Metrics for sqrt A (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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 10 to 4 computations (60% saved)

sample550.0ms (36%)

Memory

-19.2MiB live, 451.4MiB allocated; 173ms collecting garbage

Samples

380.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 223.0ms

ival-hypot: 221.0ms (99.2% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

preprocess151.0ms (9.9%)

Memory

-7.1MiB live, 38.0MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	34	19
2	100	19
3	171	19
4	422	19
5	2055	19
6	7408	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 10 to 8 computations (20% saved)

series4.0ms (0.2%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite515.0ms (33.8%)

Memory

21.5MiB live, 161.8MiB allocated; 31ms collecting garbage

Counts

9 → 194

Calls

Call 1

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

Outputs
(.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 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 1/2 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 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(/.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)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (sqrt.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(hypot.f64 x x)
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 (neg.f64 x) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (fabs.f64 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)) (neg.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (exp.f64 (log.f64 x)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (neg.f64 (neg.f64 x)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (fabs.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) (pow.f64 x #s(literal 1 binary64)))
(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)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (neg.f64 (neg.f64 x)) (fabs.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) x)
(hypot.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x))
(hypot.f64 (neg.f64 (fabs.f64 x)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (fabs.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 (fabs.f64 x)) x)
(hypot.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 x))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (neg.f64 x))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (neg.f64 (fabs.f64 x)))
(hypot.f64 x (fabs.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (fabs.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (fabs.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 x) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 x) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) x)
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 x))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 x))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) x)
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 x))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 x))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (exp.f64 (log.f64 x)))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (neg.f64 x)))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (fabs.f64 x)))
(hypot.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 x (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (fabs.f64 x) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 x) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 x (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (fabs.f64 x) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 x) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (exp.f64 (log.f64 x)) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 (neg.f64 x)) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(hypot.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 (+.f64 x x) x)
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 x (-.f64 x (neg.f64 x)))
(.f64 x (.f64 x #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (+.f64 (fabs.f64 x) (fabs.f64 x)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)))
(*.f64 (neg.f64 x) (-.f64 (neg.f64 x) x))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64))))
(+.f64 (.f64 x x) (.f64 x x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64))))
(+.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 x)) x))
(-.f64 (.f64 x x) (neg.f64 (.f64 x x)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)))
(-.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (.f64 x x) (.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 (.f64 x x) (.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 #s(literal 0 binary64)) (neg.f64 #s(literal 0 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (neg.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 0 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (pow.f64 (neg.f64 (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) x (.f64 (.f64 x x) (neg.f64 (*.f64 x x))))))
(fma.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 (pow.f64 x #s(literal 1 binary64)) 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 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (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 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (*.f64 x x))
(fma.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal 1 binary64))) (*.f64 x x))
(fma.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal 1 binary64))) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) x (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 x x (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(*.f64 x x)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1 binary64))) (fabs.f64 (pow.f64 x #s(literal 1 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal 1 binary64))))
(fabs.f64 (*.f64 x x))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(neg.f64 (neg.f64 (*.f64 x x)))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
x
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (/ 0 0) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))

eval18.0ms (1.2%)

Memory: 17.3MiB live, 17.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 020 to 364 computations (64.3% saved)

prune8.0ms (0.5%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	5	192

Accuracy

100.0%

Counts

192 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	56.2%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	2.3%	#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
▶	99.2%	#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 56 to 56 computations (0% saved)

series9.0ms (0.6%)

Memory

-40.4MiB live, 5.5MiB allocated; 3ms collecting garbage

Counts

15 → 16

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (/ 0 0)) (*.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 (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) x (sqrt (/ 0 0)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (/ 0 0)) (* (sqrt 2) (neg x)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)))
3.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) x (sqrt (/ 0 0)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (/ 0 0)) (* (sqrt 2) (neg x)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)))
2.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) x (sqrt (/ 0 0)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (/ 0 0)) (* (sqrt 2) (neg x)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)))

Time

Variable

Point

Expression

4.0ms

inf

((sqrt (+ (* x x) (* x x))) x (sqrt (/ 0 0)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (/ 0 0)) (* (sqrt 2) (neg x)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)))

3.0ms

-inf

((sqrt (+ (* x x) (* x x))) x (sqrt (/ 0 0)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (/ 0 0)) (* (sqrt 2) (neg x)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)))

2.0ms

((sqrt (+ (* x x) (* x x))) x (sqrt (/ 0 0)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (/ 0 0)) (* (sqrt 2) (neg x)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)))

rewrite213.0ms (14%)

Memory

8.6MiB live, 54.4MiB allocated; 7ms collecting garbage

Counts

31 → 32

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (/ 0 0)) (*.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 (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x x))
#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) (neg x)) #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 (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* (sqrt x) (sqrt 2))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* (+ x x) x)) #s(hole binary64 (* -1 (* x (sqrt 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))))))

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

eval2.0ms (0.1%)

Memory: 1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 150 to 86 computations (42.7% saved)

prune3.0ms (0.2%)

Memory

2.6MiB live, 2.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	22	5	27

Accuracy

100.0%

Counts

27 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	56.2%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	2.3%	#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
✓	99.2%	#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 54 to 49 computations (9.3% saved)

regimes10.0ms (0.7%)

Memory

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

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Calls

4 calls:

3.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes9.0ms (0.6%)

Memory

8.7MiB live, 8.7MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

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

Calls

4 calls:

2.0ms	x
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 x x)`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes7.0ms (0.5%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Accuracy

Total -62.1b remaining (-12920.2%)

Threshold costs -62.1b (-12920.2%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(sqrt.f64 (*.f64 (+.f64 x x) x))

Outputs
#s(approx (sqrt (/ 0 0)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(*.f64 x x)
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.2%	1	`(*.f64 x x)`
99.2%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.2%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.2%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

derivations1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 13 computations (0% saved)

preprocess26.0ms (1.7%)

Memory: -16.9MiB live, 29.5MiB allocated; 3ms collecting garbage
Compiler: Compiled 48 to 47 computations (2.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample550.0ms (36%)

preprocess151.0ms (9.9%)

series4.0ms (0.2%)

rewrite515.0ms (33.8%)

eval18.0ms (1.2%)

prune8.0ms (0.5%)

series9.0ms (0.6%)

rewrite213.0ms (14%)

eval2.0ms (0.1%)

prune3.0ms (0.2%)

regimes10.0ms (0.7%)

regimes9.0ms (0.6%)

regimes7.0ms (0.5%)

derivations1.0ms (0%)

preprocess26.0ms (1.7%)

end0.0ms (0%)

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