Metrics for Main:bigenough3 from C

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

3.2MiB live, 3.2MiB 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
80%	50%	12.5%	0%	0%	37.5%	0%	4
88.9%	50%	6.2%	0%	0%	43.7%	0%	5
94.1%	50%	3.1%	0%	0%	46.9%	0%	6
97%	50%	1.6%	0%	0%	48.4%	0%	7
98.5%	50%	0.8%	0%	0%	49.2%	0%	8
99.2%	50%	0.4%	0%	0%	49.6%	0%	9
99.6%	50%	0.2%	0%	0%	49.8%	0%	10
99.8%	50%	0.1%	0%	0%	49.9%	0%	11
99.9%	50%	0%	0%	0%	49.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.1s (19.6%)

Memory

76.4MiB live, 1 849.5MiB allocated

Samples

613.0ms	4 101×	1	valid
206.0ms	4 155×	0	valid
0.0ms	5×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 570.0ms

ival-sqrt: 247.0ms (43.4% of total)

adjust: 124.0ms (21.8% of total)

ival-add: 102.0ms (17.9% of total)

ival-sub: 83.0ms (14.6% of total)

ival-true: 6.0ms (1.1% of total)

exact: 5.0ms (0.9% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain116.0ms (2%)

Memory

-14.5MiB live, 129.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
146	-	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(sqrt.f64 x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	146	0

Confusion

	Predicted +	Predicted -
+	146	0
-	0	110

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	0	0
-	0	0	110

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	110
1	146

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms	292×	1	valid
10.0ms	220×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-add: 30.0ms (56.5% of total)

ival-sqrt: 11.0ms (20.7% of total)

adjust: 7.0ms (13.2% of total)

ival-sub: 4.0ms (7.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess12.0ms (0.2%)

Memory

19.2MiB live, 19.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	11	19
0	6	7
0	10	7
1	13	7
0	13	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	45.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
0	13	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize70.0ms (1.2%)

Memory

-3.0MiB live, 42.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	34.592734837938565	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

58.0ms	146×	1	valid
6.0ms	110×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

adjust: 46.0ms (81.3% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

4 → 27

Calls

Call 1

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

Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -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)))))))

Calls

3 calls:

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

simplify317.0ms (5.5%)

Memory

-19.0MiB live, 174.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	451
1	331	393
2	1209	387
3	4903	387
0	8229	353

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 26

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -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)))))))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 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 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(sqrt x)
(sqrt.f64 x)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (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 -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)

rewrite159.0ms (2.7%)

Memory

18.9MiB live, 111.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	42	16
2	271	16
3	2932	16
0	9099	16

Stop Event

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

Counts

4 → 281

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(*.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (pow.f64 (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)) #s(literal 2 binary64))) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
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(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sinh.f64 (acosh.f64 x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (cosh.f64 (asinh.f64 (pow.f64 x #s(literal 3/2 binary64))))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64))) (fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (sinh.f64 (acosh.f64 x)) (cosh.f64 (asinh.f64 (pow.f64 x #s(literal 3/2 binary64))))) (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x)))
(/.f64 (.f64 (cosh.f64 (asinh.f64 (pow.f64 x #s(literal 3/2 binary64)))) (sinh.f64 (acosh.f64 x))) (.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (hypot.f64 (*.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))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (sinh.f64 (acosh.f64 (*.f64 x x))) (sinh.f64 (acosh.f64 x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(neg.f64 (-.f64 #s(literal 1 binary64) x))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 x #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(sin.f64 (acos.f64 x))
(cosh.f64 (asinh.f64 x))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(fabs.f64 (-.f64 #s(literal 1 binary64) x))
(cos.f64 (asin.f64 x))
(hypot.f64 (fabs.f64 (hypot.f64 (sqrt.f64 x) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(hypot.f64 (hypot.f64 (sqrt.f64 x) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (fabs.f64 (hypot.f64 (sqrt.f64 x) x)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (hypot.f64 (sqrt.f64 x) x))
(exp.f64 (log1p.f64 x))
(+.f64 (cosh.f64 (log1p.f64 x)) (sinh.f64 (log1p.f64 x)))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval54.0ms (0.9%)

Memory: -7.8MiB live, 46.8MiB allocated
Compiler: Compiled 5 730 to 1 085 computations (81.1% saved)

prune24.0ms (0.4%)

Memory

-21.0MiB live, 24.0MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	297	9	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	297	10	307

Accuracy

99.9%

Counts

307 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.0%	(-.f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))) (sqrt.f64 x))
✓	45.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	43.4%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
▶	45.1%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
	3.5%	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
▶	43.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	45.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
	58.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
▶	57.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶	59.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 273 to 216 computations (20.9% saved)

simplify16.0ms (0.3%)

Memory

10.0MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	182
0	43	182
1	63	182
2	106	182
3	192	182
4	358	182
5	506	182
6	630	182
7	739	182
8	747	182
0	747	182

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize120.0ms (2.1%)

Memory

12.3MiB live, 101.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0.140625	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.22265625	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy	27.28753050906904	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
accuracy	0.0	(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
accuracy	0.0	(sqrt.f64 x)
accuracy	34.592734837938565	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	36.34874061332724	#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 x)
accuracy	34.203311459573776	#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	34.592734837938565	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	0.0	(sqrt.f64 x)
accuracy	34.48805000585239	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy	34.592734837938565	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.0	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
accuracy	0.140625	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	25.909880603621396	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Samples

87.0ms	146×	1	valid
17.0ms	110×	0	valid

Compiler

Compiled 140 to 23 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-mult: 44.0ms (53.7% of total)

ival-sqrt: 12.0ms (14.7% of total)

adjust: 10.0ms (12.2% of total)

ival-add: 9.0ms (11% of total)

ival-div: 4.0ms (4.9% of total)

ival-sub: 2.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory

-37.7MiB live, 14.5MiB allocated

Counts

17 → 49

Calls

Call 1

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

Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ 1 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
1/2
(+ 1/2 (* -1/8 x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 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))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -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 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))
2.0ms	x	@	0	((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))
2.0ms	x	@	inf	((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))

Time

Variable

Point

Expression

7.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

simplify170.0ms (2.9%)

Memory

31.0MiB live, 220.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	665
1	423	583
2	1625	574
3	5856	574
0	8214	530

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 49

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ 1 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
1/2
(+ 1/2 (* -1/8 x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 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))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -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 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.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 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(*.f64 (fma.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/8 binary64)) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (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 -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)

rewrite303.0ms (5.2%)

Memory

-3.2MiB live, 313.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	149
0	43	149
1	177	141
2	1234	139
0	8358	136

Stop Event

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

Counts

17 → 367

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (neg.f64 x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 x))) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 x) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 (/.f64 x (*.f64 x x)))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))
(exp.f64 (/.f64 (neg.f64 (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (neg.f64 (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x)
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (sqrt.f64 (neg.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 x)))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (neg.f64 x))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (neg.f64 (log.f64 x)))
(+.f64 (cosh.f64 (neg.f64 (log.f64 x))) (sinh.f64 (neg.f64 (log.f64 x))))
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(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x))) (neg.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal 1/4 binary64) x)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64))))) (neg.f64 (neg.f64 (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (.f64 #s(literal 1/4 binary64) x))) (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(/.f64 (fma.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)))) (.f64 (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal 1/4 binary64) x))) (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))))
(/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal 1/4 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64))) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)))
(fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/8 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1/8 binary64)))
(-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -1/512 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))))
(+.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (.f64 (neg.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))

eval95.0ms (1.6%)

Memory: 17.3MiB live, 200.5MiB allocated
Compiler: Compiled 17 659 to 2 106 computations (88.1% saved)

prune24.0ms (0.4%)

Memory

1.1MiB live, 57.6MiB allocated

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	534	6	540
Fresh	2	2	4
Picked	1	4	5
Done	0	1	1
Total	537	13	550

Accuracy

100.0%

Counts

550 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.2%	(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) x) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))
✓	45.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	43.4%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	45.1%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
▶	3.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	43.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	45.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	29.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
▶	58.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
	57.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
▶	59.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
▶	59.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	59.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 353 to 266 computations (24.6% saved)

simplify108.0ms (1.9%)

Memory

7.9MiB live, 147.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
cost-diff	0	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
cost-diff	0	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
cost-diff	2	(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
cost-diff	4	(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	278
0	61	278
1	105	275
2	271	271
3	1014	267
4	4039	267
5	6821	267
0	8182	261

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt.f64 x)
x
#s(literal 1/2 binary64)
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
(sqrt.f64 x)
x
(.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 x x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
#s(literal 1/16 binary64)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal -1/8 binary64)
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)

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

localize276.0ms (4.8%)

Memory

-14.6MiB live, 235.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.140625	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.20703125	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
accuracy	21.339440758450074	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
accuracy	26.38389576416052	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
accuracy	0.1328125	(.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
accuracy	0.2890625	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	21.659694887432646	(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x))
accuracy	27.28753050906904	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.2890625	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy	25.909880603621396	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0.0	(sqrt.f64 x)
accuracy	26.395578155628964	#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
accuracy	34.203311459573776	#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
accuracy	34.592734837938565	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
accuracy	0.0	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.22265625	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
accuracy	25.909880603621396	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))

Samples

82.0ms	146×	1	valid
66.0ms	110×	0	valid

Compiler

Compiled 213 to 34 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-div: 24.0ms (29.1% of total)

adjust: 19.0ms (23.1% of total)

ival-mult: 15.0ms (18.2% of total)

ival-add: 9.0ms (10.9% of total)

ival-sqrt: 9.0ms (10.9% of total)

ival-pow: 3.0ms (3.6% of total)

ival-sub: 2.0ms (2.4% of total)

exact: 1.0ms (1.2% of total)

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

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

series12.0ms (0.2%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

20 → 57

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt x))
(sqrt x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt x))
(+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))
(* -1/8 (sqrt (/ 1 x)))
(* 1/16 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(sqrt (/ 1 (pow x 3)))
(* 1/2 (sqrt (pow x 3)))
(sqrt (/ 1 x))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
(* x (+ 1/2 (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

((- (sqrt (+ x 1)) (sqrt x)) (/ (* (sqrt x) 1/2) x) (* (sqrt x) 1/2) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (* 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (/ (+ (* (/ -1/8 (sqrt x)) x) (* x (* (sqrt x) 1/2))) (* x x)) (+ (* (/ -1/8 (sqrt x)) x) (* x (* (sqrt x) 1/2))) (- (sqrt (+ x 1)) (sqrt x)) (/ -1/8 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 (pow x 3))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) x) (+ (* (sqrt (/ 1 (pow x 3))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (sqrt (/ 1 (pow x 3))) (* x (* (sqrt x) 1/2)) (sqrt (/ 1 x)))

3.0ms

((- (sqrt (+ x 1)) (sqrt x)) (/ (* (sqrt x) 1/2) x) (* (sqrt x) 1/2) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (* 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (/ (+ (* (/ -1/8 (sqrt x)) x) (* x (* (sqrt x) 1/2))) (* x x)) (+ (* (/ -1/8 (sqrt x)) x) (* x (* (sqrt x) 1/2))) (- (sqrt (+ x 1)) (sqrt x)) (/ -1/8 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 (pow x 3))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) x) (+ (* (sqrt (/ 1 (pow x 3))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (sqrt (/ 1 (pow x 3))) (* x (* (sqrt x) 1/2)) (sqrt (/ 1 x)))

3.0ms

inf

((- (sqrt (+ x 1)) (sqrt x)) (/ (* (sqrt x) 1/2) x) (* (sqrt x) 1/2) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (* 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (/ (+ (* (/ -1/8 (sqrt x)) x) (* x (* (sqrt x) 1/2))) (* x x)) (+ (* (/ -1/8 (sqrt x)) x) (* x (* (sqrt x) 1/2))) (- (sqrt (+ x 1)) (sqrt x)) (/ -1/8 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 (pow x 3))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) x) (+ (* (sqrt (/ 1 (pow x 3))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (sqrt (/ 1 (pow x 3))) (* x (* (sqrt x) 1/2)) (sqrt (/ 1 x)))

simplify189.0ms (3.3%)

Memory

-19.1MiB live, 210.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	165	908
1	526	794
2	2273	782
3	7447	782
0	8144	726

Stop Event

1×	iter limit
1×	node limit

Counts

57 → 57

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt x))
(sqrt x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt x))
(+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))
(* -1/8 (sqrt (/ 1 x)))
(* 1/16 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(sqrt (/ 1 (pow x 3)))
(* 1/2 (sqrt (pow x 3)))
(sqrt (/ 1 x))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
(* x (+ 1/2 (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt x)
(sqrt.f64 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 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* -1/8 (sqrt x))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* 1/16 (sqrt (/ 1 (pow x 5))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(* 1/2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (*.f64 x x))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (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 -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* -1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (*.f64 x x))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))) x))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

rewrite193.0ms (3.3%)

Memory

24.9MiB live, 259.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	223
0	61	215
1	225	203
2	1533	192
0	8292	183

Stop Event

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

Counts

20 → 741

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

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

eval227.0ms (3.9%)

Memory: 13.2MiB live, 251.9MiB allocated
Compiler: Compiled 31 564 to 3 743 computations (88.1% saved)

prune74.0ms (1.3%)

Memory

-14.4MiB live, 89.7MiB allocated

Pruning

14 alts after pruning (6 fresh and 8 done)

	Pruned	Kept	Total
New	1 034	3	1 037
Fresh	0	3	3
Picked	2	3	5
Done	0	5	5
Total	1 036	14	1 050

Accuracy

100.0%

Counts

1 050 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.2%	(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) x) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))
✓	45.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	43.4%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	45.1%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	3.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	43.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶	45.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	58.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
▶	29.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
▶	57.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
▶	29.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
✓	59.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
✓	59.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	59.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 342 to 252 computations (26.3% saved)

simplify103.0ms (1.8%)

Memory

-26.0MiB live, 66.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
cost-diff	1	(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x))
cost-diff	4	(-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
cost-diff	1	(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
cost-diff	3	(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
cost-diff	0	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
cost-diff	0	(pow.f64 x #s(literal -3/2 binary64))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
cost-diff	0	(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	282
0	58	279
1	108	279
2	286	267
3	1046	259
4	4176	259
5	6612	259
0	8134	257

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)
(fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(pow.f64 x #s(literal -3/2 binary64))
x
#s(literal -3/2 binary64)
#s(literal 1/16 binary64)
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
#s(literal 1/2 binary64)
(sqrt.f64 x)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(sqrt.f64 x)
x
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
(*.f64 x x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x))
(-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
(sqrt.f64 x)
x
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))
#s(literal -1/2 binary64)
(*.f64 x x)

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

localize163.0ms (2.8%)

Memory

1.1MiB live, 146.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x))
accuracy	0.1328125	(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)
accuracy	21.659694887432646	(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x))
accuracy	27.28753050906904	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0625	(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy	21.659694887432646	(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
accuracy	27.28753050906904	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
accuracy	0.0234375	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy	0.22265625	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
accuracy	0.2890625	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	27.28753050906904	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.00390625	(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.00390625	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	35.121160911264056	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
accuracy	0.0234375	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy	0.20703125	(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)
accuracy	0.2890625	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	26.38389576416052	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))

Samples

88.0ms	146×	1	valid
46.0ms	110×	0	valid

Compiler

Compiled 228 to 35 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-sqrt: 27.0ms (27.4% of total)

ival-mult: 21.0ms (21.3% of total)

adjust: 16.0ms (16.2% of total)

ival-div: 12.0ms (12.2% of total)

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

ival-pow: 6.0ms (6.1% of total)

ival-sub: 5.0ms (5.1% of total)

exact: 1.0ms (1% of total)

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

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

series12.0ms (0.2%)

Memory

34.7MiB live, 34.7MiB allocated

Counts

22 → 57

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)
(fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(pow.f64 x #s(literal -3/2 binary64))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x))
(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)

Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/16 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(sqrt (/ 1 (pow x 3)))
(sqrt x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* -1/8 (sqrt x))
(+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))
(* 1/2 (sqrt x))
(* -1/2 (sqrt (pow x 3)))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* 1/2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* (pow x 2) (- (* -1/8 (sqrt (/ 1 (pow x 3)))) (* -1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 x)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* 1/8 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (pow x -3/2) 1/16) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x)))) x) (+ (* (pow x -3/2) 1/16) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x)))) (pow x -3/2) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) (+ (* (* 1/2 (sqrt x)) x) (* -1/8 (sqrt x))) (/ (+ (* (* 1/2 (sqrt x)) x) (* -1/8 (sqrt x))) (* x x)) (- (sqrt (+ x 1)) (sqrt x)) (* 1/2 (sqrt x)) (- (* -1/8 (sqrt x)) (* (* -1/2 (sqrt x)) x)) (/ (- (* -1/8 (sqrt x)) (* (* -1/2 (sqrt x)) x)) (* x x)) (- (sqrt (+ x 1)) (sqrt x)) (* -1/8 (sqrt x)) (/ -1/8 (sqrt x)) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x))) (* (* -1/2 (sqrt x)) x))

3.0ms

inf

((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (pow x -3/2) 1/16) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x)))) x) (+ (* (pow x -3/2) 1/16) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x)))) (pow x -3/2) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) (+ (* (* 1/2 (sqrt x)) x) (* -1/8 (sqrt x))) (/ (+ (* (* 1/2 (sqrt x)) x) (* -1/8 (sqrt x))) (* x x)) (- (sqrt (+ x 1)) (sqrt x)) (* 1/2 (sqrt x)) (- (* -1/8 (sqrt x)) (* (* -1/2 (sqrt x)) x)) (/ (- (* -1/8 (sqrt x)) (* (* -1/2 (sqrt x)) x)) (* x x)) (- (sqrt (+ x 1)) (sqrt x)) (* -1/8 (sqrt x)) (/ -1/8 (sqrt x)) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x))) (* (* -1/2 (sqrt x)) x))

3.0ms

((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (pow x -3/2) 1/16) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x)))) x) (+ (* (pow x -3/2) 1/16) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x)))) (pow x -3/2) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) (+ (* (* 1/2 (sqrt x)) x) (* -1/8 (sqrt x))) (/ (+ (* (* 1/2 (sqrt x)) x) (* -1/8 (sqrt x))) (* x x)) (- (sqrt (+ x 1)) (sqrt x)) (* 1/2 (sqrt x)) (- (* -1/8 (sqrt x)) (* (* -1/2 (sqrt x)) x)) (/ (- (* -1/8 (sqrt x)) (* (* -1/2 (sqrt x)) x)) (* x x)) (- (sqrt (+ x 1)) (sqrt x)) (* -1/8 (sqrt x)) (/ -1/8 (sqrt x)) (+ (* 1/2 (sqrt x)) (/ -1/8 (sqrt x))) (* (* -1/2 (sqrt x)) x))

simplify163.0ms (2.8%)

Memory

4.1MiB live, 148.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	778
1	457	724
2	1733	715
3	6447	713
0	8307	670

Stop Event

1×	iter limit
1×	node limit

Counts

57 → 57

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/16 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(sqrt (/ 1 (pow x 3)))
(sqrt x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* -1/8 (sqrt x))
(+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))
(* 1/2 (sqrt x))
(* -1/2 (sqrt (pow x 3)))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* 1/2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* (pow x 2) (- (* -1/8 (sqrt (/ 1 (pow x 3)))) (* -1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 x)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* 1/8 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/16 (sqrt (/ 1 (pow x 5))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64) (.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(sqrt x)
(sqrt.f64 x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(* -1/8 (sqrt x))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1/2 (sqrt (pow x 3)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 #s(literal -5/128 binary64) (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 -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x)
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64)))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* 1/2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x) x)
(* (pow x 2) (- (* -1/8 (sqrt (/ 1 (pow x 3)))) (* -1/2 (sqrt (/ 1 x)))))
(.f64 (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 x)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64))) x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x)
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))
(.f64 (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x) x)
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
(* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x) x)
(* 1/8 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(* 1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))

rewrite304.0ms (5.3%)

Memory

-35.3MiB live, 339.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	239
0	58	236
1	235	235
2	1708	223
0	8880	217

Stop Event

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

Counts

22 → 1 061

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)
(fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(pow.f64 x #s(literal -3/2 binary64))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x))
(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)

Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (-.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (-.f64 (*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(.f64 (/.f64 (fma.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal -3 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)))))) (fma.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal -3 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64))))))) (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (+.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 9/2 binary64)))) (fma.f64 (fma.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (-.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64)) (.f64 (fma.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) #s(literal 3 binary64)) (.f64 #s(literal 1/4096 binary64) (pow.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) (.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) #s(literal 2 binary64)) (.f64 (*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/16 binary64)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64))) (neg.f64 x) (.f64 x (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))) (*.f64 x x))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64))) x (.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (*.f64 (neg.f64 x) x))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)))) (neg.f64 x) (.f64 x (neg.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (*.f64 (neg.f64 x) x))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -3/2 binary64)))) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (.f64 x #s(literal 1/8 binary64))) (*.f64 x (neg.f64 (pow.f64 x #s(literal 3/2 binary64)))))
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(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) x) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (pow.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)))) (pow.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 2 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal 1/4 binary64) x)) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x))) (neg.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (neg.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) x) (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 x))) (/.f64 x (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 x (neg.f64 (sqrt.f64 x))) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (/.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 x (sqrt.f64 x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 x #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) x) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (/.f64 (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(+.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (/.f64 (pow.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 3/2 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) x) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 (.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(.f64 (.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)
(*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (sqrt.f64 x) (.f64 #s(literal -1/2 binary64) x))
(.f64 x (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))

eval179.0ms (3.1%)

Memory: 20.0MiB live, 197.6MiB allocated
Compiler: Compiled 36 873 to 4 307 computations (88.3% saved)

prune23.0ms (0.4%)

Memory

29.4MiB live, 76.1MiB allocated

Pruning

14 alts after pruning (2 fresh and 12 done)

	Pruned	Kept	Total
New	1 104	2	1 106
Fresh	1	0	1
Picked	1	4	5
Done	0	8	8
Total	1 106	14	1 120

Accuracy

100.0%

Counts

1 120 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	45.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	43.4%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	45.1%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	3.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	43.2%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	45.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
	58.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 x) (*.f64 x x)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
✓	29.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
✓	57.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
✓	29.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
✓	59.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
✓	59.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
	45.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
✓	59.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 575 to 263 computations (54.3% saved)

regimes12.0ms (0.2%)

Memory

-23.1MiB live, 23.5MiB allocated

Counts

21 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(-.f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x)) (.f64 x x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x (.f64 x (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 x) (*.f64 x x)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) x) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))

Outputs

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

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

Calls

2 calls:

6.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.7%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.7%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes9.0ms (0.2%)

Memory

23.1MiB live, 23.1MiB allocated

Counts

17 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.7%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.7%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes11.0ms (0.2%)

Memory

-30.3MiB live, 22.8MiB allocated

Counts

11 → 2

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
4.0ms	x

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes6.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.2%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.2%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

7 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.0%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.0%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes8.0ms (0.1%)

Memory

-37.8MiB live, 7.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
45.1%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
45.1%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
45.1%	1	`x`
45.1%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Accuracy

Total -26.5b remaining (-73%)

Threshold costs -26.5b (-73%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
43.2%	1	`x`
43.2%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch13.0ms (0.2%)

Memory

17.6MiB live, 17.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.002061333070855042	570485.0807126733

Samples

6.0ms

144×

valid

Compiler

Compiled 307 to 235 computations (23.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (58.2% of total)

ival-sub: 1.0ms (29.1% of total)

ival-add: 1.0ms (29.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch11.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.002061333070855042	570485.0807126733

Samples

4.0ms	48×	1	valid
2.0ms	48×	0	valid

Compiler

Compiled 235 to 199 computations (15.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sqrt: 2.0ms (51.3% of total)

adjust: 1.0ms (25.6% of total)

ival-add: 1.0ms (25.6% of total)

ival-sub: 1.0ms (25.6% of total)

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

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

exact: 0.0ms (0% of total)

bsearch17.0ms (0.3%)

Memory

-26.6MiB live, 19.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	570485.0807126733	37236989.86761047

Samples

10.0ms

112×

valid

Compiler

Compiled 157 to 150 computations (4.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 4.0ms (52.5% of total)

adjust: 2.0ms (26.2% of total)

ival-sub: 1.0ms (13.1% of total)

ival-add: 1.0ms (13.1% of total)

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

exact: 0.0ms (0% of total)

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

bsearch12.0ms (0.2%)

Memory

15.7MiB live, 15.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.002061333070855042	570485.0807126733

Samples

5.0ms

128×

valid

Compiler

Compiled 271 to 244 computations (10% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (64.4% of total)

ival-sub: 1.0ms (32.2% of total)

ival-add: 1.0ms (32.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.002061333070855042	570485.0807126733

Compiler

Compiled 253 to 226 computations (10.7% saved)

bsearch4.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.002061333070855042	570485.0807126733

Samples

1.0ms

32×

valid

Compiler

Compiled 262 to 235 computations (10.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

simplify71.0ms (1.2%)

Memory

-14.4MiB live, 77.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	227
1	74	227
2	90	227
3	109	227
4	135	227
5	165	227
6	215	227
7	285	227
8	353	227
9	378	227
10	569	227
11	3350	227

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 4800 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 x) (*.f64 x x)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)))
(if (<=.f64 x #s(literal 125000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(if (<=.f64 x #s(literal 36000000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))

Outputs
(if (<=.f64 x #s(literal 4800 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 x) (*.f64 x x)) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)))
(if (<=.f64 x #s(literal 125000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(if (<=.f64 x #s(literal 36000000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 36000000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))

derivations828.0ms (14.3%)

Memory

29.6MiB live, 586.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	223
0	61	215
1	225	203
2	1533	192
0	8292	183
0	113	451
1	331	393
2	1209	387
3	4903	387
0	8229	353
0	26	149
0	43	149
1	177	141
2	1234	139
0	8358	136
0	35	239
0	58	236
1	235	235
2	1708	223
0	8880	217

Stop Event

1×	fuel
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 227 to 59 computations (74% saved)

preprocess104.0ms (1.8%)

Memory: -12.4MiB live, 131.0MiB allocated
Compiler: Compiled 486 to 144 computations (70.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	26	182
0	43	182
1	63	182
2	106	182
3	192	182
4	358	182
5	506	182
6	630	182
7	739	182
8	747	182
0	747	182

Iter	Nodes	Cost
0	26	182
0	43	182
1	63	182
2	106	182
3	192	182
4	358	182
5	506	182
6	630	182
7	739	182
8	747	182
0	747	182

start0.0ms (0%)

analyze1.0ms (0%)

sample1.1s (19.6%)

explain116.0ms (2%)

preprocess12.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize70.0ms (1.2%)

series4.0ms (0.1%)

simplify317.0ms (5.5%)

rewrite159.0ms (2.7%)

eval54.0ms (0.9%)

prune24.0ms (0.4%)

simplify16.0ms (0.3%)

localize120.0ms (2.1%)

series11.0ms (0.2%)

simplify170.0ms (2.9%)

rewrite303.0ms (5.2%)

eval95.0ms (1.6%)

prune24.0ms (0.4%)

simplify108.0ms (1.9%)

localize276.0ms (4.8%)

series12.0ms (0.2%)

simplify189.0ms (3.3%)

rewrite193.0ms (3.3%)

eval227.0ms (3.9%)

prune74.0ms (1.3%)

simplify103.0ms (1.8%)

localize163.0ms (2.8%)

series12.0ms (0.2%)

simplify163.0ms (2.8%)

rewrite304.0ms (5.3%)

eval179.0ms (3.1%)

prune23.0ms (0.4%)

regimes12.0ms (0.2%)

regimes9.0ms (0.2%)

regimes11.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes8.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

bsearch13.0ms (0.2%)

bsearch11.0ms (0.2%)

bsearch17.0ms (0.3%)

bsearch12.0ms (0.2%)

bsearch1.0ms (0%)

bsearch4.0ms (0.1%)

simplify71.0ms (1.2%)

derivations828.0ms (14.3%)

preprocess104.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	26	182
0	43	182
1	63	182
2	106	182
3	192	182
4	358	182
5	506	182
6	630	182
7	739	182
8	747	182
0	747	182