶	2.7%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	64.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
✓	63.7%	(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
✓	62.0%	(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))))))))
✓	61.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
	1.9%	(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
▶	3.2%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
▶	20.9%	(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64))))))
	2.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/10077696 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))))) (+.f64 #s(literal 1/64 binary64) (.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))))))))
	2.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))))
✓	2.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	2.0%	(sqrt.f64 x)
✓	68.8%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 420 to 288 computations (31.4% saved)

simplify686.0ms (4.1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	256	(.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64)))
✓	cost-diff	384	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) x) #s(literal 1/6 binary64))))
✓	cost-diff	512	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64)))))
✓	cost-diff	512	(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal -1/4 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))

Rules

4864×	`-lowering-.f32`
4864×	`-lowering-.f64`
2708×	`fma-define`
2186×	`associate-/r/`
1998×	`/-lowering-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	192
1	76	170
2	210	167
3	492	153
4	1165	149
5	2672	149
6	4076	149
7	4661	149
8	5100	149
9	5502	149
10	5899	149
11	6329	149
0	8733	149

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize367.0ms (2.2%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x)
✓	accuracy	99.9%	(/.f64 #s(literal 2 binary64) (*.f64 x x))
✓	accuracy	99.9%	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64)))))
✓	accuracy	60.0%	(.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x 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	71.5%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.6%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/4 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))

Results

183.0ms	159×	0	valid
79.0ms	97×	0	invalid

Compiler

Compiled 201 to 31 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-mult: 38.0ms (32.6% of total)

ival-add: 26.0ms (22.3% of total)

ival-div: 18.0ms (15.4% of total)

ival-sqrt: 17.0ms (14.6% of total)

ival-pow: 8.0ms (6.9% of total)

...c/correct-round.rkt:119:19: 7.0ms (6% of total)

const: 2.0ms (1.7% of total)

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

series36.0ms (0.2%)

Counts

20 → 228

Calls

Call 1

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

Calls

57 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
2.0ms	x	@	inf	(sqrt (/ 1 (+ 1/2 (* x -1/4))))
2.0ms	x	@	-inf	(sqrt (* x (+ (+ 1 (* 1/2 x)) (* (* x x) (+ (/ (/ 2 (* x x)) x) 1/6)))))
2.0ms	x	@	inf	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
1.0ms	x	@	0	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))

rewrite891.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3590×	`-lowering-.f32`
3590×	`-lowering-.f64`
2952×	`/-lowering-/.f32`
2952×	`/-lowering-/.f64`
1594×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	154
1	201	132
2	1691	123
0	8129	123

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 549

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(fabs.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal 1/4 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (-.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/4 binary64) x))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (-.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/4 binary64) x))))
(.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (-.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/4 binary64) x))))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))))) #s(literal 1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))))) #s(literal 1/2 binary64))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))))
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simplify723.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

4970×	`-lowering-.f32`
4970×	`-lowering-.f64`
3850×	`+-lowering-+.f64`
3850×	`+-lowering-+.f32`
1408×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	428	2214
1	1403	1974
2	4802	1913
0	8205	1913

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (*.f64 #s(literal 5/64 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 #s(literal -4 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 (.f64 x #s(literal 16 binary64)) #s(literal -4 binary64))) (sqrt.f64 #s(literal -4 binary64)))))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(literal -2 binary64))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(literal -2 binary64))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(literal -2 binary64)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64)))) (.f64 #s(literal 4 binary64) (sqrt.f64 x)))) (.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 (* 1/4 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 1/4 binary64)))))))
(/ -4 x)
(/.f64 #s(literal -4 binary64) x)
(* -1 (/ (+ 4 (* 8 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -8 binary64) x)) x)
(/ (- (* -1 (/ (+ 8 (* 16 (/ 1 x))) x)) 4) x)
(/.f64 (-.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 16 binary64) x)) x)) x)
(/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))) (+ 4 (* 8 (/ 1 x)))) x)
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal -8 binary64) (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) x)) x) #s(literal -4 binary64)) x)
(/ -4 x)
(/.f64 #s(literal -4 binary64) x)
(* -1 (/ (+ 4 (* 8 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -8 binary64) x)) x)
(* -1 (/ (+ 4 (+ (* 8 (/ 1 x)) (/ 16 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal 4 binary64) (+.f64 (/.f64 #s(literal 8 binary64) x) (/.f64 #s(literal 16 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ 4 (* -1 (/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) x)) 8) x))) x))
(/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 #s(literal -8 binary64) (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) x)) x)) (-.f64 #s(literal 0 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) x)))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) x)))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) x)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
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(.f64 (.f64 x x) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (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)))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x #s(literal -3/8 binary64))) (sqrt.f64 #s(literal 1/6 binary64)))))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))))
(* (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)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (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))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 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 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(literal -1/4 binary64))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (pow (sqrt -1) 2) (+ 2 (* -1/16 (/ x (pow (sqrt 1/6) 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))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.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)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal -1/4 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1 binary64) (+.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64))) (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x #s(literal -3/8 binary64))) (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (.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 (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/6 binary64)) (/.f64 #s(literal 2 binary64) (.f64 x (*.f64 x x))))) #s(literal 1 binary64)))
(* 1/6 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 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 (+.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 x (.f64 x (-.f64 #s(literal 0 binary64) x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 x) x)
(/.f64 (+.f64 #s(literal 2 binary64) x) x)
(/ (+ 2 (* x (+ 1 (* 1/2 x)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))) x)
(/ (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) x)
(/.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))))))) x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/6 binary64)) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (* -1 (/ (- (* -1 (/ (+ 1 (* 2 (/ 1 x))) x)) 1/2) x))))
(.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* 1/6 (pow x 3))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) x)
(/ (+ 2 (* 1/6 (pow x 3))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) x)
(/ (+ 2 (* 1/6 (pow x 3))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 3)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 3)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 3)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 3)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 3)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 3)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x 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))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))
(/ 2 (pow x 3))
(/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x)))

eval292.0ms (1.7%)

Compiler: Compiled 25745 to 2889 computations (88.8% saved)

prune244.0ms (1.4%)

Pruning

15 alts after pruning (7 fresh and 8 done)

	Pruned	Kept	Total
New	817	6	823
Fresh	4	1	5
Picked	3	2	5
Done	1	6	7
Total	825	15	840

Accuracy

100.0%

Counts

840 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.4%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
	63.5%	(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))
	2.3%	(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
✓	2.7%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	61.9%	(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 1/4 binary64))))))))
✓	62.0%	(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))))))))
✓	61.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
	1.9%	(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
✓	3.2%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
	61.9%	(sqrt.f64 (.f64 x (/.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))))))) x)))
	68.7%	(sqrt.f64 (*.f64 x (/.f64 #s(literal 2 binary64) x)))
✓	2.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	2.0%	(sqrt.f64 x)
✓	68.8%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 700 to 269 computations (61.6% saved)

regimes58.0ms (0.3%)

Counts

33 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 x (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.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 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 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 1/4 binary64))))))))
(sqrt.f64 (.f64 x (/.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))))))) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/10077696 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))))) (+.f64 #s(literal 1/64 binary64) (.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))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (.f64 (-.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 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))
(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:

22.0ms

12.0ms

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

12.0ms

(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)

regimes17.0ms (0.1%)

Accuracy

Total -43.6b remaining (-218.2%)

Threshold costs -43.6b (-218.2%)

Counts

31 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 x (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.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 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 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 1/4 binary64))))))))
(sqrt.f64 (.f64 x (/.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))))))) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/216 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/10077696 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/6 binary64)) #s(literal -1/12 binary64)))))) (+.f64 #s(literal 1/64 binary64) (.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))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))) (.f64 (-.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 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))) (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))

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

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
68.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify15.0ms (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))

soundness1.1s (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)

preprocess70.0ms (0.4%)

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

analyze423.0ms (2.5%)

sample4.1s (24%)

preprocess523.0ms (3.1%)

explain668.0ms (3.9%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify7.0ms (0%)

localize47.0ms (0.3%)

series4.0ms (0%)

rewrite784.0ms (4.6%)

simplify519.0ms (3.1%)

eval85.0ms (0.5%)

prune82.0ms (0.5%)

simplify116.0ms (0.7%)

localize284.0ms (1.7%)

series41.0ms (0.2%)

rewrite881.0ms (5.2%)

simplify675.0ms (4%)

eval317.0ms (1.9%)

prune221.0ms (1.3%)

simplify215.0ms (1.3%)

localize429.0ms (2.5%)

series33.0ms (0.2%)

rewrite832.0ms (4.9%)

simplify721.0ms (4.3%)

eval255.0ms (1.5%)

prune207.0ms (1.2%)

simplify686.0ms (4.1%)

localize367.0ms (2.2%)

series36.0ms (0.2%)

rewrite891.0ms (5.3%)

simplify723.0ms (4.3%)

eval292.0ms (1.7%)

prune244.0ms (1.4%)

regimes58.0ms (0.3%)

regimes17.0ms (0.1%)

simplify15.0ms (0.1%)

soundness1.1s (6.4%)

preprocess70.0ms (0.4%)

end0.0ms (0%)

Profiling