Metrics for Numeric.Log:$clog1p from log-domain-0.10.2.1, B

analyze1.0ms (0%)

Memory

3.3MiB live, 3.3MiB allocated

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
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample649.0ms (6.5%)

Memory

15.1MiB live, 1 036.7MiB allocated

Samples

434.0ms	8 254×	0	valid
0.0ms	2×	2	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 281.0ms

ival-add: 105.0ms (37.4% of total)

ival-sqrt: 105.0ms (37.4% of total)

ival-div: 57.0ms (20.3% of total)

ival-true: 6.0ms (2.1% of total)

exact: 4.0ms (1.4% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess24.0ms (0.2%)

Memory

10.7MiB live, 49.9MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`associate-l`
42×	`distribute-lft-neg-in`
42×	`times-frac`
38×	`unsub-neg`
36×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

explain74.0ms (0.7%)

Memory

5.3MiB live, 144.2MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
-	-	`(+.f64 x #s(literal 1 binary64))`
-	-	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
-	-	`#s(literal 1 binary64)`
-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

29.0ms

512×

valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-div: 8.0ms (45.4% of total)

ival-add: 5.0ms (28.4% of total)

ival-sqrt: 4.0ms (22.7% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.1%)

Memory

-30.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

8×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-+.f64`
4×	`+-commutative`
2×	`lift-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	14	23
0	14	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.2%)

Memory

34.9MiB live, 34.9MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

12.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (45.5% of total)

ival-div: 2.0ms (30.3% of total)

ival-sqrt: 2.0ms (30.3% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

-32.1MiB live, 8.6MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))>
#<alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (+.f64 x #s(literal 1 binary64))>

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

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/ x (+ 1 (sqrt (+ x 1))))
1.0ms	x	@	-inf	(/ x (+ 1 (sqrt (+ x 1))))
0.0ms	x	@	-inf	(sqrt (+ x 1))
0.0ms	x	@	-inf	(+ 1 (sqrt (+ x 1)))
0.0ms	x	@	inf	(sqrt (+ x 1))

simplify552.0ms (5.5%)

Memory

32.5MiB live, 504.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18 662×	`lower-fma.f64`
18 662×	`lower-fma.f32`
3 776×	`lower-*.f64`
3 776×	`lower-*.f32`
2 642×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	600
1	485	505
2	1633	483
3	5433	474
0	8374	430

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

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

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

rewrite666.0ms (6.7%)

Memory

6.5MiB live, 322.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 950×	`lower-fma.f64`
3 950×	`lower-fma.f32`
3 308×	`lower-/.f32`
3 306×	`lower-/.f64`
2 908×	`lower-*.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20

Stop Event

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

Counts

4 → 474

Calls

Call 1

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

Outputs
(+.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(+.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(+.f64 (/.f64 x (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x))))
(+.f64 (.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(+.f64 (.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64)) (.f64 (/.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(+.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(fma.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 x (/.f64 #s(literal -1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x))))
(fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))
(fma.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)))
(fma.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64) (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x))))
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (+.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x))))
(fma.f64 (/.f64 x (fma.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (/.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (*.f64 x (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 x))
(/.f64 (.f64 x (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))) (*.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) (*.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (neg.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 x (neg.f64 x)) (.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (*.f64 (neg.f64 x) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))) (fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) (+.f64 (neg.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 (/.f64 x (neg.f64 x)) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (+.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) #s(literal -1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (neg.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) x)
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 x))
(*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(*.f64 (/.f64 x (neg.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (.f64 x (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
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(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))
(.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x)))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (fabs.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) (fabs.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))
(*.f64 (fabs.f64 (fma.f64 x x #s(literal -1 binary64))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) (fabs.f64 (fma.f64 x x #s(literal -1 binary64))))
(.f64 (fabs.f64 (fma.f64 (.f64 x x) (neg.f64 x) #s(literal -1 binary64))) (fabs.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))))
(*.f64 (fabs.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (fabs.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (fabs.f64 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (fabs.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (fabs.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (+.f64 x #s(literal 1 binary64)))
(.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64)))
(.f64 (fabs.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (fabs.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(.f64 (fabs.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)))) (fabs.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)))
(.f64 (fabs.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))) (fabs.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fabs.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))

eval114.0ms (1.1%)

Memory: -11.7MiB live, 142.7MiB allocated
Compiler: Compiled 11 091 to 2 091 computations (81.1% saved)

prune106.0ms (1.1%)

Memory

3.0MiB live, 172.0MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	513	7	520
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	513	8	521

Accuracy

100.0%

Counts

521 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	65.2%	(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
	39.4%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	35.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
▶	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
▶	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
▶	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
▶	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 115 to 74 computations (35.7% saved)

simplify10.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
✓	cost-diff	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	cost-diff	(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))

Rules

132×	`lower-fma.f32`
126×	`lower-fma.f64`
70×	`lower-*.f32`
64×	`lower-*.f64`
64×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	122
0	34	122
1	63	122
2	91	122
3	118	122
4	125	122
0	125	122

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
x
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(sqrt.f64 x)
x
#s(literal -1 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
#s(literal 1/16 binary64)
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)

Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
x
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(sqrt.f64 x)
x
#s(literal -1 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
#s(literal 1/16 binary64)
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)

localize99.0ms (1%)

Memory

-30.0MiB live, 123.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
✓	accuracy	100.0%	(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
✓	accuracy	67.1%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
✓	accuracy	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	68.2%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))

Samples

25.0ms	175×	0	valid
11.0ms	81×	0	invalid

Compiler

Compiled 102 to 23 computations (77.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 9.0ms (40.7% of total)

ival-add: 7.0ms (31.7% of total)

ival-sqrt: 3.0ms (13.6% of total)

ival-div: 2.0ms (9% of total)

exact: 1.0ms (4.5% of total)

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

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

series8.0ms (0.1%)

Memory

18.2MiB live, 18.2MiB allocated

Counts

13 → 156

Calls

Call 1

Inputs
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))>
#<alt (sqrt.f64 x)>
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))>
#<alt (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))>
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))>
#<alt (+.f64 (sqrt.f64 x) #s(literal -1 binary64))>
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))>
#<alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))>

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

Calls

39 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x (+ (* x (+ (* x 1/16) -1/8)) 1/2))
1.0ms	x	@	inf	(* 1/2 x)
0.0ms	x	@	-inf	(sqrt x)
0.0ms	x	@	inf	(* x (+ (* x -1/8) 1/2))
0.0ms	x	@	inf	(* x (+ (* x (+ (* x 1/16) -1/8)) 1/2))

simplify577.0ms (5.8%)

Memory

-6.2MiB live, 967.7MiB allocated

Algorithm

1×	egg-herbie

Rules

22 598×	`lower-fma.f64`
22 598×	`lower-fma.f32`
3 778×	`lower-*.f64`
3 778×	`lower-*.f32`
3 642×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	1477
1	375	1262
2	1258	1181
3	4155	1171
0	8370	1053

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) 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)
(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)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1/8 x))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1/8 x))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x))
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* 1/16 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/16 binary64))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* 1/16 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/16 binary64))))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/16 x) 1/8)))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(* 1/16 (pow x 2))
(.f64 x (.f64 x #s(literal 1/16 binary64)))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(* 1/16 (pow x 2))
(.f64 x (.f64 x #s(literal 1/16 binary64)))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
-1/8
#s(literal -1/8 binary64)
(- (* 1/16 x) 1/8)
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(- (* 1/16 x) 1/8)
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(- (* 1/16 x) 1/8)
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(* 1/16 x)
(*.f64 x #s(literal 1/16 binary64))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))

rewrite378.0ms (3.8%)

Memory

6.2MiB live, 678.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 354×	`lower-fma.f32`
9 348×	`lower-fma.f64`
5 484×	`lower-*.f32`
5 478×	`lower-*.f64`
3 930×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	108
0	34	108
1	145	108
2	966	103
0	8579	103

Stop Event

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

Counts

13 → 405

Calls

Call 1

Inputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))

Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 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 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(fabs.f64 (sqrt.f64 x))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(neg.f64 (neg.f64 (sqrt.f64 x)))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))))
(fma.f64 x (.f64 x #s(literal -1/8 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 -1/8 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 x #s(literal -1/8 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/8 binary64) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) x (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x) (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(fma.f64 (.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x #s(literal -1/16 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64)))) (.f64 x (fma.f64 (.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64)))) (.f64 (fma.f64 (.f64 x (*.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) x)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x #s(literal -1/16 binary64)))))
(/.f64 (.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/16 binary64)))))
(/.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) x) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64)))))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) x) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 x #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) (neg.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)))) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) x)) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) x)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(/.f64 (fma.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 -1/512 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal -1/8 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal -1/8 binary64)))))
(/.f64 (.f64 x (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64))))))
(/.f64 (.f64 x (neg.f64 (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)))) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) x)
(.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))))) x))
(.f64 (fma.f64 x (.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) x))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (*.f64 x #s(literal -1/16 binary64))))))
(.f64 (.f64 (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))
(.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))))))
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))
(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))))))
(.f64 (.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))
(.f64 (.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(.f64 (.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1 binary64) #s(literal 1/2 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (sqrt.f64 x) #s(literal 1/2 binary64))
(neg.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64)))))))
(neg.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/64 binary64)) #s(literal -1/16 binary64)))) (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/64 binary64)) #s(literal -1/16 binary64)))))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/64 binary64)) #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64))) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal -1/134217728 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/262144 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/4096 binary64)))) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/262144 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/16 binary64) (.f64 (*.f64 x x) #s(literal 1/64 binary64))))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (+.f64 #s(literal 1/64 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/256 binary64)) #s(literal -1/128 binary64)))))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/256 binary64)) #s(literal -1/128 binary64))))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64))) (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)))
(/.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64))) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)) #s(literal 1/64 binary64))) (*.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/68719476736 binary64) #s(literal -1/134217728 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/16777216 binary64) (-.f64 #s(literal 1/262144 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/2097152 binary64)))) (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/16777216 binary64) #s(literal -1/262144 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal 1/512 binary64)) (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (*.f64 x x) #s(literal 1/256 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/16777216 binary64) #s(literal -1/262144 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/65536 binary64) #s(literal 1/4096 binary64)) (.f64 (.f64 x x) #s(literal 1/16384 binary64))) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/65536 binary64) #s(literal -1/4096 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/256 binary64)) #s(literal 1/64 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (*.f64 x x) #s(literal 1/256 binary64)))))
(/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64)))) (neg.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (fma.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))) (.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (*.f64 x x) #s(literal 1/256 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 x (-.f64 (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/128 binary64))))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (.f64 (*.f64 x x) #s(literal 1/256 binary64)))))))
(.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64))))
(.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal -1/16 binary64)))))

eval120.0ms (1.2%)

Memory: -21.1MiB live, 141.3MiB allocated
Compiler: Compiled 10 572 to 1 211 computations (88.5% saved)

prune59.0ms (0.6%)

Memory

17.0MiB live, 137.6MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	588	2	590
Fresh	1	1	2
Picked	0	5	5
Done	0	1	1
Total	589	9	598

Accuracy

100.0%

Counts

598 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	39.4%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
▶	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	35.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
✓	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 74 to 47 computations (36.5% saved)

simplify100.0ms (1%)

Memory

-5.9MiB live, 110.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	128	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))

Rules

1 608×	`lower-fma.f32`
1 602×	`lower-fma.f64`
680×	`lower-*.f32`
676×	`lower-*.f64`
390×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	101
0	32	101
1	52	96
2	89	96
3	138	96
4	226	96
5	253	96
6	274	96
7	294	96
8	324	96
9	384	96
10	637	96
11	1565	96
12	2086	96
13	2810	96
14	2814	96
15	2814	96
16	2815	96
0	2815	92

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x x)
x
#s(literal -1/8 binary64)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
x
#s(literal 1/16 binary64)
#s(literal -1/8 binary64)
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x

Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(*.f64 x x)
x
#s(literal -1/8 binary64)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
x
#s(literal 1/16 binary64)
#s(literal -1/8 binary64)
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x

localize93.0ms (0.9%)

Memory

24.3MiB live, 177.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	39.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.7%	(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))

Samples

27.0ms	102×	1	valid
20.0ms	62×	2	valid
18.0ms	92×	0	valid

Compiler

Compiled 86 to 21 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-add: 13.0ms (27% of total)

ival-mult: 12.0ms (24.9% of total)

adjust: 8.0ms (16.6% of total)

ival-sqrt: 7.0ms (14.5% of total)

ival-div: 3.0ms (6.2% of total)

ival-sub: 2.0ms (4.2% of total)

ival-neg: 2.0ms (4.2% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory

-31.6MiB live, 12.2MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#<alt (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))>
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))>
#<alt (*.f64 x x)>
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))>
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))>
#<alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))>
#<alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))>
#<alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (+.f64 x #s(literal 1 binary64))>

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

Calls

33 calls:

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

simplify414.0ms (4.2%)

Memory

2.0MiB live, 525.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 524×	`lower-fma.f64`
11 524×	`lower-fma.f32`
3 494×	`lower-+.f64`
3 494×	`lower-+.f32`
3 016×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	1317
1	662	1158
2	2260	1106
3	6280	1095
0	8081	1023

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 130

Calls

Call 1

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

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

rewrite375.0ms (3.8%)

Memory

19.0MiB live, 615.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 350×	`lower-fma.f32`
6 344×	`lower-fma.f64`
4 644×	`lower-*.f32`
4 640×	`lower-*.f64`
3 870×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	86
0	32	86
1	124	81
2	917	81
0	8362	76

Stop Event

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

Counts

11 → 446

Calls

Call 1

Inputs
(fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))

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

eval105.0ms (1.1%)

Memory: -6.5MiB live, 145.7MiB allocated
Compiler: Compiled 13 553 to 1 599 computations (88.2% saved)

prune65.0ms (0.6%)

Memory

-12.8MiB live, 166.6MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	609	1	610
Fresh	0	0	0
Picked	1	2	3
Done	0	6	6
Total	610	9	619

Accuracy

100.0%

Counts

619 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	39.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	35.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
✓	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 73 to 46 computations (37% saved)

simplify5.0ms (0%)

Memory

7.5MiB live, 7.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

8×	`lower-+.f32`
6×	`lower-+.f64`
4×	`+-commutative`
2×	`lift-sqrt.f64`
2×	`lift-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	15	15
0	15	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize30.0ms (0.3%)

Memory

19.8MiB live, 58.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	39.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))

Samples

9.0ms	101×	1	valid
8.0ms	63×	2	valid
5.0ms	92×	0	valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sqrt: 6.0ms (42.9% of total)

adjust: 3.0ms (21.5% of total)

ival-add: 3.0ms (21.5% of total)

ival-sub: 2.0ms (14.3% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

-35.6MiB live, 1.4MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (+.f64 x #s(literal 1 binary64))>

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

Calls

9 calls:

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

simplify2.7s (27.2%)

Memory

8.0MiB live, 568.1MiB allocated

Algorithm

1×	egg-herbie

Rules

16 374×	`lower-fma.f64`
16 374×	`lower-fma.f32`
3 902×	`lower-*.f64`
3 902×	`lower-*.f32`
2 204×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	415
1	312	375
2	921	358
3	2747	347
4	6290	347
0	8163	312

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 34

Calls

Call 1

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

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

rewrite1.1s (10.7%)

Memory

34.0MiB live, 386.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 738×	`lower-fma.f64`
6 738×	`lower-fma.f32`
3 568×	`lower-*.f64`
3 568×	`lower-*.f32`
3 076×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	39	13
2	260	13
3	3407	13
0	8287	12

Stop Event

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

Counts

3 → 368

Calls

Call 1

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

Outputs
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(+.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x #s(literal 2 binary64)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))))
(expm1.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(expm1.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 1 binary64)))
(expm1.f64 (.f64 (.f64 #s(literal 2 binary64) (log1p.f64 x)) #s(literal 1/4 binary64)))
(expm1.f64 (.f64 (.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(expm1.f64 (-.f64 (log1p.f64 x) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(fma.f64 (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 0 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))) (-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/4 binary64)) #s(literal -1 binary64))
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(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))
(.f64 (pow.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) #s(literal 1 binary64)) (pow.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x)))))
(.f64 (pow.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x)))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))

eval300.0ms (3%)

Memory: -0.2MiB live, 116.0MiB allocated
Compiler: Compiled 8 266 to 1 240 computations (85% saved)

prune55.0ms (0.6%)

Memory

-17.5MiB live, 148.0MiB allocated

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	401	1	402
Fresh	0	0	0
Picked	0	1	1
Done	0	8	8
Total	401	10	411

Accuracy

100.0%

Counts

411 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	39.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
	4.4%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	35.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
✓	64.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 164 to 78 computations (52.4% saved)

regimes9.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

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

Calls

2 calls:

4.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
4.0ms	x

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes10.0ms (0.1%)

Memory

-12.5MiB live, 26.7MiB allocated

Counts

11 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))))

Outputs

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

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

Calls

2 calls:

5.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
4.0ms	x

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Memory

-12.7MiB live, 26.7MiB allocated

Counts

9 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Outputs

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

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

Calls

2 calls:

4.0ms	x
4.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Memory

23.6MiB live, 23.6MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes7.0ms (0.1%)

Memory

-17.1MiB live, 22.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

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

#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))

Calls

2 calls:

3.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
99.1%	2	`x`
99.1%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
2.0ms	x

Results

Accuracy	Segments	Branch
99.1%	2	`x`
99.1%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Memory

-23.1MiB live, 17.7MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.7%	2	`x`
98.7%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

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

Calls

2 calls:

2.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
2.0ms	x

Results

Accuracy	Segments	Branch
98.5%	2	`x`
98.5%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
2.0ms	x

Results

Accuracy	Segments	Branch
66.6%	1	`x`
66.6%	1	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0%)

Memory

-30.9MiB live, 8.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))

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

Calls

2 calls:

1.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
1.0ms	x

Results

Accuracy	Segments	Branch
4.4%	1	`x`
4.4%	1	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4464767903928303e-6	3.8222508402632625

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify8.0ms (0.1%)

Memory

30.1MiB live, 30.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
2×	`mul-1-neg_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	285
1	57	285
2	61	285
3	66	285

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))

Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/2361183241434822606848 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
(+.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal -1 binary64))

soundness1.0s (10.3%)

Memory

-12.2MiB live, 832.2MiB allocated

Rules

18 662×	`lower-fma.f64`
18 662×	`lower-fma.f32`
16 374×	`lower-fma.f64`
16 374×	`lower-fma.f32`
9 354×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	86
0	32	86
1	124	81
2	917	81
0	8362	76
0	110	415
1	312	375
2	921	358
3	2747	347
4	6290	347
0	8163	312
0	23	108
0	34	108
1	145	108
2	966	103
0	8579	103
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20
0	161	600
1	485	505
2	1633	483
3	5433	474
0	8374	430

Stop Event

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

Compiler

Compiled 409 to 164 computations (59.9% saved)

preprocess52.0ms (0.5%)

Memory: -11.1MiB live, 105.1MiB allocated
Compiler: Compiled 390 to 76 computations (80.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

analyze1.0ms (0%)

sample649.0ms (6.5%)

preprocess24.0ms (0.2%)

explain74.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize20.0ms (0.2%)

series7.0ms (0.1%)

simplify552.0ms (5.5%)

rewrite666.0ms (6.7%)

eval114.0ms (1.1%)

prune106.0ms (1.1%)

simplify10.0ms (0.1%)

localize99.0ms (1%)

series8.0ms (0.1%)

simplify577.0ms (5.8%)

rewrite378.0ms (3.8%)

eval120.0ms (1.2%)

prune59.0ms (0.6%)

simplify100.0ms (1%)

localize93.0ms (0.9%)

series11.0ms (0.1%)

simplify414.0ms (4.2%)

rewrite375.0ms (3.8%)

eval105.0ms (1.1%)

prune65.0ms (0.6%)

simplify5.0ms (0%)

localize30.0ms (0.3%)

series3.0ms (0%)

simplify2.7s (27.2%)

rewrite1.1s (10.7%)

eval300.0ms (3%)

prune55.0ms (0.6%)

regimes9.0ms (0.1%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.0s (10.3%)

preprocess52.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8