Metrics for sqrt times

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory

0.4MiB live, 0.4MiB 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)

sample475.0ms (51.3%)

Memory

2.9MiB live, 166.5MiB allocated; 16ms collecting garbage

Samples

303.0ms	8 247×	74	valid
1.0ms	9×	148	valid
0.0ms	11×	74	invalid

Precisions

Click to see histograms. Total time spent on operations: 174.0ms

ival-sqrt: 104.0ms (59.7% of total)

ival-mult!: 33.0ms (18.9% of total)

ival-sub!: 30.0ms (17.2% of total)

adjust: 8.0ms (4.6% of total)

Bogosity

explain50.0ms (5.4%)

Memory

-2.2MiB live, 30.6MiB allocated; 1ms 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

21.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sqrt: 7.0ms (65.2% of total)

ival-sub!: 2.0ms (18.6% of total)

ival-mult!: 2.0ms (18.6% of total)

adjust: 0.0ms (0% of total)

preprocess201.0ms (21.7%)

Memory

4.2MiB live, 34.3MiB allocated; 5ms 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

0.3MiB live, 0.3MiB 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 (0.6%)

Memory

-5.4MiB live, 2.2MiB 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))

rewrite52.0ms (5.6%)

Memory

4.7MiB live, 12.0MiB allocated; 1ms 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))))

eval5.0ms (0.6%)

Memory: -4.0MiB live, 3.6MiB allocated; 1ms collecting garbage
Compiler: Compiled 760 to 210 computations (72.4% saved)

prune1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	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
▶	51.3%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 15 to 12 computations (20% saved)

series2.0ms (0.2%)

Memory

1.1MiB live, 1.1MiB 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)
0.0ms	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)

0.0ms

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)

rewrite47.0ms (5%)

Memory

-11.5MiB live, 5.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	755
0	152	624
0	792	612

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)) (fma.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)) (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 (neg.f64 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 (neg.f64 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 (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)) (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 (neg.f64 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 (neg.f64 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 (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 (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 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 (* (- 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) (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 (* (sqrt (- x 1)) (sqrt x)) (*.f64 (neg.f64 x) (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))))
#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) (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 (* (sqrt (- x 1)) (sqrt x)) (.f64 (neg.f64 x) (fma.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(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 (0.4%)

Memory: 3.1MiB live, 3.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 567 to 153 computations (73% saved)

prune2.0ms (0.2%)

Memory

2.4MiB live, 2.4MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	41	2	43

Accuracy

100.0%

Counts

43 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.3%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 37 to 26 computations (29.7% saved)

regimes4.0ms (0.4%)

Memory

-4.6MiB live, 3.4MiB 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 (0.3%)

Memory

3.1MiB live, 3.1MiB 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 (0.2%)

Memory

2.9MiB live, 2.9MiB 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
98.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch2.0ms (0.2%)

Memory

-7.4MiB live, 0.6MiB allocated; 1ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	685335381795491.5	1534577144595369200.0

Samples

1.0ms

16×

valid

Compiler

Compiled 25 to 24 computations (4% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

adjust: 0.0ms (0% of total)

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

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

simplify48.0ms (5.1%)

Memory

0.8MiB live, 8.4MiB allocated; 0ms 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 1000000000000000 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 1000000000000000 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 (0.5%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 35 to 17 computations (51.4% saved)

preprocess18.0ms (1.9%)

Memory: 2.6MiB live, 10.9MiB allocated; 1ms 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%)

analyze1.0ms (0.1%)

sample475.0ms (51.3%)

explain50.0ms (5.4%)

preprocess201.0ms (21.7%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.6%)

rewrite52.0ms (5.6%)

eval5.0ms (0.6%)

prune1.0ms (0.1%)

series2.0ms (0.2%)

rewrite47.0ms (5%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

regimes4.0ms (0.4%)

regimes3.0ms (0.3%)

regimes2.0ms (0.2%)

bsearch2.0ms (0.2%)

simplify48.0ms (5.1%)

derivations4.0ms (0.5%)

preprocess18.0ms (1.9%)

end0.0ms (0%)

Profiling