Metrics for sqrt C (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample579.0ms (61.8%)

Memory

-5.4MiB live, 560.0MiB allocated; 159ms collecting garbage

Samples

378.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 181.0ms

ival-mult!: 107.0ms (59.1% of total)

ival-sqrt: 72.0ms (39.8% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

preprocess121.0ms (12.9%)

Memory

-27.2MiB live, 67.1MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	35	19
2	114	19
3	252	19
4	1070	19
5	7204	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.7%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series6.0ms (0.6%)

Memory

16.9MiB live, 16.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	45

Stop Event

1×	iter-limit

Counts

5 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite42.0ms (4.5%)

Memory

-11.4MiB live, 77.4MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	25	15
0	131	13

Stop Event

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

Counts

5 → 93

Calls

Call 1

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

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

eval9.0ms (1%)

Memory: 36.5MiB live, 36.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 437 to 207 computations (52.6% saved)

prune27.0ms (2.9%)

Memory

-21.5MiB live, 28.7MiB allocated; 20ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	5	95

Accuracy

100.0%

Counts

95 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
▶	56.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 50 to 50 computations (0% saved)

series9.0ms (1%)

Memory

22.1MiB live, 22.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	149

Stop Event

1×	iter-limit

Counts

14 → 15

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

inf

((sqrt (+ (* x x) (* x x))) x (sqrt (* 2 (* x x))) (* x (sqrt 2)) (sqrt 2) 2 (* (sqrt 2) (fabs x)) (fabs x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

2.0ms

-inf

((sqrt (+ (* x x) (* x x))) x (sqrt (* 2 (* x x))) (* x (sqrt 2)) (sqrt 2) 2 (* (sqrt 2) (fabs x)) (fabs x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

2.0ms

((sqrt (+ (* x x) (* x x))) x (sqrt (* 2 (* x x))) (* x (sqrt 2)) (sqrt 2) 2 (* (sqrt 2) (fabs x)) (fabs x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

rewrite25.0ms (2.6%)

Memory

-7.9MiB live, 36.1MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	56
0	29	44
0	84	44

Stop Event

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

Counts

14 → 100

Calls

Call 1

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

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

eval5.0ms (0.6%)

Memory: 18.7MiB live, 18.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 342 to 180 computations (47.4% saved)

prune17.0ms (1.8%)

Memory

-28.3MiB live, 9.7MiB allocated; 15ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	65	6	71

Accuracy

100.0%

Counts

71 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
▶	99.0%	(.f64 #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))) (sqrt.f64 x))
✓	56.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 35 to 35 computations (0% saved)

series5.0ms (0.6%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	124

Stop Event

1×	iter-limit

Counts

8 → 12

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (* x (sqrt (/ 2 x))) x (sqrt (/ 2 x)) (/ 2 x) 2 (sqrt x))
1.0ms	x	@	inf	((* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (* x (sqrt (/ 2 x))) x (sqrt (/ 2 x)) (/ 2 x) 2 (sqrt x))
1.0ms	x	@	0	((* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (* x (sqrt (/ 2 x))) x (sqrt (/ 2 x)) (/ 2 x) 2 (sqrt x))

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite16.0ms (1.7%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
0	15	42
0	50	42

Stop Event

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

Counts

8 → 18

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 167 to 100 computations (40.1% saved)

prune3.0ms (0.3%)

Memory

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

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	23	6	29

Accuracy

100.0%

Counts

29 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	99.0%	(.f64 #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))) (sqrt.f64 x))
✓	56.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 65 to 63 computations (3.1% saved)

regimes12.0ms (1.3%)

Memory

-31.0MiB live, 16.6MiB allocated; 4ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

4.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
4.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

regimes8.0ms (0.9%)

Memory

13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

regimes6.0ms (0.7%)

Memory

11.7MiB live, 11.7MiB allocated; 0ms collecting garbage

Accuracy

Total -27.5b remaining (-5961.8%)

Threshold costs -27.5b (-5961.8%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

derivations4.0ms (0.4%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess40.0ms (4.3%)

Memory: -8.4MiB live, 44.6MiB allocated; 23ms collecting garbage
Compiler: Compiled 51 to 51 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample579.0ms (61.8%)

preprocess121.0ms (12.9%)

series6.0ms (0.6%)

rewrite42.0ms (4.5%)

eval9.0ms (1%)

prune27.0ms (2.9%)

series9.0ms (1%)

rewrite25.0ms (2.6%)

eval5.0ms (0.6%)

prune17.0ms (1.8%)

series5.0ms (0.6%)

rewrite16.0ms (1.7%)

eval2.0ms (0.2%)

prune3.0ms (0.3%)

regimes12.0ms (1.3%)

regimes8.0ms (0.9%)

regimes6.0ms (0.7%)

derivations4.0ms (0.4%)

preprocess40.0ms (4.3%)

end0.0ms (0%)

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