Metrics for sqrt times

start0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

analyze6.0ms (0.4%)

Memory

-40.8MiB live, 3.2MiB allocated; 7ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample887.0ms (59.5%)

Memory

67.1MiB live, 752.1MiB allocated; 756ms collecting garbage

Samples

373.0ms	8 247×	0	valid
1.0ms	9×	1	valid
1.0ms	13×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 224.0ms

ival-sqrt: 110.0ms (49.2% of total)

ival-sub: 54.0ms (24.2% of total)

ival-mult: 49.0ms (21.9% of total)

exact: 6.0ms (2.7% of total)

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

adjust: 2.0ms (0.9% of total)

Bogosity

explain63.0ms (4.3%)

Memory

-2.0MiB live, 90.3MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

30.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-mult: 7.0ms (39.9% of total)

ival-sqrt: 7.0ms (39.9% of total)

ival-sub: 3.0ms (17.1% 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)

preprocess229.0ms (15.4%)

Memory

-2.3MiB live, 177.6MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	20	26
2	25	26
3	35	26
4	69	26
5	250	26
6	1936	26
7	5071	26
0	6	7
0	10	7
1	13	7
2	16	7
3	25	7
4	55	7
5	214	7
6	1678	7
7	4741	7
0	8282	7

Stop Event

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

series6.0ms (0.4%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Counts

6 → 32

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
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (- x 1) #s(hole binary64 -1))
#s(approx (- x 1) #s(hole binary64 (- x 1)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))

rewrite58.0ms (3.9%)

Memory

11.4MiB live, 57.0MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	188	753
0	193	596
0	1106	575

Stop Event

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

Counts

38 → 44

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)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (- x 1) #s(hole binary64 -1))
#s(approx (- x 1) #s(hole binary64 (- x 1)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))

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

eval5.0ms (0.3%)

Memory: 10.2MiB live, 10.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 883 to 209 computations (76.3% saved)

prune25.0ms (1.7%)

Memory

-24.2MiB live, 31.8MiB allocated; 7ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	2	47

Accuracy

100.0%

Counts

47 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	99.7%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) #s(literal -1 binary64) #s(literal 1 binary64)) x))

Status

Accuracy

Program

✓

99.3%

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

▶

99.7%

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

Compiler

Compiled 28 to 22 computations (21.4% saved)

series4.0ms (0.3%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Counts

11 → 36

Calls

Call 1

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

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) #s(hole binary64 (/ -1/8 (pow x 2))))
#s(approx (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) #s(hole binary64 (/ (- (* -1/2 x) 1/8) (pow x 2))))
#s(approx (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) (pow x 2))))
#s(approx (/ (+ (* 1/8 (pow x -1)) 1/2) x) #s(hole binary64 (/ 1/8 (pow x 2))))
#s(approx (/ (+ (* 1/8 (pow x -1)) 1/2) x) #s(hole binary64 (/ (+ 1/8 (* 1/2 x)) (pow x 2))))
#s(approx (+ (* 1/8 (pow x -1)) 1/2) #s(hole binary64 (/ 1/8 x)))
#s(approx (+ (* 1/8 (pow x -1)) 1/2) #s(hole binary64 (/ (+ 1/8 (* 1/2 x)) x)))
#s(approx (pow x -1) #s(hole binary64 (/ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) #s(hole binary64 1))
#s(approx (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) #s(hole binary64 (- 1 (* 1/2 (/ 1 x)))))
#s(approx (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) #s(hole binary64 (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
#s(approx (/ (+ (* 1/8 (pow x -1)) 1/2) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (+ (* 1/8 (pow x -1)) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
#s(approx (+ (* 1/8 (pow x -1)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* 1/8 (pow x -1)) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) (/ (+ (* 1/8 (pow x -1)) 1/2) x) (+ (* 1/8 (pow x -1)) 1/2) 1/8 (pow x -1) x -1 1/2 1)
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) (/ (+ (* 1/8 (pow x -1)) 1/2) x) (+ (* 1/8 (pow x -1)) 1/2) 1/8 (pow x -1) x -1 1/2 1)
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (* (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) x) (+ (* (/ (+ (* 1/8 (pow x -1)) 1/2) x) -1) 1) (/ (+ (* 1/8 (pow x -1)) 1/2) x) (+ (* 1/8 (pow x -1)) 1/2) 1/8 (pow x -1) x -1 1/2 1)

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

rewrite40.0ms (2.7%)

Memory

-8.8MiB live, 37.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	166	833
0	175	701
0	890	693

Stop Event

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

Counts

47 → 79

Calls

Call 1

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

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

eval10.0ms (0.6%)

Memory: 19.1MiB live, 19.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 292 to 377 computations (83.6% saved)

prune65.0ms (4.3%)

Memory

-38.7MiB live, 53.4MiB allocated; 7ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	83	2	85

Accuracy

100.0%

Counts

85 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	99.7%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) #s(literal -1 binary64) #s(literal 1 binary64)) x))

Status

Accuracy

Program

✓

99.3%

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

✓

99.7%

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

Compiler

Compiled 56 to 42 computations (25% saved)

regimes3.0ms (0.2%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Accuracy

Total -0.5b remaining (-222.1%)

Threshold costs -0.5b (-222.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs

#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) #s(literal -1 binary64) #s(literal 1 binary64)) 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
99.7%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.7%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify48.0ms (3.2%)

Memory

40.9MiB live, 40.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
2	21	21
3	31	21
4	56	21
5	240	21
6	2399	21
7	5814	21

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

Outputs

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

derivations28.0ms (1.9%)

Memory

-40.8MiB live, 7.0MiB allocated; 8ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 21 to 16 computations (23.8% saved)

preprocess12.0ms (0.8%)

Memory: 22.7MiB live, 22.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 56 to 44 computations (21.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze6.0ms (0.4%)

sample887.0ms (59.5%)

explain63.0ms (4.3%)

preprocess229.0ms (15.4%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.4%)

rewrite58.0ms (3.9%)

eval5.0ms (0.3%)

prune25.0ms (1.7%)

series4.0ms (0.3%)

rewrite40.0ms (2.7%)

eval10.0ms (0.6%)

prune65.0ms (4.3%)

regimes3.0ms (0.2%)

simplify48.0ms (3.2%)

derivations28.0ms (1.9%)

preprocess12.0ms (0.8%)

end0.0ms (0%)

Profiling