Metrics for sqrt times

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms 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)

sample991.0ms (34.2%)

Memory

55.6MiB live, 835.4MiB allocated; 812ms collecting garbage

Samples

721.0ms	8 250×	0	valid
0.0ms	6×	1	valid
0.0ms	9×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 550.0ms

ival-mult: 334.0ms (60.7% of total)

ival-sqrt: 137.0ms (24.9% of total)

ival-sub: 63.0ms (11.4% of total)

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

exact: 5.0ms (0.9% of total)

adjust: 3.0ms (0.5% of total)

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

Bogosity

explain76.0ms (2.6%)

Memory

-12.8MiB live, 79.8MiB allocated; 9ms 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

39.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sqrt: 6.0ms (45.6% of total)

ival-sub: 3.0ms (22.8% of total)

ival-mult: 3.0ms (22.8% 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)

preprocess233.0ms (8.1%)

Memory

26.4MiB live, 168.6MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	15	19
2	20	19
3	29	19
4	59	19
5	218	19
6	1680	19
7	4738	19
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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

simplify281.0ms (9.7%)

Memory

-31.2MiB live, 155.4MiB allocated; 24ms collecting garbage

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
2	16	18
3	25	18
4	55	18
5	214	18
6	1678	18
7	4741	18
0	8282	18

Stop Event

1×	iter limit
1×	node limit
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 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize17.0ms (0.6%)

Memory

22.3MiB live, 22.3MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.41796875	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

12.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sqrt: 3.0ms (45.6% of total)

ival-sub: 2.0ms (30.4% of total)

ival-mult: 2.0ms (30.4% 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)

series6.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Counts

4 → 31

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
#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 (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
2.0ms	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))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

simplify133.0ms (4.6%)

Memory

1.3MiB live, 145.0MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	183	644
1	529	575
2	2419	564
0	8365	534

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 31

Calls

Call 1

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

rewrite55.0ms (1.9%)

Memory

-18.7MiB live, 26.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	15
1	32	15
0	181	15

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 22

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

eval5.0ms (0.2%)

Memory: 5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 764 to 198 computations (74.1% saved)

prune2.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	5	48

Accuracy

100.0%

Counts

48 → 5

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))
▶	52.7%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	99.1%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
▶	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (/.f64 x x) x))
▶	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 54 to 41 computations (24.1% saved)

simplify126.0ms (4.4%)

Memory

-3.9MiB live, 108.3MiB allocated; 38ms collecting garbage

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	93
0	32	87
1	48	79
2	77	79
3	184	79
4	767	79
5	7107	79
0	8157	79

Stop Event

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

Calls

Call 1

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

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

localize72.0ms (2.5%)

Memory

-31.6MiB live, 59.6MiB allocated; 10ms collecting garbage

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x #s(literal 1 binary64))
accuracy	0.0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	30.272629645656643	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	0.0	(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
accuracy	0.0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	0.5740955547020364	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
accuracy	0.0	(/.f64 x x)
accuracy	0.0	(/.f64 #s(literal -1/8 binary64) x)
accuracy	0.00390625	(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
accuracy	0.4451848804968737	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (/.f64 x x) x))
accuracy	1.0915688493958753	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Samples

59.0ms

256×

valid

Compiler

Compiled 77 to 21 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sub: 31.0ms (62.9% of total)

ival-mult: 6.0ms (12.2% of total)

ival-div: 5.0ms (10.1% of total)

ival-sqrt: 5.0ms (10.1% of total)

ival-add: 2.0ms (4.1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Counts

12 → 53

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (/ x x) (+ (* (- (/ -1/8 x) 1/2) (/ x x)) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) 1/2) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ -1/8 x))
1.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (/ x x) (+ (* (- (/ -1/8 x) 1/2) (/ x x)) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) 1/2) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ -1/8 x))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (/ x x) (+ (* (- (/ -1/8 x) 1/2) (/ x x)) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) 1/2) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ -1/8 x))

Time

Variable

Point

Expression

2.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

simplify181.0ms (6.3%)

Memory

19.5MiB live, 120.6MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	881
1	467	751
2	1897	726
0	7273	714

Stop Event

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

Counts

53 → 53

Calls

Call 1

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

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

rewrite61.0ms (2.1%)

Memory

-5.7MiB live, 37.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	85
0	32	76
1	105	68
0	792	68

Stop Event

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

Counts

12 → 89

Calls

Call 1

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

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

eval29.0ms (1%)

Memory: -15.7MiB live, 27.2MiB allocated; 7ms collecting garbage
Compiler: Compiled 2 622 to 464 computations (82.3% saved)

prune4.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	0	0
Picked	2	2	4
Done	0	1	1
Total	131	5	136

Accuracy

100.0%

Counts

136 → 5

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))
✓	52.7%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/2 binary64)))
▶	99.1%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 48 to 39 computations (18.8% saved)

simplify161.0ms (5.6%)

Memory

-10.2MiB live, 95.8MiB allocated; 9ms collecting garbage

Localize:

Found 6 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
0	18	49
1	23	49
2	27	49
3	37	49
4	66	49
5	223	49
6	1725	49
7	4760	49
0	8301	49

Stop Event

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

Calls

Call 1

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

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

localize26.0ms (0.9%)

Memory

27.5MiB live, 27.5MiB allocated; 0ms collecting garbage

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/8 binary64) x)
accuracy	0.0	(-.f64 x (/.f64 #s(literal 1/8 binary64) x))
accuracy	0.00390625	(-.f64 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/2 binary64))
accuracy	0.4451848804968737	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/2 binary64)))
accuracy	0.0	(-.f64 x #s(literal 1/2 binary64))
accuracy	0.5740955547020364	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 39 to 14 computations (64.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 5.0ms (42.6% of total)

ival-sqrt: 3.0ms (25.6% of total)

ival-div: 2.0ms (17% of total)

ival-mult: 1.0ms (8.5% 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)

series3.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Counts

6 → 31

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

simplify146.0ms (5.1%)

Memory

-9.9MiB live, 125.2MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	495
1	388	477
2	1571	433
0	5839	425

Stop Event

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

Counts

31 → 31

Calls

Call 1

Inputs
#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 (- x 1/2) #s(hole binary64 -1/2))
#s(approx (- x 1/2) #s(hole binary64 (- x 1/2)))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (/ -1/8 x)))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (- x (/ 1/8 x)) #s(hole binary64 (/ -1/8 x)))
#s(approx (- x (/ 1/8 x)) #s(hole binary64 (/ (- (pow x 2) 1/8) x)))
#s(approx (/ 1/8 x) #s(hole binary64 (/ 1/8 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 (- x 1/2) #s(hole binary64 x))
#s(approx (- x 1/2) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 x))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (- x (/ 1/8 x)) #s(hole binary64 x))
#s(approx (- x (/ 1/8 x)) #s(hole binary64 (* x (- 1 (* 1/8 (/ 1 (pow x 2)))))))
#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 (- x 1/2) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (- (- x (/ 1/8 x)) 1/2) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
#s(approx (- x (/ 1/8 x)) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ 1 (pow x 2))) 1)))))

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

rewrite47.0ms (1.6%)

Memory

-10.4MiB live, 46.5MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
0	18	42
1	76	42
0	550	42

Stop Event

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

Counts

6 → 31

Calls

Call 1

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

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

eval5.0ms (0.2%)

Memory: 13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 153 to 218 computations (81.1% saved)

prune7.0ms (0.3%)

Memory

-33.1MiB live, 11.4MiB allocated; 4ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	50	5	55

Accuracy

100.0%

Counts

55 → 5

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))
✓	52.7%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/2 binary64)))
✓	99.1%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 128 to 71 computations (44.5% saved)

regimes5.0ms (0.2%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

-36.4MiB live, 8.9MiB allocated; 3ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify53.0ms (1.8%)

Memory

44.0MiB live, 44.0MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	29	42
2	46	42
3	70	42
4	115	42
5	380	42
6	3239	42
7	7217	42

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations132.0ms (4.6%)

Memory

-50.4MiB live, 52.7MiB allocated; 14ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 42 to 20 computations (52.4% saved)

preprocess17.0ms (0.6%)

Memory: 30.2MiB live, 30.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 98 to 52 computations (46.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze3.0ms (0.1%)

sample991.0ms (34.2%)

explain76.0ms (2.6%)

preprocess233.0ms (8.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify281.0ms (9.7%)

localize17.0ms (0.6%)

series6.0ms (0.2%)

simplify133.0ms (4.6%)

rewrite55.0ms (1.9%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

simplify126.0ms (4.4%)

localize72.0ms (2.5%)

series5.0ms (0.2%)

simplify181.0ms (6.3%)

rewrite61.0ms (2.1%)

eval29.0ms (1%)

prune4.0ms (0.1%)

simplify161.0ms (5.6%)

localize26.0ms (0.9%)

series3.0ms (0.1%)

simplify146.0ms (5.1%)

rewrite47.0ms (1.6%)

eval5.0ms (0.2%)

prune7.0ms (0.3%)

regimes5.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

simplify53.0ms (1.8%)

derivations132.0ms (4.6%)

preprocess17.0ms (0.6%)

end0.0ms (0%)

Profiling