Metrics for sqrt times

start0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

analyze58.0ms (3.7%)

Memory

-35.7MiB live, 4.2MiB allocated; 190ms 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)

sample981.0ms (62%)

Memory

74.5MiB live, 803.4MiB allocated; 810ms collecting garbage

Samples

711.0ms	8 247×	0	valid
2.0ms	13×	0	invalid
1.0ms	9×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 258.0ms

ival-sqrt: 129.0ms (50.1% of total)

ival-mult: 58.0ms (22.5% of total)

ival-sub: 58.0ms (22.5% of total)

exact: 7.0ms (2.7% of total)

adjust: 3.0ms (1.2% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain65.0ms (4.1%)

Memory

-1.4MiB live, 90.6MiB 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

26.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sqrt: 7.0ms (49.4% of total)

ival-sub: 3.0ms (21.2% of total)

ival-mult: 3.0ms (21.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess246.0ms (15.5%)

Memory

-11.9MiB live, 213.9MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB 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)

series6.0ms (0.4%)

Memory

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

Counts

6 → 32

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite71.0ms (4.5%)

Memory

20.5MiB live, 75.8MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

38 → 44

Calls

Call 1

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

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

eval7.0ms (0.4%)

Memory: -36.4MiB live, 10.0MiB allocated; 2ms collecting garbage
Compiler: Compiled 782 to 230 computations (70.6% saved)

prune2.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Accuracy

100.0%

Counts

47 → 3

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))
▶	51.5%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	98.2%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 22 to 18 computations (18.2% saved)

series2.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated; 0ms collecting garbage

Counts

6 → 34

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
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))
#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 x #s(hole binary64 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 (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 (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)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1)
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1)
0.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1)

Time

Variable

Point

Expression

1.0ms

-inf

((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1)

1.0ms

inf

((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1)

0.0ms

((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1)

rewrite54.0ms (3.4%)

Memory

-2.3MiB live, 43.5MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	755
0	152	624
0	792	624

Stop Event

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

Counts

40 → 46

Calls

Call 1

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

eval4.0ms (0.3%)

Memory: 5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 574 to 163 computations (71.6% saved)

prune2.0ms (0.2%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	41	3	44

Accuracy

100.0%

Counts

44 → 3

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))
✓	51.5%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	98.2%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 44 to 32 computations (27.3% saved)

regimes3.0ms (0.2%)

Memory

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

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt 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
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 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
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 (0.2%)

Memory

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

Counts

2 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#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
100.0%	2	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
100.0%	2	`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
98.2%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.2%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch4.0ms (0.2%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
3.0ms	416756564943403.0	102252519007531620.0

Samples

1.0ms	16×	1	valid
1.0ms	16×	0	valid

Compiler

Compiled 40 to 38 computations (5% saved)

Precisions

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

ival-sqrt: 1.0ms (82.8% of total)

adjust: 0.0ms (0% of total)

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

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

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

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

exact: 0.0ms (0% of total)

simplify51.0ms (3.2%)

Memory

-28.7MiB live, 17.8MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	21	35
2	28	35
3	43	35
4	78	35
5	316	35
6	2865	35
7	6922	35

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal 10000000000000000 binary64)) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #s(approx (* (sqrt (- x 1)) (sqrt x)) x))

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

Outputs

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

(if (<=.f64 x #s(literal 10000000000000000 binary64)) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #s(approx (* (sqrt (- x 1)) (sqrt x)) x))

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

derivations4.0ms (0.3%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 35 to 17 computations (51.4% saved)

preprocess15.0ms (1%)

Memory: 21.1MiB live, 21.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 84 to 46 computations (45.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze58.0ms (3.7%)

sample981.0ms (62%)

explain65.0ms (4.1%)

preprocess246.0ms (15.5%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.4%)

rewrite71.0ms (4.5%)

eval7.0ms (0.4%)

prune2.0ms (0.1%)

series2.0ms (0.1%)

rewrite54.0ms (3.4%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

regimes3.0ms (0.2%)

regimes3.0ms (0.2%)

regimes2.0ms (0.1%)

bsearch4.0ms (0.2%)

simplify51.0ms (3.2%)

derivations4.0ms (0.3%)

preprocess15.0ms (1%)

end0.0ms (0%)

Profiling