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

1.1MiB live, 1.1MiB 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)

sample651.0ms (67.9%)

Memory

-11.8MiB live, 595.3MiB allocated; 152ms collecting garbage

Samples

432.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 240.0ms

ival-pow2: 137.0ms (57% of total)

ival-sqrt: 57.0ms (23.7% of total)

ival-mult!: 45.0ms (18.7% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

preprocess100.0ms (10.4%)

Memory

-22.3MiB live, 35.0MiB allocated; 9ms 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	5307	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.5%	(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)

series3.0ms (0.3%)

Memory

3.8MiB live, 3.8MiB 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	@	-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)

rewrite31.0ms (3.3%)

Memory

34.1MiB live, 34.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	21	60
1	44	57
0	158	51

Stop Event

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

Counts

10 → 61

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 (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
#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))))

eval5.0ms (0.5%)

Memory: 8.1MiB live, 8.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 279 to 138 computations (50.5% saved)

prune5.0ms (0.6%)

Memory

-40.6MiB live, 6.3MiB allocated; 3ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Accuracy

100.0%

Counts

59 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	53.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	99.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 25 to 25 computations (0% saved)

series5.0ms (0.5%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Counts

12 → 6

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

rewrite21.0ms (2.2%)

Memory

21.4MiB live, 21.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	105
0	43	91
0	107	91

Stop Event

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

Counts

18 → 86

Calls

Call 1

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

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

eval5.0ms (0.5%)

Memory: 11.4MiB live, 11.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 268 to 150 computations (44% saved)

prune8.0ms (0.9%)

Memory

-35.8MiB live, 8.8MiB allocated; 5ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	58	5	63

Accuracy

100.0%

Counts

63 → 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)))
✓	53.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 30 to 30 computations (0% saved)

series3.0ms (0.3%)

Memory

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

Counts

5 → 10

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)

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

Calls

3 calls:

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

rewrite21.0ms (2.2%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	121
0	41	114
0	118	114

Stop Event

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

Counts

15 → 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)
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#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 (* 2 x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))

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

eval1.0ms (0.2%)

Memory: 4.0MiB live, 4.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 129 to 86 computations (33.3% saved)

prune2.0ms (0.2%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	21	6	27

Accuracy

100.0%

Counts

27 → 6

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)))
▶	99.3%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
✓	53.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 40 to 40 computations (0% saved)

series4.0ms (0.4%)

Memory

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

Counts

8 → 12

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite30.0ms (3.1%)

Memory

-25.4MiB live, 20.7MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	166
0	48	160
0	131	160

Stop Event

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

Counts

20 → 30

Calls

Call 1

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

eval1.0ms (0.1%)

Memory: 1.6MiB live, 1.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 149 to 101 computations (32.2% saved)

prune3.0ms (0.3%)

Memory

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

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	21	6	27

Accuracy

100.0%

Counts

27 → 6

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)))
✓	99.3%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
✓	53.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 76 to 69 computations (9.2% saved)

regimes9.0ms (0.9%)

Memory

10.2MiB live, 10.2MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

regimes9.0ms (1%)

Memory

-34.1MiB live, 16.3MiB allocated; 7ms collecting garbage

Accuracy

Total -62.2b remaining (-15023.9%)

Threshold costs -62.2b (-15023.9%)

Counts

3 → 1

Calls

Call 1

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

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(*.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
99.4%	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`

Compiler

Compiled 15 to 13 computations (13.3% saved)

derivations8.0ms (0.8%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess25.0ms (2.6%)

Memory: -2.6MiB live, 43.4MiB allocated; 2ms collecting garbage
Compiler: Compiled 52 to 51 computations (1.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample651.0ms (67.9%)

preprocess100.0ms (10.4%)

series3.0ms (0.3%)

rewrite31.0ms (3.3%)

eval5.0ms (0.5%)

prune5.0ms (0.6%)

series5.0ms (0.5%)

rewrite21.0ms (2.2%)

eval5.0ms (0.5%)

prune8.0ms (0.9%)

series3.0ms (0.3%)

rewrite21.0ms (2.2%)

eval1.0ms (0.2%)

prune2.0ms (0.2%)

series4.0ms (0.4%)

rewrite30.0ms (3.1%)

eval1.0ms (0.1%)

prune3.0ms (0.3%)

regimes9.0ms (0.9%)

regimes7.0ms (0.7%)

regimes9.0ms (1%)

derivations8.0ms (0.8%)

preprocess25.0ms (2.6%)

end0.0ms (0%)

Profiling