Metrics for sqrt E (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample640.0ms (51.9%)

Memory

4.1MiB live, 600.2MiB allocated; 109ms collecting garbage

Samples

432.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 270.0ms

ival-pow2: 179.0ms (66.3% of total)

ival-sqrt: 52.0ms (19.3% of total)

ival-add: 35.0ms (13% of total)

adjust: 3.0ms (1.1% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain73.0ms (5.9%)

Memory

-30.0MiB live, 61.8MiB allocated; 8ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	2	(2.0508404249783888e-156)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	68	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	68
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	136
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	68	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	68
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	136

Confusion

	Predicted +	Predicted -
+	136	2
-	0	118

Precision

1.0

Recall

0.9855072463768116

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	2
-	0	0	118

Precision?

1.0

Recall?

0.9855072463768116

Freqs

test

number	freq
0	120
1	136

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow2: 6.0ms (48.5% of total)

ival-sqrt: 3.0ms (24.3% of total)

ival-add: 2.0ms (16.2% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess156.0ms (12.6%)

Memory

31.0MiB live, 82.4MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	16	19
2	46	19
3	125	19
4	271	19
5	817	19
6	4664	19
0	5	8
0	8	6
1	12	6
2	28	6
3	80	6
4	244	6
5	826	6
6	5361	6
0	8499	3

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 8 to 5 computations (37.5% saved)

series4.0ms (0.3%)

Memory

5.5MiB live, 5.5MiB 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	@	0	((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)

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

((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)

rewrite51.0ms (4.1%)

Memory

-17.5MiB live, 29.5MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	22	56
1	50	36
0	246	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 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 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 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.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))))

eval4.0ms (0.3%)

Memory: 3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 352 to 101 computations (71.3% saved)

prune7.0ms (0.6%)

Memory

5.4MiB live, 5.3MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	3	39

Accuracy

99.6%

Counts

39 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
	16.6%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
	50.2%	(sqrt.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 2 binary64))))
▶	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Status

Accuracy

Program

16.6%

(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))

50.2%

(sqrt.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 2 binary64))))

▶

99.3%

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

Compiler

Compiled 36 to 29 computations (19.4% saved)

series2.0ms (0.1%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Counts

5 → 4

Calls

Call 1

Inputs
#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(literal 2 binary64))
#s(literal 2 binary64)
x

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 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))) (* (sqrt 2) x) (sqrt 2) 2 x)
0.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x)
0.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x)

rewrite40.0ms (3.3%)

Memory

-29.8MiB live, 16.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	20	54
1	47	42
0	234	42

Stop Event

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

Counts

9 → 17

Calls

Call 1

Inputs
#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(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 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
#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(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 #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 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 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)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (sqrt 2) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) 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 (0.1%)

Memory: 2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 250 to 60 computations (76% saved)

prune2.0ms (0.2%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Accuracy

99.9%

Counts

19 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

50.2%

(sqrt.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 2 binary64))))

▶

99.1%

#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) x))

✓

99.3%

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

Compiler

Compiled 41 to 28 computations (31.7% saved)

series2.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Counts

7 → 4

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) x))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 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)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
x

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (* (pow 2 1/4) (pow 2 1/4)) x) #s(hole binary64 (* x (sqrt 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 2 1/4) (pow 2 1/4)) x) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 x)
0.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* (* (pow 2 1/4) (pow 2 1/4)) x) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 x)
0.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* (* (pow 2 1/4) (pow 2 1/4)) x) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 x)

Time

Variable

Point

Expression

1.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (* (* (pow 2 1/4) (pow 2 1/4)) x) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 x)

0.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (* (* (pow 2 1/4) (pow 2 1/4)) x) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 x)

0.0ms

((sqrt (+ (pow x 2) (pow x 2))) (* (* (pow 2 1/4) (pow 2 1/4)) x) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 x)

rewrite20.0ms (1.6%)

Memory

16.4MiB live, 16.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	85
0	24	58
0	73	49

Stop Event

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

Counts

11 → 21

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) x))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 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)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (* (pow 2 1/4) (pow 2 1/4)) x) #s(hole binary64 (* x (sqrt 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
#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 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (* (pow 2 1/4) (pow 2 1/4)) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

eval2.0ms (0.2%)

Memory: 3.7MiB live, 3.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 439 to 67 computations (84.7% saved)

prune5.0ms (0.4%)

Memory

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

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	24	4	28

Accuracy

100.0%

Counts

28 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.2%	(sqrt.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 2 binary64))))
▶	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)))
✓	99.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) x))
✓	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 59 to 39 computations (33.9% saved)

series67.0ms (5.4%)

Memory

3.0MiB live, 91.9MiB allocated; 16ms collecting garbage

Counts

7 → 5

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)
x

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (pow 2 1/4) (* (pow 2 1/4) x)) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (pow 2 1/4) x) #s(hole binary64 (* (pow 2 1/4) x)))
#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
53.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* (pow 2 1/4) (* (pow 2 1/4) x)) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) x) x)
7.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (* (pow 2 1/4) (* (pow 2 1/4) x)) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) x) x)
7.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* (pow 2 1/4) (* (pow 2 1/4) x)) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) x) x)

Time

Variable

Point

Expression

53.0ms

((sqrt (+ (pow x 2) (pow x 2))) (* (pow 2 1/4) (* (pow 2 1/4) x)) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) x) x)

7.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (* (pow 2 1/4) (* (pow 2 1/4) x)) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) x) x)

7.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (* (pow 2 1/4) (* (pow 2 1/4) x)) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) x) x)

rewrite55.0ms (4.5%)

Memory

-8.2MiB live, 37.0MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	94
0	27	92
1	65	60
0	296	60

Stop Event

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

Counts

12 → 28

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (pow 2 1/4) (* (pow 2 1/4) x)) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (pow 2 1/4) x) #s(hole binary64 (* (pow 2 1/4) x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))
(.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (pow 2 1/4) (* (pow 2 1/4) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (pow 2 1/4) x) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
#s(approx x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

eval4.0ms (0.3%)

Memory: 5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 754 to 111 computations (85.3% saved)

prune23.0ms (1.8%)

Memory

-21.7MiB live, 21.4MiB allocated; 8ms collecting garbage

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	36	6	42

Accuracy

100.0%

Counts

42 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.2%	(sqrt.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 2 binary64))))
✓	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)))
	99.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) x))))
	99.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))))
✓	99.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) x))
✓	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 227 to 113 computations (50.2% saved)

regimes10.0ms (0.8%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Accuracy

Total -53.2b remaining (-15469%)

Threshold costs -53.2b (-15469%)

Counts

8 → 1

Calls

Call 1

Inputs
#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 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x)))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) x))))

Outputs

#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))))

Calls

4 calls:

3.0ms	x
2.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
2.0ms	(+.f64 (pow.f64 x #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 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.5%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify48.0ms (3.9%)

Memory

-2.9MiB live, 43.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	17	20
2	33	20
3	86	20
4	251	20
5	1467	20
6	5176	20

Stop Event

1×	node limit

Calls

Call 1

Inputs

#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))))

Outputs

#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))))

derivations4.0ms (0.4%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess13.0ms (1.1%)

Memory: 22.4MiB live, 22.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 104 to 66 computations (36.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample640.0ms (51.9%)

explain73.0ms (5.9%)

preprocess156.0ms (12.6%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite51.0ms (4.1%)

eval4.0ms (0.3%)

prune7.0ms (0.6%)

series2.0ms (0.1%)

rewrite40.0ms (3.3%)

eval2.0ms (0.1%)

prune2.0ms (0.2%)

series2.0ms (0.1%)

rewrite20.0ms (1.6%)

eval2.0ms (0.2%)

prune5.0ms (0.4%)

series67.0ms (5.4%)

rewrite55.0ms (4.5%)

eval4.0ms (0.3%)

prune23.0ms (1.8%)

regimes10.0ms (0.8%)

simplify48.0ms (3.9%)

derivations4.0ms (0.4%)

preprocess13.0ms (1.1%)

end0.0ms (0%)

Profiling