Metrics for sqrt B (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample716.0ms (58.3%)

Memory

46.3MiB live, 461.6MiB allocated; 660ms collecting garbage

Samples

557.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-mult!: 83.0ms (55.3% of total)

ival-sqrt: 66.0ms (44% of total)

adjust: 1.0ms (0.7% of total)

Bogosity

preprocess88.0ms (7.2%)

Memory

-26.0MiB live, 17.1MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	28	19
2	68	19
3	213	19
4	402	19
5	2482	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series3.0ms (0.3%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x

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

Calls

3 calls:

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

rewrite33.0ms (2.7%)

Memory

24.1MiB live, 24.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	48	60
0	150	51

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

10 → 58

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) (neg.f64 x))
(hypot.f64 (fabs.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 (neg.f64 x) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 (exp.f64 (log.f64 x)) (fabs.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x x) x)) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 (+.f64 x x) x)
(*.f64 x (+.f64 x x))
(.f64 #s(literal 2 binary64) (.f64 x x))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 x x (*.f64 x x))
(-.f64 (.f64 x x) (.f64 (neg.f64 x) x))
(+.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1 binary64) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x))
(+.f64 x x)
#s(literal 2 binary64)
x
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (* 2 x) x) (*.f64 (+.f64 x x) x))
#s(approx (* 2 x) (+.f64 x x))
#s(approx x x)
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval5.0ms (0.4%)

Memory: 5.5MiB live, 5.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 259 to 130 computations (49.8% saved)

prune3.0ms (0.3%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	5	56

Accuracy

100.0%

Counts

56 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	56.0%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	2.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 60 to 60 computations (0% saved)

series7.0ms (0.6%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Counts

15 → 14

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(sqrt.f64 x)

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* (* 2 x) x)) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

2.0ms

-inf

((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* (* 2 x) x)) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

2.0ms

inf

((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* (* 2 x) x)) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

rewrite84.0ms (6.8%)

Memory

-15.1MiB live, 39.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	209
0	76	162
1	162	102
0	701	102

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

29 → 199

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
x
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
#s(approx (* (sqrt (+ x x)) (sqrt x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(neg.f64 (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(.f64 #s(literal -1 binary64) (.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 x) (sqrt.f64 x))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) x)))
(neg.f64 (.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) x))
(neg.f64 x)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
#s(literal 2 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx x x)
#s(approx (* (neg x) (sqrt 2)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
#s(approx (neg x) (neg.f64 x))
#s(approx (* (+ x x) x) #s(literal 2 binary64))
#s(approx (* (+ x x) x) #s(literal 2 binary64))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt x) (*.f64 #s(literal 1 binary64) x))
#s(approx (* (sqrt (+ x x)) (sqrt x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt x) (neg.f64 x))

eval5.0ms (0.4%)

Memory: 5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 243 to 152 computations (37.4% saved)

prune4.0ms (0.3%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	56	7	63

Accuracy

100.0%

Counts

63 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(hypot.f64 x x)
▶	99.1%	(.f64 (sqrt.f64 (+.f64 x x)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
✓	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	56.0%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	5.4%	(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 44 to 43 computations (2.3% saved)

series56.0ms (4.6%)

Memory

2.2MiB live, 48.5MiB allocated; 4ms collecting garbage

Counts

10 → 15

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (* (+ x x) x) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (sqrt.f64 (+.f64 x x)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
x
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)

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

Calls

3 calls:

Time	Variable		Point	Expression
41.0ms	x	@	0	((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (sqrt (+ x x)) (* (pow x 1/4) (pow x 1/4))) (sqrt (+ x x)) (+ x x) x (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)
8.0ms	x	@	-inf	((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (sqrt (+ x x)) (* (pow x 1/4) (pow x 1/4))) (sqrt (+ x x)) (+ x x) x (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)
7.0ms	x	@	inf	((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (sqrt (+ x x)) (* (pow x 1/4) (pow x 1/4))) (sqrt (+ x x)) (+ x x) x (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)

Time

Variable

Point

Expression

41.0ms

((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (sqrt (+ x x)) (* (pow x 1/4) (pow x 1/4))) (sqrt (+ x x)) (+ x x) x (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)

8.0ms

-inf

((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (sqrt (+ x x)) (* (pow x 1/4) (pow x 1/4))) (sqrt (+ x x)) (+ x x) x (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)

7.0ms

inf

((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (sqrt (+ x x)) (* (pow x 1/4) (pow x 1/4))) (sqrt (+ x x)) (+ x x) x (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)

rewrite26.0ms (2.1%)

Memory

-33.5MiB live, 12.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	248
0	62	213
0	160	213

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

25 → 43

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 2.8MiB live, 2.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 236 to 122 computations (48.3% saved)

prune3.0ms (0.2%)

Memory

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

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	33	8	41

Accuracy

100.0%

Counts

41 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(hypot.f64 x x)
▶	99.1%	(.f64 (.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
▶	99.1%	(*.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	56.0%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	5.4%	(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 52 to 51 computations (1.9% saved)

series26.0ms (2.1%)

Memory

-9.4MiB live, 36.8MiB allocated; 3ms collecting garbage

Counts

10 → 15

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
x
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(.f64 (.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 x #s(literal 1/4 binary64)))

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

Calls

3 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	((* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt (+ x x)) (+ x x) x (pow (pow x 1/4) 2) (pow x 1/4) 1/4 2 (* (* (sqrt (+ x x)) (pow x 1/4)) (pow x 1/4)) (* (sqrt (+ x x)) (pow x 1/4)))
7.0ms	x	@	inf	((* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt (+ x x)) (+ x x) x (pow (pow x 1/4) 2) (pow x 1/4) 1/4 2 (* (* (sqrt (+ x x)) (pow x 1/4)) (pow x 1/4)) (* (sqrt (+ x x)) (pow x 1/4)))
7.0ms	x	@	0	((* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt (+ x x)) (+ x x) x (pow (pow x 1/4) 2) (pow x 1/4) 1/4 2 (* (* (sqrt (+ x x)) (pow x 1/4)) (pow x 1/4)) (* (sqrt (+ x x)) (pow x 1/4)))

Time

Variable

Point

Expression

11.0ms

-inf

((* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt (+ x x)) (+ x x) x (pow (pow x 1/4) 2) (pow x 1/4) 1/4 2 (* (* (sqrt (+ x x)) (pow x 1/4)) (pow x 1/4)) (* (sqrt (+ x x)) (pow x 1/4)))

7.0ms

inf

((* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt (+ x x)) (+ x x) x (pow (pow x 1/4) 2) (pow x 1/4) 1/4 2 (* (* (sqrt (+ x x)) (pow x 1/4)) (pow x 1/4)) (* (sqrt (+ x x)) (pow x 1/4)))

7.0ms

((* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt (+ x x)) (+ x x) x (pow (pow x 1/4) 2) (pow x 1/4) 1/4 2 (* (* (sqrt (+ x x)) (pow x 1/4)) (pow x 1/4)) (* (sqrt (+ x x)) (pow x 1/4)))

rewrite76.0ms (6.2%)

Memory

1.7MiB live, 56.9MiB allocated; 64ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	265
0	66	276
1	148	128
0	620	128

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

25 → 99

Calls

Call 1

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

Outputs
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
x
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sinh.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/8 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/8 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/8 binary64))) (neg.f64 (pow.f64 x #s(literal 1/8 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/4 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64))))
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx x x)
#s(approx (pow (pow x 1/4) 2) (sqrt.f64 x))
#s(approx (pow x 1/4) (pow.f64 x #s(literal 1/4 binary64)))
#s(approx (* (sqrt (+ x x)) (pow x 1/4)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
#s(approx (* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
#s(approx (* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (pow (pow x 1/4) 2) #s(literal 1 binary64))
#s(approx (pow x 1/4) #s(literal 1 binary64))
#s(approx (* (sqrt (+ x x)) (pow x 1/4)) (.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
#s(approx (* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (+ x x)) (pow (pow x 1/4) 2)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (sqrt (+ x x)) (pow x 1/4)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval5.0ms (0.4%)

Memory: 12.5MiB live, 12.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 492 to 214 computations (56.5% saved)

prune3.0ms (0.3%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	2	0	2
Done	0	6	6
Total	78	7	85

Accuracy

100.0%

Counts

85 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
	99.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
✓	56.0%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	5.4%	(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 43 to 42 computations (2.3% saved)

regimes32.0ms (2.6%)

Memory

11.6MiB live, 58.0MiB allocated; 5ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

5 → 1

7 → 1

11 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))

Outputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))

Call 2

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

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

Call 3

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))

Outputs
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))

Call 4

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (+.f64 x x)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 (+.f64 x x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))

Outputs
(hypot.f64 x x)

Calls

12 calls:

7.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
3.0ms	x
3.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)
2.0ms	x
2.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Results

Accuracy	Segments	Branch
5.4%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
5.4%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
5.4%	1	`x`
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.3%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.3%	1	`x`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.5%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.5%	1	`x`
99.9%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.9%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.9%	1	`x`

Compiler

Compiled 90 to 76 computations (15.6% saved)

derivations13.0ms (1%)

Memory

-35.8MiB live, 10.1MiB allocated; 6ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 18 to 18 computations (0% saved)

preprocess38.0ms (3.1%)

Memory: -1.1MiB live, 94.6MiB allocated; 9ms collecting garbage
Remove: (abs x)
Compiler: Compiled 67 to 67 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample716.0ms (58.3%)

preprocess88.0ms (7.2%)

series3.0ms (0.3%)

rewrite33.0ms (2.7%)

eval5.0ms (0.4%)

prune3.0ms (0.3%)

series7.0ms (0.6%)

rewrite84.0ms (6.8%)

eval5.0ms (0.4%)

prune4.0ms (0.3%)

series56.0ms (4.6%)

rewrite26.0ms (2.1%)

eval2.0ms (0.2%)

prune3.0ms (0.2%)

series26.0ms (2.1%)

rewrite76.0ms (6.2%)

eval5.0ms (0.4%)

prune3.0ms (0.3%)

regimes32.0ms (2.6%)

derivations13.0ms (1%)

preprocess38.0ms (3.1%)

end0.0ms (0%)

Profiling