Metrics for sqrt D (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample549.0ms (53.5%)

Memory

3.4MiB live, 624.8MiB allocated; 118ms collecting garbage

Samples

383.0ms	8 255×	0	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-pow2: 96.0ms (46.7% of total)

ival-sqrt: 55.0ms (26.7% of total)

ival-mult!: 52.0ms (25.3% of total)

adjust: 2.0ms (1% of total)

Bogosity

preprocess68.0ms (6.6%)

Memory

-2.5MiB live, 44.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	21	19
2	55	19
3	182	19
4	505	19
5	2438	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.2%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series4.0ms (0.4%)

Memory

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

Counts

5 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite31.0ms (3%)

Memory

-4.5MiB live, 41.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	21	60
1	42	54
0	138	49

Stop Event

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

Counts

10 → 46

Calls

Call 1

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

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

eval4.0ms (0.4%)

Memory: 5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 213 to 109 computations (48.8% saved)

prune3.0ms (0.3%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	5	44

Accuracy

100.0%

Counts

44 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	52.9%	(.f64 (pow.f64 (.f64 x (+.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/4 binary64)))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 58 to 52 computations (10.3% saved)

series45.0ms (4.4%)

Memory

20.6MiB live, 63.6MiB allocated; 7ms collecting garbage

Counts

14 → 16

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
30.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) x (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (* (pow (* x (+ x x)) 1/4) (pow (* x (+ x x)) 1/4)) (pow (* x (+ x x)) 1/4) 1/4)
7.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) x (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (* (pow (* x (+ x x)) 1/4) (pow (* x (+ x x)) 1/4)) (pow (* x (+ x x)) 1/4) 1/4)
7.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) x (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (* (pow (* x (+ x x)) 1/4) (pow (* x (+ x x)) 1/4)) (pow (* x (+ x x)) 1/4) 1/4)

Time

Variable

Point

Expression

30.0ms

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

7.0ms

inf

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

7.0ms

-inf

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

rewrite39.0ms (3.8%)

Memory

-17.8MiB live, 30.8MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	256
0	70	193
0	157	193

Stop Event

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

Counts

30 → 128

Calls

Call 1

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

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

eval7.0ms (0.7%)

Memory: 16.4MiB live, 16.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 590 to 199 computations (66.3% saved)

prune4.0ms (0.4%)

Memory

8.9MiB live, 8.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	82	6	88

Accuracy

100.0%

Counts

88 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 32 to 32 computations (0% saved)

series29.0ms (2.8%)

Memory

5.6MiB live, 51.3MiB allocated; 10ms collecting garbage

Counts

10 → 13

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
13.0ms	x	@	0	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x) (pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) 1/4 2)
8.0ms	x	@	-inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x) (pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) 1/4 2)
7.0ms	x	@	inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x) (pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) 1/4 2)

Time

Variable

Point

Expression

13.0ms

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

8.0ms

-inf

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

7.0ms

inf

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

rewrite26.0ms (2.5%)

Memory

-15.8MiB live, 30.8MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	195
0	65	169
0	167	169

Stop Event

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

Counts

23 → 42

Calls

Call 1

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

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

eval3.0ms (0.3%)

Memory: 8.0MiB live, 8.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 241 to 135 computations (44% saved)

prune2.0ms (0.2%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	38	6	44

Accuracy

100.0%

Counts

44 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(pow.f64 #s(approx (pow (* (+ x x) x) 1/4) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 37 to 37 computations (0% saved)

series25.0ms (2.5%)

Memory

-3.4MiB live, 42.0MiB allocated; 6ms collecting garbage

Counts

8 → 9

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
12.0ms	x	@	0	((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (pow 2 1/4) (sqrt x)) (pow 2 1/4) 2 1/4 (sqrt x) x)
7.0ms	x	@	-inf	((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (pow 2 1/4) (sqrt x)) (pow 2 1/4) 2 1/4 (sqrt x) x)
6.0ms	x	@	inf	((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (pow 2 1/4) (sqrt x)) (pow 2 1/4) 2 1/4 (sqrt x) x)

Time

Variable

Point

Expression

12.0ms

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

7.0ms

-inf

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

6.0ms

inf

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

rewrite88.0ms (8.6%)

Memory

-36.4MiB live, 29.3MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	160
0	40	145
0	122	145

Stop Event

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

Counts

17 → 24

Calls

Call 1

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

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

eval2.0ms (0.1%)

Memory: 4.7MiB live, 4.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 157 to 76 computations (51.6% saved)

prune3.0ms (0.3%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	17	6	23

Accuracy

100.0%

Counts

23 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(pow.f64 #s(approx (pow (* (+ x x) x) 1/4) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 82 to 72 computations (12.2% saved)

regimes49.0ms (4.8%)

Memory

-6.8MiB live, 40.1MiB allocated; 3ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

40.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
3.0ms	x
3.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
3.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`(pow.f64 x #s(literal 2 binary64))`
100.0%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
100.0%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes7.0ms (0.7%)

Memory

20.4MiB live, 20.4MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
2.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
99.5%	1	`(pow.f64 x #s(literal 2 binary64))`
99.5%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.5%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.5%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes7.0ms (0.7%)

Memory

-31.3MiB live, 15.7MiB allocated; 1ms collecting garbage

Accuracy

Total -62.2b remaining (-14606.4%)

Threshold costs -62.2b (-14606.4%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
1.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
99.3%	1	`(pow.f64 x #s(literal 2 binary64))`
99.3%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.3%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.3%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

derivations3.0ms (0.3%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 9 to 9 computations (0% saved)

preprocess27.0ms (2.6%)

Memory: 19.8MiB live, 65.2MiB allocated; 6ms collecting garbage
Compiler: Compiled 37 to 36 computations (2.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample549.0ms (53.5%)

preprocess68.0ms (6.6%)

series4.0ms (0.4%)

rewrite31.0ms (3%)

eval4.0ms (0.4%)

prune3.0ms (0.3%)

series45.0ms (4.4%)

rewrite39.0ms (3.8%)

eval7.0ms (0.7%)

prune4.0ms (0.4%)

series29.0ms (2.8%)

rewrite26.0ms (2.5%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

series25.0ms (2.5%)

rewrite88.0ms (8.6%)

eval2.0ms (0.1%)

prune3.0ms (0.3%)

regimes49.0ms (4.8%)

regimes7.0ms (0.7%)

regimes7.0ms (0.7%)

derivations3.0ms (0.3%)

preprocess27.0ms (2.6%)

end0.0ms (0%)

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