Metrics for sqrt times

start0.0ms (0%)

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

analyze8.0ms (0.6%)

Memory

-42.2MiB live, 3.5MiB allocated; 9ms 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)

sample727.0ms (55.2%)

Memory

60.3MiB live, 1 291.9MiB allocated; 225ms collecting garbage

Samples

510.0ms	8 244×	0	valid
1.0ms	12×	1	valid
1.0ms	15×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 264.0ms

ival-sqrt: 195.0ms (73.9% of total)

ival-mult!: 40.0ms (15.2% of total)

ival-sub!: 27.0ms (10.2% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

preprocess104.0ms (7.9%)

Memory

-38.1MiB live, 53.6MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	30	23
2	48	23
3	76	23
4	255	23
5	2233	23

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 14 to 12 computations (14.3% saved)

series4.0ms (0.3%)

Memory

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

Counts

6 → 26

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 -1) (sqrt x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (/ (* x (sqrt x)) (sqrt -1))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* -1/8 (/ (* x (sqrt x)) (pow (sqrt -1) 3))) (* 1/2 (/ (sqrt x) (sqrt -1))))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* 1/2 (/ (sqrt x) (sqrt -1))) (* x (+ (* -1/8 (/ (sqrt x) (pow (sqrt -1) 3))) (* 1/16 (/ (* x (sqrt x)) (pow (sqrt -1) 5))))))) (* (sqrt -1) (sqrt x)))))
#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 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (pow (sqrt (/ 1 x)) 2) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))) (pow x 2))) (pow (sqrt (/ 1 x)) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 2))) (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 4))))) (pow x 4))) (pow (sqrt (/ 1 x)) 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))))))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 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)) (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))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))

rewrite46.0ms (3.5%)

Memory

29.1MiB live, 74.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	673
0	161	589
0	823	573

Stop Event

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

Counts

32 → 38

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 -1) (sqrt x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (/ (* x (sqrt x)) (sqrt -1))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* -1/8 (/ (* x (sqrt x)) (pow (sqrt -1) 3))) (* 1/2 (/ (sqrt x) (sqrt -1))))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* 1/2 (/ (sqrt x) (sqrt -1))) (* x (+ (* -1/8 (/ (sqrt x) (pow (sqrt -1) 3))) (* 1/16 (/ (* x (sqrt x)) (pow (sqrt -1) 5))))))) (* (sqrt -1) (sqrt x)))))
#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 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (pow (sqrt (/ 1 x)) 2) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))) (pow x 2))) (pow (sqrt (/ 1 x)) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 2))) (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 4))))) (pow x 4))) (pow (sqrt (/ 1 x)) 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))))))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))

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

eval3.0ms (0.2%)

Memory: 9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 750 to 182 computations (75.7% saved)

prune12.0ms (0.9%)

Memory

-36.3MiB live, 17.9MiB allocated; 6ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Accuracy

99.8%

Counts

33 → 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 #s(approx (sqrt (- x 1)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)) (sqrt.f64 x))
▶	53.4%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	0.0%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (*.f64 #s(literal -1 binary64) x)))

Compiler

Compiled 39 to 31 computations (20.5% saved)

series7.0ms (0.5%)

Memory

17.2MiB live, 17.2MiB allocated; 0ms collecting garbage

Counts

14 → 48

Calls

Call 1

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

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt -1) (sqrt x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (/ (* x (sqrt x)) (sqrt -1))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* -1/8 (/ (* x (sqrt x)) (pow (sqrt -1) 3))) (* 1/2 (/ (sqrt x) (sqrt -1))))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* 1/2 (/ (sqrt x) (sqrt -1))) (* x (+ (* -1/8 (/ (sqrt x) (pow (sqrt -1) 3))) (* 1/16 (/ (* x (sqrt x)) (pow (sqrt -1) 5))))))) (* (sqrt -1) (sqrt x)))))
#s(approx (sqrt (* -1 x)) #s(hole binary64 (sqrt (* -1 x))))
#s(approx (* -1 x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* 1/2 (/ (pow x 2) (sqrt (* -1 x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (* -1 x)) 3))) (* 1/2 (/ 1 (sqrt (* -1 x)))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (* -1 x)) 5))) (* 1/8 (/ 1 (pow (sqrt (* -1 x)) 3))))) (* 1/2 (/ 1 (sqrt (* -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 (* (/ 1 (sqrt x)) x) #s(hole binary64 (/ x (sqrt x))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (pow (sqrt (/ 1 x)) 2) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))) (pow x 2))) (pow (sqrt (/ 1 x)) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 2))) (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 4))))) (pow x 4))) (pow (sqrt (/ 1 x)) 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (* -1 x)) #s(hole binary64 (* x (sqrt (/ -1 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 (- 1 (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))))))
#s(approx (* (/ 1 (sqrt x)) x) #s(hole binary64 (/ 1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (* -1 x)) #s(hole binary64 (* -1 (* x (sqrt (/ -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 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (* (/ 1 (sqrt x)) x) #s(hole binary64 (/ -1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ -1 (* x (sqrt (/ 1 x))))))

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

2.0ms

-inf

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

2.0ms

inf

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

rewrite53.0ms (4.1%)

Memory

-21.8MiB live, 71.4MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	248	1126
0	262	989
0	1271	968

Stop Event

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

Counts

62 → 81

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (*.f64 #s(literal -1 binary64) x)))
(sqrt.f64 (*.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 #s(approx (sqrt (- x 1)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)) (sqrt.f64 x))
#s(approx (sqrt (- x 1)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt -1) (sqrt x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (/ (* x (sqrt x)) (sqrt -1))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* -1/8 (/ (* x (sqrt x)) (pow (sqrt -1) 3))) (* 1/2 (/ (sqrt x) (sqrt -1))))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* 1/2 (/ (sqrt x) (sqrt -1))) (* x (+ (* -1/8 (/ (sqrt x) (pow (sqrt -1) 3))) (* 1/16 (/ (* x (sqrt x)) (pow (sqrt -1) 5))))))) (* (sqrt -1) (sqrt x)))))
#s(approx (sqrt (* -1 x)) #s(hole binary64 (sqrt (* -1 x))))
#s(approx (* -1 x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* 1/2 (/ (pow x 2) (sqrt (* -1 x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (* -1 x)) 3))) (* 1/2 (/ 1 (sqrt (* -1 x)))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (* -1 x)) 5))) (* 1/8 (/ 1 (pow (sqrt (* -1 x)) 3))))) (* 1/2 (/ 1 (sqrt (* -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 (* (/ 1 (sqrt x)) x) #s(hole binary64 (/ x (sqrt x))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (pow (sqrt (/ 1 x)) 2) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))) (pow x 2))) (pow (sqrt (/ 1 x)) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 2))) (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 4))))) (pow x 4))) (pow (sqrt (/ 1 x)) 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (* -1 x)) #s(hole binary64 (* x (sqrt (/ -1 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 (- 1 (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))))))
#s(approx (* (/ 1 (sqrt x)) x) #s(hole binary64 (/ 1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (* -1 x)) #s(hole binary64 (* -1 (* x (sqrt (/ -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 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/2 (/ 1 (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 3))))) (pow x 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 5)))) (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 3)))) (pow x 4)))) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (* (/ 1 (sqrt x)) x) #s(hole binary64 (/ -1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ -1 (* x (sqrt (/ 1 x))))))

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

eval6.0ms (0.4%)

Memory: 15.7MiB live, 15.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 395 to 330 computations (76.3% saved)

prune3.0ms (0.2%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	2	1	3
Done	1	0	1
Total	68	4	72

Accuracy

100.0%

Counts

72 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.4%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	50.1%	(sqrt.f64 #s(approx (* (- x 1) x) (*.f64 x x)))
▶	0.0%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (neg.f64 x)))
▶	98.3%	#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))

Compiler

Compiled 41 to 32 computations (22% saved)

series6.0ms (0.4%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Counts

13 → 33

Calls

Call 1

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

Outputs
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (sqrt (* -1 x))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* 1/2 (/ (pow x 2) (sqrt (* -1 x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (* -1 x)) 3))) (* 1/2 (/ 1 (sqrt (* -1 x)))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (* -1 x)) 5))) (* 1/8 (/ 1 (pow (sqrt (* -1 x)) 3))))) (* 1/2 (/ 1 (sqrt (* -1 x)))))))))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(hole binary64 -1/2))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(hole binary64 (- x 1/2)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ -1/2 x)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ (- x 1/2) x)))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt -1) (sqrt x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (/ (* x (sqrt x)) (sqrt -1))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* -1/8 (/ (* x (sqrt x)) (pow (sqrt -1) 3))) (* 1/2 (/ (sqrt x) (sqrt -1))))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* 1/2 (/ (sqrt x) (sqrt -1))) (* x (+ (* -1/8 (/ (sqrt x) (pow (sqrt -1) 3))) (* 1/16 (/ (* x (sqrt x)) (pow (sqrt -1) 5))))))) (* (sqrt -1) (sqrt x)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (- x 1) x) #s(hole binary64 (* x (- x 1))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#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 (- 1 (/ 1/2 x)) #s(hole binary64 1))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (- 1 (* 1/2 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (pow (sqrt (/ 1 x)) 2) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))) (pow x 2))) (pow (sqrt (/ 1 x)) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 2))) (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 4))))) (pow x 4))) (pow (sqrt (/ 1 x)) 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (neg x)) #s(hole binary64 (* x (sqrt (/ -1 x)))))
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 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 (* (- 1 (/ 1/2 x)) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (sqrt (neg x)) #s(hole binary64 (* -1 (* x (sqrt (/ -1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	((sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) (- 1 (/ 1/2 x)) 1 (/ 1/2 x) 1/2 x (* (sqrt (- x 1)) (sqrt x)) (sqrt (neg x)) (neg x) (sqrt (* (- x 1) x)) (* (- x 1) x) (* x x))
1.0ms	x	@	-inf	((sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) (- 1 (/ 1/2 x)) 1 (/ 1/2 x) 1/2 x (* (sqrt (- x 1)) (sqrt x)) (sqrt (neg x)) (neg x) (sqrt (* (- x 1) x)) (* (- x 1) x) (* x x))
1.0ms	x	@	inf	((sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) (- 1 (/ 1/2 x)) 1 (/ 1/2 x) 1/2 x (* (sqrt (- x 1)) (sqrt x)) (sqrt (neg x)) (neg x) (sqrt (* (- x 1) x)) (* (- x 1) x) (* x x))

Time

Variable

Point

Expression

3.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

rewrite109.0ms (8.2%)

Memory

-89.7MiB live, 98.4MiB allocated; 84ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	743
0	191	652
0	933	640

Stop Event

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

Counts

46 → 64

Calls

Call 1

Inputs
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (neg.f64 x)))
(sqrt.f64 (neg.f64 x))
(neg.f64 x)
(sqrt.f64 #s(approx (* (- x 1) x) (*.f64 x x)))
#s(approx (* (- x 1) x) (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (sqrt (* -1 x))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* 1/2 (/ (pow x 2) (sqrt (* -1 x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (* -1 x)) 3))) (* 1/2 (/ 1 (sqrt (* -1 x)))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (sqrt (* -1 x)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (* -1 x)) 5))) (* 1/8 (/ 1 (pow (sqrt (* -1 x)) 3))))) (* 1/2 (/ 1 (sqrt (* -1 x)))))))))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(hole binary64 -1/2))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(hole binary64 (- x 1/2)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ -1/2 x)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ (- x 1/2) x)))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt -1) (sqrt x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (/ (* x (sqrt x)) (sqrt -1))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* -1/8 (/ (* x (sqrt x)) (pow (sqrt -1) 3))) (* 1/2 (/ (sqrt x) (sqrt -1))))) (* (sqrt -1) (sqrt x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* x (+ (* 1/2 (/ (sqrt x) (sqrt -1))) (* x (+ (* -1/8 (/ (sqrt x) (pow (sqrt -1) 3))) (* 1/16 (/ (* x (sqrt x)) (pow (sqrt -1) 5))))))) (* (sqrt -1) (sqrt x)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (- x 1) x) #s(hole binary64 (* x (- x 1))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#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 (- 1 (/ 1/2 x)) #s(hole binary64 1))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (- 1 (* 1/2 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (pow (sqrt (/ 1 x)) 2) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 2))))) (pow x 2))) (pow (sqrt (/ 1 x)) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt (/ 1 x)) 2))) (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt (/ 1 x)) 4))))) (pow x 4))) (pow (sqrt (/ 1 x)) 2)) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (neg x)) #s(hole binary64 (* x (sqrt (/ -1 x)))))
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 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 (* (- 1 (/ 1/2 x)) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (sqrt (neg x)) #s(hole binary64 (* -1 (* x (sqrt (/ -1 x))))))

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

eval5.0ms (0.4%)

Memory: 16.4MiB live, 16.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 029 to 254 computations (75.3% saved)

prune2.0ms (0.2%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	0	0
Picked	3	0	3
Done	0	1	1
Total	52	3	55

Accuracy

100.0%

Counts

55 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

53.4%

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

▶

98.3%

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

▶

1.1%

#s(approx (sqrt (* (- x 1) x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))

Compiler

Compiled 40 to 30 computations (25% saved)

series2.0ms (0.1%)

Memory

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

Counts

8 → 15

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) -1/2 (sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) (- x 1/2) x 1/2)
0.0ms	x	@	0	((sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) -1/2 (sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) (- x 1/2) x 1/2)
0.0ms	x	@	inf	((sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) -1/2 (sqrt (* (- x 1) x)) (* (- 1 (/ 1/2 x)) x) (- x 1/2) x 1/2)

Time

Variable

Point

Expression

1.0ms

-inf

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

0.0ms

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

0.0ms

inf

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

rewrite123.0ms (9.3%)

Memory

-14.5MiB live, 172.9MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	374
0	91	330
1	491	326
0	4460	316

Stop Event

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

Counts

23 → 30

Calls

Call 1

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

Outputs
#s(approx (sqrt (* (- x 1) x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (sqrt (* (- x 1) x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1/4 binary64))) (neg.f64 (-.f64 x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x #s(literal -1/8 binary64))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 x x #s(literal -1/4 binary64)) (-.f64 x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1/8 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 x #s(literal -1/2 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(-.f64 x #s(literal 1/2 binary64))
(+.f64 x #s(literal -1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (sqrt (* (- x 1) x)) (sqrt.f64 (neg.f64 x)))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 x))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 x x) (sqrt.f64 (neg.f64 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x)))) x) x (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x (/.f64 x (pow.f64 (neg.f64 x) #s(literal 5/2 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (neg.f64 x)) x))) x) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x)))) x) x (sqrt.f64 (neg.f64 x))))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64))
#s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64)))
#s(approx x x)
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) x) x x))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 x x))) x x))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 x))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 x)))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) x) x x)))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 x x))) x x)))
#s(approx (* (- 1 (/ 1/2 x)) x) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (neg.f64 x)))

eval2.0ms (0.2%)

Memory: 6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 454 to 109 computations (76% saved)

prune1.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	20	3	23

Accuracy

100.0%

Counts

23 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

53.4%

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

✓

98.3%

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

✓

1.1%

#s(approx (sqrt (* (- x 1) x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))

Compiler

Compiled 40 to 30 computations (25% saved)

regimes23.0ms (1.8%)

Memory

22.6MiB live, 66.9MiB allocated; 3ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

5 → 1

7 → 2

9 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (* (- x 1) x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))

Outputs
#s(approx (sqrt (* (- x 1) x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))

Call 2

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

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

Call 3

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

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

Call 4

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

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

Calls

8 calls:

5.0ms	x
3.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms	x
2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
1.1%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
1.1%	1	`x`
98.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.3%	1	`x`
100.0%	2	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
100.0%	2	`x`
99.2%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.2%	1	`x`

Compiler

Compiled 140 to 72 computations (48.6% saved)

bsearch2.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	26720376.844871607	297027961.26008135

Samples

1.0ms

16×

valid

Compiler

Compiled 34 to 30 computations (11.8% 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)

derivations22.0ms (1.7%)

Memory

-8.8MiB live, 28.0MiB allocated; 13ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 69 to 26 computations (62.3% saved)

preprocess46.0ms (3.5%)

Memory: -2.4MiB live, 101.4MiB allocated; 25ms collecting garbage
Compiler: Compiled 76 to 32 computations (57.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze8.0ms (0.6%)

sample727.0ms (55.2%)

preprocess104.0ms (7.9%)

series4.0ms (0.3%)

rewrite46.0ms (3.5%)

eval3.0ms (0.2%)

prune12.0ms (0.9%)

series7.0ms (0.5%)

rewrite53.0ms (4.1%)

eval6.0ms (0.4%)

prune3.0ms (0.2%)

series6.0ms (0.4%)

rewrite109.0ms (8.2%)

eval5.0ms (0.4%)

prune2.0ms (0.2%)

series2.0ms (0.1%)

rewrite123.0ms (9.3%)

eval2.0ms (0.2%)

prune1.0ms (0.1%)

regimes23.0ms (1.8%)

bsearch2.0ms (0.1%)

derivations22.0ms (1.7%)

preprocess46.0ms (3.5%)

end0.0ms (0%)

Profiling