Metrics for sqrt E (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
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 6 computations (40% saved)

sample559.0ms (61.8%)

Memory

-17.2MiB live, 602.0MiB allocated; 147ms collecting garbage

Samples

376.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

ival-sqrt: 109.0ms (45.9% of total)

ival-pow2: 107.0ms (45.1% of total)

ival-add!: 21.0ms (8.8% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

preprocess60.0ms (6.7%)

Memory

-5.5MiB live, 39.1MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	19	19
2	46	19
3	138	19
4	314	19
5	1717	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.5%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Symmetry

(abs x)

Compiler

Compiled 16 to 10 computations (37.5% saved)

series3.0ms (0.3%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

1.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

1.0ms

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

rewrite45.0ms (5%)

Memory

13.9MiB live, 58.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	22	56
1	50	36
0	243	36

Stop Event

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

Counts

10 → 27

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.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))
(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(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(approx (pow x 2) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval2.0ms (0.2%)

Memory: 4.5MiB live, 4.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 248 to 74 computations (70.2% saved)

prune2.0ms (0.2%)

Memory

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

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	4	25

Accuracy

99.7%

Counts

25 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
▶	5.5%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
▶	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

series4.0ms (0.5%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Counts

13 → 6

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

rewrite64.0ms (7.1%)

Memory

-13.8MiB live, 30.2MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	133
0	40	103
1	81	79
0	376	79

Stop Event

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

Counts

19 → 78

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) x)
(.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) 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)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 x (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (neg.f64 (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
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.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))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 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 (pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.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))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
(.f64 (.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 x (.f64 #s(literal -1 binary64) (neg.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(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))))
#s(approx (sqrt (+ (pow x 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 (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(approx (* x x) (*.f64 x x))

eval6.0ms (0.6%)

Memory: 9.7MiB live, 9.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 047 to 218 computations (79.2% saved)

prune4.0ms (0.4%)

Memory

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

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	64	6	70

Accuracy

100.0%

Counts

70 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	5.5%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
✓	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	99.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 78 to 55 computations (29.5% saved)

series3.0ms (0.4%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Counts

11 → 4

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (exp (* (log 2) 1/2)) (* (log 2) 1/2) (log 2) 2 1/2 x (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x))
1.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (exp (* (log 2) 1/2)) (* (log 2) 1/2) (log 2) 2 1/2 x (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x))
1.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (exp (* (log 2) 1/2)) (* (log 2) 1/2) (log 2) 2 1/2 x (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x))

Time

Variable

Point

Expression

1.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (exp (* (log 2) 1/2)) (* (log 2) 1/2) (log 2) 2 1/2 x (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x))

1.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (exp (* (log 2) 1/2)) (* (log 2) 1/2) (log 2) 2 1/2 x (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x))

1.0ms

((sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (exp (* (log 2) 1/2)) (* (log 2) 1/2) (log 2) 2 1/2 x (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x))

rewrite88.0ms (9.8%)

Memory

-26.4MiB live, 36.2MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	101
0	35	75
1	72	62
0	289	62

Stop Event

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

Counts

15 → 50

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (pow x 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)))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(fma.f64 x (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 x (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 x (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x) (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 (sqrt.f64 #s(literal 2 binary64)))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) x)
(.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) 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 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 x (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x)))
(fma.f64 (neg.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 (neg.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (neg.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x)) (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx x x)
#s(approx (* (neg x) (exp (* (log 2) 1/2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (neg x) (neg.f64 x))

eval5.0ms (0.5%)

Memory: 11.7MiB live, 11.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 093 to 179 computations (83.6% saved)

prune3.0ms (0.4%)

Memory

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

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	53	6	59

Accuracy

100.0%

Counts

59 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	5.5%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
✓	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	99.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 78 to 55 computations (29.5% saved)

regimes20.0ms (2.2%)

Memory

-16.9MiB live, 28.9MiB allocated; 7ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

7 → 1

Calls

Call 1

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

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

Call 2

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

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

Calls

8 calls:

7.0ms	(pow.f64 x #s(literal 2 binary64))
2.0ms	x
2.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
2.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	x

Results

Accuracy	Segments	Branch
5.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
5.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
5.5%	1	`(pow.f64 x #s(literal 2 binary64))`
5.5%	1	`x`
99.4%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(pow.f64 x #s(literal 2 binary64))`
99.4%	1	`x`

Compiler

Compiled 124 to 54 computations (56.5% saved)

derivations3.0ms (0.3%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 23 to 11 computations (52.2% saved)

preprocess34.0ms (3.8%)

Memory: -15.9MiB live, 27.2MiB allocated; 6ms collecting garbage
Remove: (abs x)
Compiler: Compiled 77 to 48 computations (37.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample559.0ms (61.8%)

preprocess60.0ms (6.7%)

series3.0ms (0.3%)

rewrite45.0ms (5%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

series4.0ms (0.5%)

rewrite64.0ms (7.1%)

eval6.0ms (0.6%)

prune4.0ms (0.4%)

series3.0ms (0.4%)

rewrite88.0ms (9.8%)

eval5.0ms (0.5%)

prune3.0ms (0.4%)

regimes20.0ms (2.2%)

derivations3.0ms (0.3%)

preprocess34.0ms (3.8%)

end0.0ms (0%)

Profiling