Metrics for sqrt times

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB 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)

sample725.0ms (71.2%)

Memory

22.8MiB live, 920.1MiB allocated; 264ms collecting garbage

Samples

438.0ms	8 247×	0	valid
9.0ms	18×	0	invalid
1.0ms	9×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 208.0ms

ival-sqrt: 123.0ms (59.2% of total)

ival-sub!: 49.0ms (23.6% of total)

ival-mult!: 34.0ms (16.4% of total)

adjust: 2.0ms (1% of total)

Bogosity

preprocess74.0ms (7.2%)

Memory

-29.1MiB live, 15.8MiB allocated; 6ms 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

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series6.0ms (0.5%)

Memory

8.6MiB live, 8.6MiB 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
2.0ms	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))

rewrite94.0ms (9.2%)

Memory

14.5MiB live, 74.8MiB allocated; 56ms 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 (.f64 (.f64 x x) x) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (.f64 x x) x))) #s(literal 1/2 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)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #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))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (.f64 (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 1/16 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 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 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 (-.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) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 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 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (*.f64 x x) x))) (/.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) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (- x 1)) (.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 x x) x))) (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) (/.f64 #s(literal 1 binary64) x)) 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 (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 x x) x))) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 x x) x))) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 x x) x))) #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 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (sqrt x) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))

eval4.0ms (0.4%)

Memory: 9.0MiB live, 9.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 399 to 210 computations (47.4% saved)

prune7.0ms (0.7%)

Memory

-40.3MiB live, 5.5MiB allocated; 8ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Accuracy

100.0%

Counts

39 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	96.2%	(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
▶	55.0%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	96.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 25 to 25 computations (0% saved)

series3.0ms (0.3%)

Memory

8.6MiB live, 8.6MiB allocated; 0ms collecting garbage

Counts

10 → 48

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)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
(sqrt.f64 #s(approx (- x 1) x))
#s(approx (- x 1) x)
(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 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)) #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 (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) 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)) #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 (* (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)))))
#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 (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))

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 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite50.0ms (4.9%)

Memory

23.5MiB live, 69.1MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	221	1122
0	229	919
0	1219	892

Stop Event

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

Counts

58 → 68

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)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
(sqrt.f64 #s(approx (- x 1) x))
#s(approx (- x 1) x)
(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 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)) #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 (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) 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)) #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 (* (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)))))
#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 (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))

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

eval5.0ms (0.5%)

Memory: 10.3MiB live, 10.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 481 to 233 computations (51.6% saved)

prune3.0ms (0.3%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	49	4	53

Accuracy

100.0%

Counts

53 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	96.2%	(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
✓	55.0%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	96.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 44 to 42 computations (4.5% saved)

regimes8.0ms (0.7%)

Memory

-34.8MiB live, 9.7MiB allocated; 5ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

6.0ms	x
2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.2%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes3.0ms (0.3%)

Memory

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

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 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 7 to 7 computations (0% saved)

regimes2.0ms (0.2%)

Memory

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

Accuracy

Total -0.5b remaining (-24.8%)

Threshold costs -0.5b (-24.8%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 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
96.9%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
96.9%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

bsearch2.0ms (0.2%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	7704739781817685.0	136459942837512860.0

Samples

1.0ms

16×

valid

Compiler

Compiled 22 to 24 computations (-9.1% 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)

derivations5.0ms (0.5%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 18 to 17 computations (5.6% saved)

preprocess28.0ms (2.8%)

Memory: -3.6MiB live, 50.1MiB allocated; 11ms collecting garbage
Compiler: Compiled 24 to 23 computations (4.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0.1%)

sample725.0ms (71.2%)

preprocess74.0ms (7.2%)

series6.0ms (0.5%)

rewrite94.0ms (9.2%)

eval4.0ms (0.4%)

prune7.0ms (0.7%)

series3.0ms (0.3%)

rewrite50.0ms (4.9%)

eval5.0ms (0.5%)

prune3.0ms (0.3%)

regimes8.0ms (0.7%)

regimes3.0ms (0.3%)

regimes2.0ms (0.2%)

bsearch2.0ms (0.2%)

derivations5.0ms (0.5%)

preprocess28.0ms (2.8%)

end0.0ms (0%)

Profiling