Metrics for sqrt B (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

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

sample535.0ms (60.6%)

Memory

12.6MiB live, 760.6MiB allocated; 155ms collecting garbage

Samples

347.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 217.0ms

ival-mult!: 139.0ms (64.1% of total)

ival-sqrt: 76.0ms (35.1% of total)

adjust: 1.0ms (0.5% of total)

Bogosity

preprocess119.0ms (13.4%)

Memory

-9.9MiB live, 35.8MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	30	19
2	83	19
3	260	19
4	676	19
5	4742	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series10.0ms (1.2%)

Memory

12.9MiB live, 12.9MiB 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 (.f64 #s(literal 2 binary64) x) x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
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 (* 2 x) (*.f64 #s(literal 2 binary64) x))
#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
2.0ms	x	@	-inf	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)
2.0ms	x	@	0	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)
2.0ms	x	@	inf	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)

rewrite76.0ms (8.6%)

Memory

-17.6MiB live, 40.2MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	21	16
0	83	13

Stop Event

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

Counts

5 → 41

Calls

Call 1

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

eval8.0ms (0.9%)

Memory: 9.8MiB live, 9.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 350 to 113 computations (67.7% saved)

prune5.0ms (0.6%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Accuracy

100.0%

Counts

44 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	52.9%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	2.5%	#s(approx (sqrt (* (* 2 x) x)) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 80 to 62 computations (22.5% saved)

series15.0ms (1.7%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	136

Stop Event

1×	iter-limit

Counts

15 → 13

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)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
#s(approx (sqrt (* (* 2 x) x)) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal -1 binary64)
(*.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 (* (+ 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 (* -1 (* x (sqrt 2))) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#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)) (.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
4.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* x (sqrt 2)) (sqrt 2) 2 (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (sqrt (* (* 2 x) x)) (* -1 (* x (sqrt 2))) -1 (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))
4.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* x (sqrt 2)) (sqrt 2) 2 (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (sqrt (* (* 2 x) x)) (* -1 (* x (sqrt 2))) -1 (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))
4.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* x (sqrt 2)) (sqrt 2) 2 (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (sqrt (* (* 2 x) x)) (* -1 (* x (sqrt 2))) -1 (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

Time

Variable

Point

Expression

4.0ms

((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* x (sqrt 2)) (sqrt 2) 2 (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (sqrt (* (* 2 x) x)) (* -1 (* x (sqrt 2))) -1 (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

4.0ms

-inf

((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* x (sqrt 2)) (sqrt 2) 2 (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (sqrt (* (* 2 x) x)) (* -1 (* x (sqrt 2))) -1 (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

4.0ms

inf

((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* x (sqrt 2)) (sqrt 2) 2 (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (sqrt (* (* 2 x) x)) (* -1 (* x (sqrt 2))) -1 (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

rewrite22.0ms (2.5%)

Memory

-23.4MiB live, 25.5MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
0	30	54
0	88	54

Stop Event

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

Counts

15 → 81

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)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
#s(approx (sqrt (* (* 2 x) x)) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal -1 binary64)
(*.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))
(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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.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))
(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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(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) 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 (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 #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 (* (* 2 x) x)) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal -1 binary64))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(literal -1 binary64)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.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: 11.2MiB live, 11.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 753 to 190 computations (74.8% saved)

prune3.0ms (0.4%)

Memory

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

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	67	6	73

Accuracy

100.0%

Counts

73 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	99.2%	(.f64 #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))) (sqrt.f64 x))
✓	52.9%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	2.5%	#s(approx (sqrt (* (* 2 x) x)) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

series7.0ms (0.8%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	147

Stop Event

1×	iter-limit

Counts

12 → 14

Calls

Call 1

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

Outputs
#s(approx (sqrt (* (* 2 x) x)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (neg (* (sqrt 2) x)) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx x 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 (/ 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 (* (* 2 x) x)) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (* x (sqrt (/ 2 x))) (sqrt (/ 2 x)) (/ 2 x) (sqrt x))
2.0ms	x	@	inf	((sqrt (* (* 2 x) x)) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (* x (sqrt (/ 2 x))) (sqrt (/ 2 x)) (/ 2 x) (sqrt x))
2.0ms	x	@	0	((sqrt (* (* 2 x) x)) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (* x (sqrt (/ 2 x))) (sqrt (/ 2 x)) (/ 2 x) (sqrt x))

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

rewrite20.0ms (2.2%)

Memory

-30.4MiB live, 16.4MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65
0	25	65
0	73	65

Stop Event

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

Counts

12 → 27

Calls

Call 1

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

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

eval2.0ms (0.3%)

Memory: 5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 488 to 128 computations (73.8% saved)

prune2.0ms (0.3%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	31	6	37

Accuracy

100.0%

Counts

37 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.2%	(.f64 #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))) (sqrt.f64 x))
✓	52.9%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	2.5%	#s(approx (sqrt (* (* 2 x) x)) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

regimes23.0ms (2.6%)

Memory

-7.0MiB live, 40.1MiB allocated; 2ms collecting garbage

Accuracy

Total -62.0b remaining (-7449.5%)

Threshold costs -62b (-7449.5%)

Counts

5 → 1

7 → 1

8 → 1

Calls

Call 1

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

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

Call 2

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

Call 3

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

9 calls:

4.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
3.0ms	x
2.0ms	x
2.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)
2.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Results

Accuracy	Segments	Branch
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.3%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.3%	1	`x`
99.4%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.4%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.4%	1	`x`
100.0%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
100.0%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
100.0%	1	`x`

Compiler

Compiled 108 to 62 computations (42.6% saved)

derivations3.0ms (0.3%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 21 to 14 computations (33.3% saved)

preprocess27.0ms (3.1%)

Memory: -5.0MiB live, 44.2MiB allocated; 6ms 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%)

sample535.0ms (60.6%)

preprocess119.0ms (13.4%)

series10.0ms (1.2%)

rewrite76.0ms (8.6%)

eval8.0ms (0.9%)

prune5.0ms (0.6%)

series15.0ms (1.7%)

rewrite22.0ms (2.5%)

eval5.0ms (0.6%)

prune3.0ms (0.4%)

series7.0ms (0.8%)

rewrite20.0ms (2.2%)

eval2.0ms (0.3%)

prune2.0ms (0.3%)

regimes23.0ms (2.6%)

derivations3.0ms (0.3%)

preprocess27.0ms (3.1%)

end0.0ms (0%)

Profiling