Metrics for sqrt times

start0.0ms (0%)

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

analyze3.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.2s (53.4%)

Memory

60.7MiB live, 838.5MiB allocated; 941ms collecting garbage

Samples

813.0ms	8 255×	0	valid
3.0ms	21×	0	invalid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 338.0ms

ival-sqrt: 159.0ms (47.1% of total)

ival-sub: 85.0ms (25.2% of total)

ival-mult: 79.0ms (23.4% of total)

exact: 8.0ms (2.4% of total)

adjust: 3.0ms (0.9% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain153.0ms (7%)

Memory

0.5MiB live, 92.7MiB allocated; 12ms 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

44.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 12.0ms (49.1% of total)

ival-mult: 6.0ms (24.5% of total)

ival-sub: 5.0ms (20.5% of total)

ival-true: 1.0ms (4.1% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess360.0ms (16.5%)

Memory

-24.8MiB live, 161.3MiB allocated; 28ms 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)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

series11.0ms (0.5%)

Memory

9.7MiB live, 9.7MiB 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
5.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))
3.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))
3.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))

rewrite120.0ms (5.5%)

Memory

-20.9MiB live, 76.3MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

38 → 44

Calls

Call 1

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

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

eval9.0ms (0.4%)

Memory: 8.7MiB live, 8.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 760 to 210 computations (72.4% saved)

prune16.0ms (0.7%)

Memory

14.0MiB live, 14.0MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Accuracy

100.0%

Counts

47 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	99.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1 binary64) #s(literal 1 binary64)) x))

Status

Accuracy

Program

✓

99.3%

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

▶

99.5%

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

Compiler

Compiled 27 to 22 computations (18.5% saved)

series8.0ms (0.4%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Counts

11 → 36

Calls

Call 1

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

2.0ms

-inf

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

2.0ms

inf

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

rewrite65.0ms (3%)

Memory

-2.9MiB live, 42.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	164	806
0	174	701
0	877	693

Stop Event

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

Counts

47 → 78

Calls

Call 1

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

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

eval17.0ms (0.8%)

Memory: 20.2MiB live, 20.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 028 to 365 computations (82% saved)

prune159.0ms (7.3%)

Memory

-6.7MiB live, 131.9MiB allocated; 20ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	81	2	83

Accuracy

100.0%

Counts

83 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	99.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1 binary64) #s(literal 1 binary64)) x))

Status

Accuracy

Program

✓

99.3%

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

✓

99.5%

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

Compiler

Compiled 54 to 42 computations (22.2% saved)

regimes6.0ms (0.3%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Accuracy

Total -0.5b remaining (-164.8%)

Threshold costs -0.5b (-164.8%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.5%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify64.0ms (2.9%)

Memory

-21.8MiB live, 65.4MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	18	20
2	21	20
3	31	20
4	56	20
5	240	20
6	2399	20
7	5814	20

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations6.0ms (0.3%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess21.0ms (1%)

Memory: 30.6MiB live, 30.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 54 to 44 computations (18.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze3.0ms (0.1%)

sample1.2s (53.4%)

explain153.0ms (7%)

preprocess360.0ms (16.5%)

eval0.0ms (0%)

prune1.0ms (0%)

series11.0ms (0.5%)

rewrite120.0ms (5.5%)

eval9.0ms (0.4%)

prune16.0ms (0.7%)

series8.0ms (0.4%)

rewrite65.0ms (3%)

eval17.0ms (0.8%)

prune159.0ms (7.3%)

regimes6.0ms (0.3%)

simplify64.0ms (2.9%)

derivations6.0ms (0.3%)

preprocess21.0ms (1%)

end0.0ms (0%)

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