Metrics for sqrt times

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB 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)

sample840.0ms (30%)

Memory

51.9MiB live, 726.4MiB allocated; 707ms collecting garbage

Samples

610.0ms	8 249×	0	valid
1.0ms	12×	0	invalid
1.0ms	7×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 466.0ms

ival-sqrt: 357.0ms (76.7% of total)

ival-sub: 47.0ms (10.1% of total)

ival-mult: 46.0ms (9.9% of total)

ival-true: 5.0ms (1.1% of total)

exact: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.6% of total)

adjust: 2.0ms (0.4% of total)

Bogosity

explain98.0ms (3.5%)

Memory

8.6MiB live, 116.4MiB allocated; 113ms 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

57.0ms	510×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-sqrt: 40.0ms (85.7% of total)

ival-mult: 3.0ms (6.4% of total)

ival-sub: 3.0ms (6.4% 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)

preprocess263.0ms (9.4%)

Memory

-12.7MiB live, 176.3MiB allocated; 20ms 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

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

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify158.0ms (5.6%)

Memory

2.8MiB live, 93.1MiB allocated; 7ms 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)

localize46.0ms (1.6%)

Memory

-2.2MiB live, 53.2MiB allocated; 9ms 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	0.44921875	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

12.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sqrt: 3.0ms (47% of total)

ival-mult: 1.0ms (15.7% of total)

ival-sub: 1.0ms (15.7% 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)

series6.0ms (0.2%)

Memory

11.2MiB live, 11.2MiB 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))

simplify150.0ms (5.4%)

Memory

-14.1MiB live, 118.0MiB allocated; 15ms 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))

rewrite50.0ms (1.8%)

Memory

-6.2MiB live, 46.5MiB allocated; 12ms 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: 11.1MiB live, 11.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 764 to 198 computations (74.1% saved)

prune2.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Accuracy

100.0%

Counts

48 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.3%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	99.7%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
▶	98.8%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify271.0ms (9.7%)

Memory

-35.6MiB live, 170.2MiB allocated; 43ms collecting garbage

Localize:

Found 7 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	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	51
0	20	51
1	30	51
2	45	45
3	90	45
4	241	45
5	1596	45
6	7682	45
0	8169	45

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 #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 #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)

localize47.0ms (1.7%)

Memory

12.4MiB live, 57.6MiB allocated; 4ms collecting garbage

Localize:

Found 7 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	31.834371600126993	(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	0.22088489789981264	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
accuracy	0.7430489050044757	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Samples

39.0ms	255×	0	valid
0.0ms	1×	5	exit

Compiler

Compiled 45 to 14 computations (68.9% saved)

Precisions

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

ival-sqrt: 22.0ms (69% of total)

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

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

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

ival-add: 1.0ms (3.1% 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)

series3.0ms (0.1%)

Memory

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

Counts

7 → 39

Calls

Call 1

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

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx (+ (* (/ -1/2 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 (* (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 (+ (* (/ -1/2 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 (+ (* (/ -1/2 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
1.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

simplify148.0ms (5.3%)

Memory

6.3MiB live, 96.5MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	697
1	411	656
2	1684	578
0	6037	566

Stop Event

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

Counts

39 → 39

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

rewrite58.0ms (2.1%)

Memory

-24.9MiB live, 31.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
0	20	44
1	61	44
0	363	44

Stop Event

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

Counts

7 → 45

Calls

Call 1

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

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

eval7.0ms (0.3%)

Memory: 11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 301 to 252 computations (80.6% saved)

prune3.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	76	4	80

Accuracy

100.0%

Counts

80 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	99.8%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
▶	99.7%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	98.8%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify171.0ms (6.1%)

Memory

-3.3MiB live, 85.4MiB allocated; 11ms 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 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
cost-diff	0	(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.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	15	49
0	19	49
1	24	49
2	28	49
3	39	49
4	69	49
5	227	49
6	1757	49
7	4817	49
0	8356	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 x (-.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)))
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)
#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 x (-.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)))
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)
#s(literal -1/2 binary64)

localize30.0ms (1.1%)

Memory

11.3MiB live, 53.9MiB allocated; 7ms 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 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
accuracy	0.0	(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
accuracy	0.1168016444237873	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
accuracy	0.0	(-.f64 x #s(literal 1/2 binary64))
accuracy	0.22088489789981264	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))

Samples

23.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 39 to 15 computations (61.5% saved)

Precisions

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

ival-sqrt: 7.0ms (44.4% of total)

ival-sub: 5.0ms (31.7% of total)

ival-div: 2.0ms (12.7% of total)

ival-mult: 2.0ms (12.7% 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)

series3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Counts

6 → 30

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

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

simplify164.0ms (5.9%)

Memory

7.8MiB live, 110.3MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	478
1	374	460
2	1528	414
0	5782	408

Stop Event

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

Counts

30 → 30

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

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

rewrite35.0ms (1.3%)

Memory

-20.8MiB live, 26.5MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	44
0	19	42
1	79	42
0	568	42

Stop Event

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

Counts

6 → 32

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 x (-.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 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(/.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 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (*.f64 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) (-.f64 x (/.f64 #s(literal 1/8 binary64) x))) #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 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) (-.f64 #s(literal 1/4 binary64) (*.f64 (-.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x)))
(/.f64 (neg.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)))) (neg.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x) (*.f64 x x))))
(/.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 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x))
(/.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 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) 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 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x) (.f64 x x))) (/.f64 (pow.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x) (.f64 x x))))
(-.f64 x (-.f64 (/.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 #s(literal -1/2 binary64) (-.f64 x (/.f64 #s(literal 1/8 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 (-.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 (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 #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: 8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 150 to 221 computations (80.8% saved)

prune3.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	51	4	55

Accuracy

100.0%

Counts

55 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.3%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	99.8%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
✓	99.7%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	98.8%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 103 to 59 computations (42.7% saved)

regimes5.0ms (0.2%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Counts

6 → 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 x (-.f64 (/.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))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.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
99.8%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.8%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes28.0ms (1%)

Memory

-39.2MiB live, 6.3MiB allocated; 3ms 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:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms 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
98.8%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.8%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify49.0ms (1.8%)

Memory

30.2MiB live, 30.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	25	35
2	41	35
3	68	35
4	109	35
5	311	35
6	2513	35
7	6021	35

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

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

derivations133.0ms (4.7%)

Memory

-41.1MiB live, 58.5MiB allocated; 10ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 35 to 16 computations (54.3% saved)

preprocess14.0ms (0.5%)

Memory: 22.8MiB live, 22.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 84 to 44 computations (47.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0.1%)

sample840.0ms (30%)

explain98.0ms (3.5%)

preprocess263.0ms (9.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify158.0ms (5.6%)

localize46.0ms (1.6%)

series6.0ms (0.2%)

simplify150.0ms (5.4%)

rewrite50.0ms (1.8%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

simplify271.0ms (9.7%)

localize47.0ms (1.7%)

series3.0ms (0.1%)

simplify148.0ms (5.3%)

rewrite58.0ms (2.1%)

eval7.0ms (0.3%)

prune3.0ms (0.1%)

simplify171.0ms (6.1%)

localize30.0ms (1.1%)

series3.0ms (0.1%)

simplify164.0ms (5.9%)

rewrite35.0ms (1.3%)

eval5.0ms (0.2%)

prune3.0ms (0.1%)

regimes5.0ms (0.2%)

regimes28.0ms (1%)

regimes2.0ms (0.1%)

simplify49.0ms (1.8%)

derivations133.0ms (4.7%)

preprocess14.0ms (0.5%)

end0.0ms (0%)

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