Metrics for sqrt D (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

sample829.0ms (67.3%)

Memory

45.4MiB live, 731.9MiB allocated; 853ms collecting garbage

Samples

395.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 199.0ms

ival-pow2: 92.0ms (46.2% of total)

ival-sqrt: 67.0ms (33.7% of total)

ival-mult!: 39.0ms (19.6% of total)

adjust: 1.0ms (0.5% of total)

Bogosity

preprocess101.0ms (8.2%)

Memory

-25.6MiB live, 19.8MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	23	19
2	69	19
3	240	19
4	877	19
5	5309	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.8%	(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)

series6.0ms (0.5%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45

Stop Event

1×	iter-limit

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	inf
1.0ms	x	-inf
1.0ms	x	0

rewrite68.0ms (5.5%)

Memory

-12.2MiB live, 43.6MiB allocated; 86ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	25	15
0	123	13

Stop Event

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

Counts

5 → 56

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

eval5.0ms (0.4%)

Memory: 12.0MiB live, 12.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 494 to 141 computations (71.5% saved)

prune3.0ms (0.3%)

Memory

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

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	5	59

Accuracy

100.0%

Counts

59 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	52.6%	(.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)) (fabs.f64 x))
▶	52.8%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	99.3%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 80 to 52 computations (35% saved)

series53.0ms (4.3%)

Memory

-1.0MiB live, 88.8MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	201

Stop Event

1×	iter-limit

Counts

14 → 13

Calls

Call 1

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

Calls

3 calls:

Time	Variable	Point
29.0ms	x	0
13.0ms	x	-inf
8.0ms	x	inf

rewrite21.0ms (1.7%)

Memory

20.3MiB live, 20.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
0	29	46
0	108	46

Stop Event

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

Counts

14 → 144

Calls

Call 1

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

eval17.0ms (1.3%)

Memory: -32.3MiB live, 13.7MiB allocated; 4ms collecting garbage
Compiler: Compiled 1 413 to 235 computations (83.4% saved)

prune3.0ms (0.2%)

Memory

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

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	91	6	97

Accuracy

100.0%

Counts

97 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.6%	(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	52.8%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 41 to 32 computations (22% saved)

series43.0ms (3.5%)

Memory

-7.0MiB live, 43.8MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	243

Stop Event

1×	iter-limit

Counts

10 → 17

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

Calls

3 calls:

Time	Variable	Point
25.0ms	x	-inf
8.0ms	x	inf
8.0ms	x	0

rewrite18.0ms (1.5%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
0	17	39
0	60	39

Stop Event

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

Counts

10 → 28

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
(*.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)
(fabs.f64 (sqrt.f64 x))
x
(pow.f64 (+.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x x))
(fabs.f64 (sqrt.f64 (+.f64 x x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x x)) x)
(*.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))))
(-.f64 x (neg.f64 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))
(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)

eval4.0ms (0.3%)

Memory: 4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 593 to 164 computations (72.3% saved)

prune2.0ms (0.2%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	42	6	48

Accuracy

100.0%

Counts

48 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.6%	(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	52.8%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 41 to 32 computations (22% saved)

regimes28.0ms (2.2%)

Memory

-1.3MiB live, 44.2MiB allocated; 3ms collecting garbage

Accuracy

Total -29.9b remaining (-3495.7%)

Threshold costs -29.9b (-3495.7%)

Counts

3 → 1

4 → 1

8 → 1

Calls

Call 1

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

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

Call 2

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

Call 3

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

12 calls:

3.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
3.0ms	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
99.3%	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`
99.4%	1	`(pow.f64 x #s(literal 2 binary64))`
99.4%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`x`
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 107 to 66 computations (38.3% saved)

derivations3.0ms (0.2%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 21 to 14 computations (33.3% saved)

preprocess27.0ms (2.2%)

Memory: 10.5MiB live, 54.1MiB allocated; 9ms collecting garbage
Compiler: Compiled 69 to 51 computations (26.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample829.0ms (67.3%)

preprocess101.0ms (8.2%)

series6.0ms (0.5%)

rewrite68.0ms (5.5%)

eval5.0ms (0.4%)

prune3.0ms (0.3%)

series53.0ms (4.3%)

rewrite21.0ms (1.7%)

eval17.0ms (1.3%)

prune3.0ms (0.2%)

series43.0ms (3.5%)

rewrite18.0ms (1.5%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

regimes28.0ms (2.2%)

derivations3.0ms (0.2%)

preprocess27.0ms (2.2%)

end0.0ms (0%)

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