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

analyze1.0ms (0%)

Memory

2.2MiB live, 2.2MiB 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)

sample1.0s (13%)

Memory

20.1MiB live, 1 011.7MiB allocated

Samples

701.0ms	8 254×	0	valid
0.0ms	2×	2	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 410.0ms

ival-sqrt: 227.0ms (55.3% of total)

ival-add: 96.0ms (23.4% of total)

ival-div: 73.0ms (17.8% of total)

ival-true: 6.0ms (1.5% of total)

exact: 5.0ms (1.2% of total)

ival-assert: 3.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess41.0ms (0.5%)

Memory

-4.6MiB live, 34.7MiB 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)))))

explain133.0ms (1.7%)

Memory

-3.8MiB live, 198.4MiB 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

55.0ms

512×

valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-add: 35.0ms (80.7% of total)

ival-sqrt: 4.0ms (9.2% of total)

ival-div: 3.0ms (6.9% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB 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))

localize24.0ms (0.3%)

Memory

-14.4MiB live, 62.1MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

14.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

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

ival-add: 3.0ms (46% of total)

ival-div: 2.0ms (30.7% of total)

ival-sqrt: 2.0ms (30.7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

Time	Variable		Point	Expression
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))

simplify692.0ms (8.9%)

Memory

-98.3MiB live, 701.1MiB 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))

rewrite280.0ms (3.6%)

Memory

6.0MiB live, 555.9MiB 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)))))

eval84.0ms (1.1%)

Memory: 2.5MiB live, 238.8MiB allocated
Compiler: Compiled 11 091 to 2 091 computations (81.1% saved)

prune72.0ms (0.9%)

Memory

-21.2MiB live, 214.4MiB 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
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	63.4%	(/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
▶	65.1%	(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64))))
	42.4%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
▶	64.4%	#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))))
▶	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
▶	64.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
	37.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 135 to 86 computations (36.3% saved)

simplify17.0ms (0.2%)

Memory

9.3MiB live, 42.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

164×	`lower-fma.f32`
154×	`lower-fma.f64`
88×	`lower-+.f32`
86×	`lower-+.f64`
70×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	175
0	40	175
1	71	175
2	106	175
3	139	175
4	146	175
0	146	175

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize78.0ms (1%)

Memory

28.6MiB live, 185.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
✓	accuracy	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
✓	accuracy	62.9%	#s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #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	99.9%	(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	64.4%	#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	62.7%	#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	64.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64))))
✓	accuracy	65.1%	#s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)))

Samples

46.0ms

256×

valid

Compiler

Compiled 133 to 23 computations (82.7% saved)

Precisions

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

ival-mult: 17.0ms (54.6% of total)

ival-add: 10.0ms (32.1% of total)

ival-div: 2.0ms (6.4% of total)

ival-sqrt: 2.0ms (6.4% of total)

exact: 1.0ms (3.2% of total)

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

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

series10.0ms (0.1%)

Memory

-14.8MiB live, 24.2MiB allocated

Counts

16 → 192

Calls

Call 1

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

Calls

48 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(* 1/2 x)
1.0ms	x	@	inf	(+ (* x (+ (* x -1/8) 1/2)) 1)
0.0ms	x	@	inf	(+ (* 1/2 x) 2)
0.0ms	x	@	inf	(* x (+ (* x -1/8) 1/2))
0.0ms	x	@	inf	(* x (+ (* x (+ (* x 1/16) -1/8)) 1/2))

simplify450.0ms (5.8%)

Memory

5.5MiB live, 771.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 744×	`lower-fma.f64`
16 744×	`lower-fma.f32`
3 620×	`lower-*.f64`
3 620×	`lower-*.f32`
2 640×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	2048
1	599	1757
2	2014	1673
3	6156	1652
0	8355	1471

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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)))))
2
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(+ 2 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 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)
(* 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)
(- (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 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* 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 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))

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

rewrite357.0ms (4.6%)

Memory

-11.6MiB live, 609.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 710×	`lower-/.f32`
4 706×	`lower-/.f64`
4 346×	`lower-*.f32`
4 340×	`lower-*.f64`
3 236×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	155
0	40	155
1	186	155
2	1327	155
0	8244	155

Stop Event

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

Counts

16 → 408

Calls

Call 1

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

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

eval98.0ms (1.3%)

Memory: 4.8MiB live, 158.1MiB allocated
Compiler: Compiled 15 368 to 1 605 computations (89.6% saved)

prune120.0ms (1.5%)

Memory

-15.9MiB live, 140.3MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	648	2	650
Fresh	0	3	3
Picked	2	3	5
Done	0	1	1
Total	650	9	659

Accuracy

100.0%

Counts

659 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	42.4%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	64.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
▶	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
▶	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	64.4%	#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))))
✓	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	64.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
▶	37.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 115 to 73 computations (36.5% saved)

simplify106.0ms (1.4%)

Memory

-7.9MiB live, 107.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 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))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
✓	cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	136
0	39	136
1	59	131
2	96	131
3	145	131
4	233	131
5	260	131
6	282	131
7	302	131
8	332	131
9	392	131
10	645	131
11	1566	131
12	2084	131
13	2781	131
14	2785	131
15	2785	131
16	2786	131
0	2786	127

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize91.0ms (1.2%)

Memory

-2.8MiB live, 166.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	69.9%	(-.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	63.1%	#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	67.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	67.8%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	64.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))

Samples

16.0ms	97×	0	valid
12.0ms	34×	2	valid
12.0ms	47×	1	valid
11.0ms	78×	0	invalid

Compiler

Compiled 113 to 24 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-add: 9.0ms (28.1% of total)

ival-mult: 7.0ms (21.9% of total)

adjust: 5.0ms (15.6% of total)

ival-sqrt: 4.0ms (12.5% of total)

ival-div: 3.0ms (9.4% of total)

ival-sub: 2.0ms (6.3% of total)

ival-neg: 2.0ms (6.3% of total)

exact: 1.0ms (3.1% of total)

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

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

series6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

15 → 180

Calls

Call 1

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

45 calls:

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

simplify425.0ms (5.5%)

Memory

-1.7MiB live, 506.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	1807
1	662	1562
2	2258	1472
3	6300	1457
0	8099	1359

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 178

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

rewrite399.0ms (5.1%)

Memory

21.6MiB live, 542.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 670×	`lower-fma.f32`
5 664×	`lower-fma.f64`
4 488×	`lower-*.f32`
4 484×	`lower-*.f64`
4 130×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	116
0	39	116
1	144	111
2	1029	111
0	8457	106

Stop Event

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

Counts

15 → 474

Calls

Call 1

Inputs
(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(*.f64 x x)
#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 #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
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))
(+.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (.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 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))
(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (/.f64 #s(literal 1 binary64) (.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 (.f64 (.f64 x x) #s(literal 1/4 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 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) x (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/256 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 x #s(literal 1/128 binary64))))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/256 binary64) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/256 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 x #s(literal 1/128 binary64))))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/256 binary64) #s(literal -1/64 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) x) (/.f64 (.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) x) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) x) (/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) x) (/.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) x) (/.f64 (.f64 (.f64 x x) (.f64 x 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 (.f64 (.f64 x x) #s(literal 1/4 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 (/.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) x) (/.f64 (.f64 x 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 (.f64 (.f64 x x) #s(literal 1/4 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 (/.f64 (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) x) (/.f64 (.f64 x 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 (.f64 (.f64 x x) #s(literal 1/4 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 (/.f64 (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 x x)) x) (/.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) x) (/.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 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (*.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 (fma.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))))))))
(neg.f64 (/.f64 (.f64 (.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)))) (.f64 (neg.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 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))))))))
(neg.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (.f64 (neg.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)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.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)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 x #s(literal -1/2 binary64))))) (fma.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) (.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))))
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(.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
(*.f64 (+.f64 #s(literal -1 binary64) (+.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 #s(literal 1 binary64) (+.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 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (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 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #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 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.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 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(+.f64 (/.f64 (*.f64 x 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 (*.f64 x 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 (*.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 #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 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (/.f64 x (+.f64 (sqrt.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)))
(neg.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.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) (-.f64 (.f64 x x) x)) (fma.f64 x (.f64 x x) #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 (.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) 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 (.f64 x x) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal -1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x))))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))

eval125.0ms (1.6%)

Memory: -9.3MiB live, 179.4MiB allocated
Compiler: Compiled 14 273 to 1 701 computations (88.1% saved)

prune113.0ms (1.5%)

Memory

-16.7MiB live, 154.2MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	715	1	716
Fresh	0	0	0
Picked	1	4	5
Done	0	4	4
Total	716	9	725

Accuracy

100.0%

Counts

725 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	42.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
✓	64.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	64.4%	#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))))
✓	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	64.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	37.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 73 to 46 computations (37% saved)

simplify5.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB 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)

localize31.0ms (0.4%)

Memory

20.0MiB live, 58.9MiB 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	42.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))

Samples

11.0ms	91×	1	valid
8.0ms	66×	2	valid
4.0ms	99×	0	valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-add: 5.0ms (34% of total)

ival-sqrt: 4.0ms (27.2% of total)

adjust: 3.0ms (20.4% of total)

ival-sub: 2.0ms (13.6% 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

1.5MiB live, 1.5MiB 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))

simplify481.0ms (6.2%)

Memory

-17.6MiB live, 708.6MiB 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))

rewrite384.0ms (4.9%)

Memory

-14.6MiB live, 504.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 368

Calls

Call 1

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

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

eval152.0ms (1.9%)

Memory: 21.7MiB live, 99.8MiB allocated
Compiler: Compiled 8 266 to 1 240 computations (85% saved)

prune192.0ms (2.5%)

Memory

-17.0MiB live, 106.7MiB allocated

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	399	3	402
Fresh	0	0	0
Picked	0	1	1
Done	0	8	8
Total	399	12	411

Accuracy

100.0%

Counts

411 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	42.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
	5.2%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
	7.4%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))
	4.4%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	64.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
✓	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	36.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))
✓	64.4%	#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))))
✓	62.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))))
✓	64.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
✓	37.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 209 to 96 computations (54.1% saved)

regimes11.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

15 → 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)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #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))))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes126.0ms (1.6%)

Memory

-22.3MiB live, 16.8MiB allocated

Counts

14 → 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)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #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))))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))
(/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))))

Outputs

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

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

Calls

2 calls:

121.0ms	x
5.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

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)

regimes9.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

13 → 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)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #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))))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64))))

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.7%	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)

regimes9.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB allocated

Counts

12 → 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)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #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))))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 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
99.7%	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)

regimes104.0ms (1.3%)

Memory

-25.3MiB live, 13.3MiB allocated

Counts

9 → 2

Calls

Call 1

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

100.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
99.5%	2	`x`
99.5%	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)

regimes7.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #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	x
3.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.2%	2	`x`
98.2%	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

11.1MiB live, 11.1MiB 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)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #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:

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

Results

Accuracy	Segments	Branch
98.2%	2	`x`
98.2%	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

-28.1MiB live, 10.4MiB 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:

6.0ms	x
2.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
97.5%	2	`x`
97.5%	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

9.1MiB live, 9.1MiB 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
96.8%	2	`x`
96.8%	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)

regimes4.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB 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:

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

Results

Accuracy	Segments	Branch
64.3%	1	`x`
64.3%	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

5.3MiB live, 5.3MiB 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	x
1.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.218969924648522e-7	1.4500863128834058

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify9.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`+-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	50	318
1	63	318
2	67	318
3	72	318

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))

Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 x (+.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64))
(+.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal -1 binary64))

soundness1.1s (14.4%)

Memory

0.2MiB live, 756.3MiB allocated

Rules

18 662×	`lower-fma.f64`
18 662×	`lower-fma.f32`
16 374×	`lower-fma.f64`
16 374×	`lower-fma.f32`
5 670×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	155
0	40	155
1	186	155
2	1327	155
0	8244	155
0	110	415
1	312	375
2	921	358
3	2747	347
4	6290	347
0	8163	312
0	25	116
0	39	116
1	144	111
2	1029	111
0	8457	106
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20
0	161	600
1	485	505
2	1633	483
3	5433	474
0	8374	430

Stop Event

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

Compiler

Compiled 480 to 191 computations (60.2% saved)

preprocess366.0ms (4.7%)

Memory: -9.6MiB live, 158.9MiB allocated
Compiler: Compiled 448 to 84 computations (81.3% 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	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

analyze1.0ms (0%)

sample1.0s (13%)

preprocess41.0ms (0.5%)

explain133.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize24.0ms (0.3%)

series5.0ms (0.1%)

simplify692.0ms (8.9%)

rewrite280.0ms (3.6%)

eval84.0ms (1.1%)

prune72.0ms (0.9%)

simplify17.0ms (0.2%)

localize78.0ms (1%)

series10.0ms (0.1%)

simplify450.0ms (5.8%)

rewrite357.0ms (4.6%)

eval98.0ms (1.3%)

prune120.0ms (1.5%)

simplify106.0ms (1.4%)

localize91.0ms (1.2%)

series6.0ms (0.1%)

simplify425.0ms (5.5%)

rewrite399.0ms (5.1%)

eval125.0ms (1.6%)

prune113.0ms (1.5%)

simplify5.0ms (0.1%)

localize31.0ms (0.4%)

series1.0ms (0%)

simplify481.0ms (6.2%)

rewrite384.0ms (4.9%)

eval152.0ms (1.9%)

prune192.0ms (2.5%)

regimes11.0ms (0.1%)

regimes126.0ms (1.6%)

regimes9.0ms (0.1%)

regimes9.0ms (0.1%)

regimes104.0ms (1.3%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

soundness1.1s (14.4%)

preprocess366.0ms (4.7%)

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