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

analyze1.0ms (0%)

Memory

2.8MiB live, 2.8MiB 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)

sample601.0ms (6.2%)

Memory

26.1MiB live, 1 443.6MiB allocated

Samples

374.0ms	8 253×	0	valid
0.0ms	3×	2	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-add: 103.0ms (44% of total)

ival-sqrt: 66.0ms (28.2% of total)

ival-div: 53.0ms (22.6% of total)

ival-true: 5.0ms (2.1% of total)

exact: 4.0ms (1.7% of total)

ival-assert: 3.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess85.0ms (0.9%)

Memory

-17.2MiB live, 40.6MiB 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)))))

explain71.0ms (0.7%)

Memory

20.0MiB live, 179.2MiB 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

28.0ms

512×

valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-add: 7.0ms (43.7% of total)

ival-div: 4.0ms (25% of total)

ival-sqrt: 4.0ms (25% of total)

exact: 1.0ms (6.2% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0%)

Memory

10.4MiB live, 10.4MiB 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))

localize22.0ms (0.2%)

Memory

-31.1MiB live, 47.4MiB 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	99.8%	(/.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: 6.0ms

ival-add: 3.0ms (47.5% of total)

ival-div: 2.0ms (31.7% of total)

ival-sqrt: 2.0ms (31.7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0%)

Memory

9.5MiB live, 9.5MiB 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
1.0ms	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))

simplify440.0ms (4.6%)

Memory

29.8MiB live, 863.2MiB 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))

rewrite269.0ms (2.8%)

Memory

-19.9MiB live, 664.9MiB 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)))))

eval82.0ms (0.8%)

Memory: 2.0MiB live, 240.6MiB allocated
Compiler: Compiled 11 091 to 2 091 computations (81.1% saved)

prune74.0ms (0.8%)

Memory

-15.4MiB live, 219.5MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	512	8	520
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	512	9	521

Accuracy

100.0%

Counts

521 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	90.3%	(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))))
✓	99.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))
	32.5%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	27.9%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
▶	73.7%	#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))))
▶	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
▶	73.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
	29.1%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 179 to 90 computations (49.7% saved)

simplify433.0ms (4.5%)

Memory

17.9MiB live, 387.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	2176	(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))))
✓	cost-diff	0	(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.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	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))))
✓	cost-diff	0	(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	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	0	(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))

Rules

7 112×	`lower-fma.f32`
7 102×	`lower-fma.f64`
2 296×	`lower-*.f32`
2 290×	`lower-*.f64`
1 764×	`div-sub`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	188
0	47	179
1	89	179
2	163	175
3	343	175
4	673	175
5	1326	175
6	2671	175
7	4265	175
8	5896	175
9	6622	175
10	6704	175
11	6783	175
12	6916	175
13	7205	175
14	7650	175
15	7872	175
16	7872	175
17	7888	175
18	7938	175
0	8002	175

Stop Event

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

Calls

Call 1

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

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

localize134.0ms (1.4%)

Memory

13.7MiB live, 247.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(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))))
✓	accuracy	99.9%	(fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	accuracy	90.6%	(/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	accuracy	32.5%	(-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	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	73.7%	#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%	(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	72.5%	#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%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	73.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	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	99.9%	(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))

Samples

44.0ms	116×	1	valid
35.0ms	65×	2	valid
12.0ms	75×	0	valid

Compiler

Compiled 181 to 28 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 17.0ms (25.1% of total)

ival-add: 15.0ms (22.2% of total)

adjust: 14.0ms (20.7% of total)

ival-div: 14.0ms (20.7% of total)

ival-sqrt: 4.0ms (5.9% of total)

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

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

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

exact: 0.0ms (0% of total)

series42.0ms (0.4%)

Memory

-16.3MiB live, 26.3MiB allocated

Counts

18 → 216

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))>
#<alt (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)>
#<alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<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)))) (*.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 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))>
#<alt (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))))>
#<alt (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))>
#<alt (+.f64 x #s(literal 1 binary64))>
#<alt (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))>
#<alt (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #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 x)>
#<alt (/ (+ 2 (* 1/2 x)) x)>
#<alt (/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)>
#<alt (/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))>
#<alt (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x))>
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x)))>
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) 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 (* 1/2 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 (* 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 (* 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)))>
#<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) 1)>
#<alt (- (+ (sqrt x) (* 2 (sqrt (/ 1 x)))) 1)>
#<alt (- (+ (sqrt x) (+ (* -1 (/ (+ x (+ (* -1 (* (sqrt (/ 1 x)) (+ x (* 3/2 (sqrt (pow x 3)))))) (+ (* 1/2 x) (* 3/2 (sqrt (pow x 3)))))) (pow x 2))) (* 2 (sqrt (/ 1 x))))) 1)>
#<alt (- (+ (sqrt x) (+ (* -2 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 3))) (+ (* 2 (sqrt (/ 1 x))) (/ 3/2 (pow x 2))))) (+ 1 (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ x (* 3/2 (sqrt (pow x 3)))))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (/ 1 x)))))))>
#<alt (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (- (* -1 (sqrt x)) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x))) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ x (pow (sqrt -1) 2))) (+ (* 3/2 (* (sqrt (pow x 3)) (/ (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* 3 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x))) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/8 x)))>
#<alt (* x (+ 1/2 (* x (+ 1/8 (* -1/16 x)))))>
#<alt (* x (+ 1/2 (* x (+ 1/8 (* x (- (* 5/128 x) 1/16))))))>
#<alt (* x (- 1 (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1 (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))) (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1 (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x))) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (+ 1 (* (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)) (+ 1 (* (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)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -3/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 3/16 x) 3/8))))>
#<alt (* x (+ 1/2 (* x (- (* x (+ 3/16 (* -7/128 x))) 3/8))))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 2)))) x)>
#<alt (/ (- (+ (sqrt x) (* -3/2 (sqrt (/ 1 (pow x 3))))) (+ (* 3/2 (sqrt (/ 1 x))) (/ 1 x))) x)>
#<alt (/ (- (+ (sqrt x) (* -1 (/ (+ (* -1 (* (sqrt x) (* (+ 1 (* 3/2 (sqrt x))) (+ x (* 3/2 (sqrt (pow x 3))))))) (* 1/2 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4)))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) x)>
#<alt (sqrt (/ 1 x))>
#<alt (* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (sqrt x)) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2))))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (sqrt x) (/ (pow (+ 1 (* 3/2 (sqrt x))) 2) (pow (sqrt -1) 2)))) (* 3/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3)))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x))>
#<alt 2>
#<alt (+ 2 (* 3/2 x))>
#<alt (+ 2 (* x (+ 3/2 (* 3/8 x))))>
#<alt (+ 2 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))>
#<alt (sqrt (pow x 3))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (/ 1 (pow x 2))))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (/ 1 (pow x 2)))))))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2))))))>

Calls

54 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(+ (* (- (+ x 1) (sqrt (+ x 1))) (/ x (+ (* (+ x 1) (sqrt (+ x 1))) 1))) (/ x (+ (* (+ x 1) (sqrt (+ x 1))) 1)))
1.0ms	x	@	inf	(+ (* (- (+ x 1) (sqrt (+ x 1))) (/ x (+ (* (+ x 1) (sqrt (+ x 1))) 1))) (/ x (+ (* (+ x 1) (sqrt (+ x 1))) 1)))
1.0ms	x	@	-inf	(/ x (+ (* (+ x 1) (sqrt (+ x 1))) 1))
1.0ms	x	@	0	(+ (* x 1/16) -1/8)
1.0ms	x	@	-inf	(/ (+ 1 (sqrt (+ x 1))) x)

simplify384.0ms (4%)

Memory

14.5MiB live, 688.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 430×	`lower-fma.f64`
11 430×	`lower-fma.f32`
4 838×	`lower-*.f64`
4 838×	`lower-*.f32`
3 690×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	449	2937
1	1429	2508
2	4811	2407
0	8473	2233

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 214

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 x)
(/ (+ 2 (* 1/2 x)) x)
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (/ 1 x))
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))
(+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) 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)))))))
(* 1/2 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)))
(* 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)))
(* 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)))
(* 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) 1)
(- (+ (sqrt x) (* 2 (sqrt (/ 1 x)))) 1)
(- (+ (sqrt x) (+ (* -1 (/ (+ x (+ (* -1 (* (sqrt (/ 1 x)) (+ x (* 3/2 (sqrt (pow x 3)))))) (+ (* 1/2 x) (* 3/2 (sqrt (pow x 3)))))) (pow x 2))) (* 2 (sqrt (/ 1 x))))) 1)
(- (+ (sqrt x) (+ (* -2 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 3))) (+ (* 2 (sqrt (/ 1 x))) (/ 3/2 (pow x 2))))) (+ 1 (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ x (* 3/2 (sqrt (pow x 3)))))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (/ 1 x)))))))
(* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (- (* -1 (sqrt x)) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(+ (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x))) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(+ (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ x (pow (sqrt -1) 2))) (+ (* 3/2 (* (sqrt (pow x 3)) (/ (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* 3 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x))) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 x)))
(* x (+ 1/2 (* x (+ 1/8 (* -1/16 x)))))
(* x (+ 1/2 (* x (+ 1/8 (* x (- (* 5/128 x) 1/16))))))
(* x (- 1 (sqrt (/ 1 x))))
(* x (- (+ 1 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1 (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))) (sqrt (/ 1 x))))
(* x (- (+ 1 (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x))) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (+ 1 (* (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)) (+ 1 (* (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)))
(* 1/2 x)
(* x (+ 1/2 (* -3/8 x)))
(* x (+ 1/2 (* x (- (* 3/16 x) 3/8))))
(* x (+ 1/2 (* x (- (* x (+ 3/16 (* -7/128 x))) 3/8))))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 2)))) x)
(/ (- (+ (sqrt x) (* -3/2 (sqrt (/ 1 (pow x 3))))) (+ (* 3/2 (sqrt (/ 1 x))) (/ 1 x))) x)
(/ (- (+ (sqrt x) (* -1 (/ (+ (* -1 (* (sqrt x) (* (+ 1 (* 3/2 (sqrt x))) (+ x (* 3/2 (sqrt (pow x 3))))))) (* 1/2 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4)))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) x)
(sqrt (/ 1 x))
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* -1 (sqrt x)) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2))))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x))
(* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (sqrt x) (/ (pow (+ 1 (* 3/2 (sqrt x))) 2) (pow (sqrt -1) 2)))) (* 3/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3)))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x))
2
(+ 2 (* 3/2 x))
(+ 2 (* x (+ 3/2 (* 3/8 x))))
(+ 2 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(sqrt (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (/ 1 (pow x 2))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (/ 1 (pow x 2)))))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2))))))

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)
(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (+.f64 (sqrt.f64 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 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 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 x (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.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)))) x)) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* 1/2 x)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)) x)
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)
(/.f64 (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)
(/.f64 (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)) x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 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 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) 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))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x)))
(neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x)))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.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)) x))
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 -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x 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)))))
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(*.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) 1)
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(- (+ (sqrt x) (* 2 (sqrt (/ 1 x)))) 1)
(fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(- (+ (sqrt x) (+ (* -1 (/ (+ x (+ (* -1 (* (sqrt (/ 1 x)) (+ x (* 3/2 (sqrt (pow x 3)))))) (+ (* 1/2 x) (* 3/2 (sqrt (pow x 3)))))) (pow x 2))) (* 2 (sqrt (/ 1 x))))) 1)
(+.f64 #s(literal -1 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 (+.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -3/2 binary64) (neg.f64 x)) x)) (.f64 x x))))
(- (+ (sqrt x) (+ (* -2 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 3))) (+ (* 2 (sqrt (/ 1 x))) (/ 3/2 (pow x 2))))) (+ 1 (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ x (* 3/2 (sqrt (pow x 3)))))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (/ 1 x)))))))
(+.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/2 binary64) x) (.f64 x (.f64 x x))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 3/2 binary64) (.f64 x x)))) (+.f64 (sqrt.f64 x) (-.f64 #s(literal -1 binary64) (-.f64 (fma.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 3/2 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/2 binary64) x))))))
(* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1 (/ (- (* -1 (sqrt x)) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) x))
(+ (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x))) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (.f64 (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -2 binary64)) (/.f64 (*.f64 (/.f64 x #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) #s(literal -1/2 binary64))) x)) x))
(+ (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ x (pow (sqrt -1) 2))) (+ (* 3/2 (* (sqrt (pow x 3)) (/ (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* 3 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x))) (sqrt x)) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (.f64 (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -2 binary64)) (/.f64 (-.f64 (.f64 (/.f64 x #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 #s(literal 3/2 binary64) (+.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -3 binary64)) (.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -2 binary64))) x)) 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 (+ 1/8 (* -1/16 x)))))
(*.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 (+ 1/8 (* x (- (* 5/128 x) 1/16))))))
(*.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)))
(* x (- 1 (sqrt (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) x)
(* x (- (+ 1 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (- (+ 1 (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))) (sqrt (/ 1 x))))
(.f64 x (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (+ 1 (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x))) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) x)
(* x (+ 1 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (+ 1 (* (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) (-.f64 #s(literal 1 binary64) (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)) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (/.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)) x) (-.f64 #s(literal 1 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))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -3/8 x)))
(*.f64 x (fma.f64 x #s(literal -3/8 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* 3/16 x) 3/8))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal -3/8 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* x (- (* x (+ 3/16 (* -7/128 x))) 3/8))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -7/128 binary64) #s(literal 3/16 binary64)) #s(literal -3/8 binary64)) #s(literal 1/2 binary64)))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 2)))) x)
(/.f64 (-.f64 (sqrt.f64 x) (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/2 binary64) x) (*.f64 x x))) x)
(/ (- (+ (sqrt x) (* -3/2 (sqrt (/ 1 (pow x 3))))) (+ (* 3/2 (sqrt (/ 1 x))) (/ 1 x))) x)
(/.f64 (+.f64 (sqrt.f64 x) (fma.f64 #s(literal -3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) x))) x)
(/ (- (+ (sqrt x) (* -1 (/ (+ (* -1 (* (sqrt x) (* (+ 1 (* 3/2 (sqrt x))) (+ x (* 3/2 (sqrt (pow x 3))))))) (* 1/2 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4)))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) x)
(/.f64 (-.f64 (+.f64 (sqrt.f64 x) (fma.f64 #s(literal -3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) x))) (/.f64 (fma.f64 (sqrt.f64 x) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -3/2 binary64) (neg.f64 x))) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64))))) (pow.f64 x #s(literal 4 binary64)))) x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2))))) x))
(neg.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) x) (sqrt.f64 x)) x))
(* -1 (/ (- (+ (* -1 (sqrt x)) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2))))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -3/2 binary64) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) x)) (sqrt.f64 x)) (neg.f64 x))
(* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (sqrt x) (/ (pow (+ 1 (* 3/2 (sqrt x))) 2) (pow (sqrt -1) 2)))) (* 3/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3)))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) x) (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 9/4 binary64))) (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 3/2 binary64) #s(literal 1 binary64))) #s(literal -1 binary64))) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/2 binary64))) (.f64 x (*.f64 x x)))) (neg.f64 x))
2
#s(literal 2 binary64)
(+ 2 (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(+ 2 (* x (+ 3/2 (* 3/8 x))))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal 3/8 binary64)) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (/ 1 (pow x 2))))))
(fma.f64 x (.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 x x) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) #s(literal 1 binary64)))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (/ 1 (pow x 2)))))))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 x x) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) #s(literal 1 binary64)))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (.f64 x (.f64 x x))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))
(fma.f64 (.f64 x x) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (*.f64 x x) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2))))))
(-.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -3/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64))))) (.f64 x (.f64 x x))) (.f64 x x)))

rewrite443.0ms (4.6%)

Memory

-21.4MiB live, 969.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 758×	`lower-*.f32`
4 752×	`lower-*.f64`
4 652×	`lower-/.f32`
4 646×	`lower-/.f64`
2 990×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	168
0	47	143
1	203	139
2	1650	139
0	8475	139

Stop Event

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

Counts

18 → 1 154

Calls

Call 1

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

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

eval289.0ms (3%)

Memory: 24.5MiB live, 651.4MiB allocated
Compiler: Compiled 90 173 to 3 970 computations (95.6% saved)

prune388.0ms (4%)

Memory

-7.8MiB live, 393.5MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1 901	1	1 902
Fresh	0	3	3
Picked	2	3	5
Done	0	1	1
Total	1 903	8	1 911

Accuracy

100.0%

Counts

1 911 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	32.5%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
▶	27.9%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	73.7%	#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))))
✓	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	73.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
▶	29.1%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify37.0ms (0.4%)

Memory

19.6MiB live, 19.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 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 #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)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Rules

472×	`lower-fma.f32`
470×	`lower-fma.f64`
312×	`lower-*.f32`
308×	`lower-*.f64`
162×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	91
0	31	91
1	45	88
2	69	88
3	89	88
4	122	88
5	143	88
6	164	88
7	184	88
8	214	88
9	265	88
10	409	88
11	732	88
12	892	88
13	927	88
14	931	88
0	931	86

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize169.0ms (1.8%)

Memory

-2.8MiB live, 69.5MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.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	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	65.6%	(-.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 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	72.8%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	63.9%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	65.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Samples

42.0ms	54×	1	valid
11.0ms	38×	2	valid
10.0ms	92×	0	invalid
8.0ms	72×	0	valid

Compiler

Compiled 77 to 19 computations (75.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-div: 34.0ms (60% of total)

ival-add: 6.0ms (10.6% of total)

ival-sqrt: 5.0ms (8.8% of total)

adjust: 4.0ms (7.1% of total)

ival-mult: 4.0ms (7.1% of total)

ival-sub: 2.0ms (3.5% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

12 → 144

Calls

Call 1

Inputs
#<alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))>
#<alt (sqrt.f64 x)>
#<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 (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 (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 (* 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 (- (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 (* -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 (- (* 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

36 calls:

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

simplify682.0ms (7.1%)

Memory

15.4MiB live, 578.3MiB allocated

Algorithm

1×	egg-herbie

Rules

17 352×	`lower-fma.f64`
17 352×	`lower-fma.f32`
3 952×	`lower-*.f64`
3 952×	`lower-*.f32`
3 144×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	203	1430
1	605	1232
2	2040	1156
3	6763	1149
0	8197	1066

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

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

rewrite366.0ms (3.8%)

Memory

-27.6MiB live, 630.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 686×	`lower-fma.f32`
8 684×	`lower-fma.f64`
5 110×	`lower-*.f32`
5 106×	`lower-*.f64`
3 706×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	81
0	31	82
1	106	80
2	729	72
0	8638	66

Stop Event

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

Counts

12 → 700

Calls

Call 1

Inputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(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))
(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
#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 (sqrt.f64 x) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x))) (/.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(expm1.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(fma.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(fma.f64 (/.f64 x (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(neg.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 x))))
(neg.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(neg.f64 (/.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)) (+.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64))) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64))) (+.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (sqrt.f64 x)) #s(literal -1 binary64)) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (-.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (.f64 x (neg.f64 (sqrt.f64 x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 x (.f64 x (sqrt.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 x (neg.f64 (sqrt.f64 x)))) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)))) (neg.f64 (+.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))))
(/.f64 (-.f64 (*.f64 x (sqrt.f64 x)) #s(literal 1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (+.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 (*.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (sqrt.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (-.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (.f64 x (neg.f64 (sqrt.f64 x)))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(*.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)) (fma.f64 x (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) (fma.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) x) (*.f64 x x)))
(.f64 (/.f64 (fma.f64 x (sqrt.f64 x) #s(literal -1 binary64)) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (+.f64 x (-.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))))
(+.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 #s(literal 1 binary64) (/.f64 (.f64 x (.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 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))))
(-.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.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 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 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 (.f64 x (.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 x (/.f64 (.f64 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 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal 1/4 binary64)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 (*.f64 x x) #s(literal -1/8 binary64)))
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(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(+.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(exp.f64 (log1p.f64 x))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(fabs.f64 (+.f64 x #s(literal 1 binary64)))
(-.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (fma.f64 x x (+.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #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 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #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) x))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.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 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (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 (.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 x (.f64 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 x) (.f64 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 x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 x x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(/.f64 (.f64 (fma.f64 x (.f64 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 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 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 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 x (/.f64 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 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 x (/.f64 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))))) (fma.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.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 (fma.f64 x x (-.f64 #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 x #s(literal -1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (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 (+.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 x (.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 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 (sqrt.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 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 x)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.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))))
(*.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 (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 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (fma.f64 x (.f64 x 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 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.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)))
(.f64 (.f64 #s(literal 1 binary64) (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 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 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 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.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 x (.f64 x (.f64 x x)))))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))
(.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))) (+.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))) (fma.f64 x x (+.f64 x #s(literal 1 binary64))))
(.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))))

eval181.0ms (1.9%)

Memory: -17.3MiB live, 294.7MiB allocated
Compiler: Compiled 17 145 to 2 063 computations (88% saved)

prune172.0ms (1.8%)

Memory

28.6MiB live, 267.8MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	870	1	871
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	871	8	879

Accuracy

100.0%

Counts

879 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	32.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	27.9%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	73.7%	#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))))
✓	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	73.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	29.1%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 60 to 38 computations (36.7% saved)

simplify4.0ms (0%)

Memory

6.6MiB live, 6.6MiB 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)

localize48.0ms (0.5%)

Memory

-35.2MiB live, 84.1MiB 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	32.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))

Samples

23.0ms	70×	2	valid
12.0ms	112×	1	valid
3.0ms	74×	0	valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-sqrt: 19.0ms (62% of total)

adjust: 6.0ms (19.6% of total)

ival-add: 3.0ms (9.8% of total)

ival-sub: 3.0ms (9.8% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.6MiB live, 2.6MiB 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))

simplify397.0ms (4.1%)

Memory

30.1MiB live, 662.6MiB 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))

rewrite455.0ms (4.7%)

Memory

-10.9MiB live, 472.5MiB 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))
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(/.f64 (-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.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 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (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))))) (fma.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.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 (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 x #s(literal -1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (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)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (-.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x x)))) (exp.f64 (log1p.f64 (-.f64 (*.f64 x x) x))))
(/.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) (exp.f64 (log.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))))) (exp.f64 (log1p.f64 (neg.f64 x))))
(/.f64 (exp.f64 (log1p.f64 (*.f64 (neg.f64 x) x))) (exp.f64 (log1p.f64 (neg.f64 x))))
(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 (*.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))
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 4 binary64))
(pow.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log1p.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log1p.f64 x)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(*.f64 #s(literal 1 binary64) (+.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 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.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))))
(.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 binary64)))
(*.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 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) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(.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)) #s(literal 1 binary64)))
(.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 binary64)))
(.f64 (fma.f64 x (.f64 x x) #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 2 binary64)))
(.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)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(.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 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64)))
(.f64 (fma.f64 x x #s(literal -1 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 1/2 binary64)))
(.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)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.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)) (+.f64 x #s(literal 1 binary64)))))
(.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))) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.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))) (+.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 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (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)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #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 (.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 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 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 binary64)))
(.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)))))

eval53.0ms (0.6%)

Memory: 16.7MiB live, 132.0MiB allocated
Compiler: Compiled 8 266 to 1 240 computations (85% saved)

prune60.0ms (0.6%)

Memory

-50.0MiB live, 131.6MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	400	2	402
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	400	10	410

Accuracy

100.0%

Counts

410 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	32.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
	6.6%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
	4.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	27.9%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	73.7%	#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))))
✓	72.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	73.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	29.1%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 185 to 79 computations (57.3% saved)

regimes26.0ms (0.3%)

Memory

21.5MiB live, 21.5MiB allocated

Counts

13 → 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))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
#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)))))
(/.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))
(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))))

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
99.8%	1	`x`
99.8%	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)

regimes8.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

10 → 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))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
#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	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
4.0ms	x

Results

Accuracy	Segments	Branch
99.8%	2	`x`
99.8%	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)

regimes8.0ms (0.1%)

Memory

-18.7MiB live, 20.2MiB allocated

Counts

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

5.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	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)

regimes6.0ms (0.1%)

Memory

17.8MiB live, 17.8MiB 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))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
#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
99.4%	2	`x`
99.4%	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

-22.5MiB live, 15.3MiB 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))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
#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:

4.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	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))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
#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:

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

Results

Accuracy	Segments	Branch
99.0%	2	`x`
99.0%	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)

regimes5.0ms (0%)

Memory

12.5MiB live, 12.5MiB 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))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
#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)

regimes5.0ms (0.1%)

Memory

-27.6MiB live, 11.5MiB allocated

Counts

3 → 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))

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
73.6%	1	`x`
73.6%	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

8.8MiB live, 8.8MiB 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
4.6%	1	`x`
4.6%	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)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6917451524874405e-8	770.0321888421079

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6917451524874405e-8	770.0321888421079

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6917451524874405e-8	770.0321888421079

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6917451524874405e-8	770.0321888421079

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6917451524874405e-8	770.0321888421079

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	1.6917451524874405e-8	770.0321888421079

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify10.0ms (0.1%)

Memory

-20.4MiB live, 19.8MiB 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	42	248
1	54	248
2	58	248
3	63	248

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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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 3022314549036573/151115727451828646838272 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))

soundness2.2s (22.6%)

Memory

3.0MiB live, 687.3MiB allocated

Rules

18 662×	`lower-fma.f64`
18 662×	`lower-fma.f32`
16 374×	`lower-fma.f64`
16 374×	`lower-fma.f32`
8 686×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	415
1	312	375
2	921	358
3	2747	347
4	6290	347
0	8163	312
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20
0	27	168
0	47	143
1	203	139
2	1650	139
0	8475	139
0	21	81
0	31	82
1	106	80
2	729	72
0	8638	66
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×	iter limit
1×	node limit

Compiler

Compiled 329 to 133 computations (59.6% saved)

preprocess965.0ms (10%)

Memory: 33.1MiB live, 71.4MiB allocated
Compiler: Compiled 332 to 72 computations (78.3% 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	21	91
0	31	91
1	45	88
2	69	88
3	89	88
4	122	88
5	143	88
6	164	88
7	184	88
8	214	88
9	265	88
10	409	88
11	732	88
12	892	88
13	927	88
14	931	88
0	931	86

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	21	91
0	31	91
1	45	88
2	69	88
3	89	88
4	122	88
5	143	88
6	164	88
7	184	88
8	214	88
9	265	88
10	409	88
11	732	88
12	892	88
13	927	88
14	931	88
0	931	86

analyze1.0ms (0%)

sample601.0ms (6.2%)

preprocess85.0ms (0.9%)

explain71.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize22.0ms (0.2%)

series5.0ms (0%)

simplify440.0ms (4.6%)

rewrite269.0ms (2.8%)

eval82.0ms (0.8%)

prune74.0ms (0.8%)

simplify433.0ms (4.5%)

localize134.0ms (1.4%)

series42.0ms (0.4%)

simplify384.0ms (4%)

rewrite443.0ms (4.6%)

eval289.0ms (3%)

prune388.0ms (4%)

simplify37.0ms (0.4%)

localize169.0ms (1.8%)

series5.0ms (0.1%)

simplify682.0ms (7.1%)

rewrite366.0ms (3.8%)

eval181.0ms (1.9%)

prune172.0ms (1.8%)

simplify4.0ms (0%)

localize48.0ms (0.5%)

series1.0ms (0%)

simplify397.0ms (4.1%)

rewrite455.0ms (4.7%)

eval53.0ms (0.6%)

prune60.0ms (0.6%)

regimes26.0ms (0.3%)

regimes8.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

soundness2.2s (22.6%)

preprocess965.0ms (10%)

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

Iter	Nodes	Cost
0	21	91
0	31	91
1	45	88
2	69	88
3	89	88
4	122	88
5	143	88
6	164	88
7	184	88
8	214	88
9	265	88
10	409	88
11	732	88
12	892	88
13	927	88
14	931	88
0	931	86