Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

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 4 computations (60% saved)

sample504.0ms (20.1%)

Memory

-6.3MiB live, 580.7MiB allocated

Samples

317.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-hypot: 142.0ms (94.5% of total)

ival-true: 6.0ms (4% of total)

ival-assert: 3.0ms (2% of total)

Bogosity

explain153.0ms (6.1%)

Memory

26.4MiB live, 109.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
129	-	4	(-7.720522716999659e-159)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	64	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	64
↳	`(*.f64 x x)`	overflow	126
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	61	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	60
↳	`(*.f64 x x)`	underflow	122

Confusion

	Predicted +	Predicted -
+	125	4
-	0	127

Precision

1.0

Recall

0.9689922480620154

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	0	4
-	0	0	127

Precision?

1.0

Recall?

0.9689922480620154

Freqs

test

number	freq
0	131
1	125

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 88 to 24 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-hypot: 8.0ms (53.9% of total)

ival-mult: 4.0ms (26.9% of total)

ival-add: 2.0ms (13.5% of total)

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

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

preprocess45.0ms (1.8%)

Memory

-26.3MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

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

Symmetry

(abs x)

Compiler

Compiled 8 to 4 computations (50% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 8 to 4 computations (50% saved)

simplify3.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-5184	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	192	(+.f64 (.f64 x x) (.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	19
0	7	15
1	11	15
2	14	15
3	17	15
0	17	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize16.0ms (0.6%)

Memory

16.6MiB live, 16.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (.f64 x x) (.f64 x x))
accuracy	29.53952379132468	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

12.0ms

256×

valid

Compiler

Compiled 40 to 10 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-hypot: 4.0ms (57.7% of total)

ival-mult: 2.0ms (28.9% of total)

ival-add: 1.0ms (14.4% of total)

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

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

series3.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated

Counts

3 → 4

Calls

Call 1

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

Outputs
(* 2 (pow x 2))
(pow x 2)
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))

Calls

3 calls:

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

simplify4.0ms (0.2%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	15	17
2	32	17
3	37	17
4	41	17
5	53	17
6	65	17
7	76	17
8	96	17
9	101	17
0	101	17

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 4

Calls

Call 1

Inputs
(* 2 (pow x 2))
(pow x 2)
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))

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

rewrite57.0ms (2.3%)

Memory

-10.3MiB live, 27.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

Outputs
(.f64 (.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 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 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(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)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))

eval4.0ms (0.2%)

Memory: 4.7MiB live, 4.7MiB allocated
Compiler: Compiled 370 to 110 computations (70.3% saved)

prune2.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	4	43

Accuracy

100.0%

Counts

43 → 4

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 #s(literal 2 binary64) x)))
▶	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify3.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(hypot.f64 x x)
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
cost-diff	-5184	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54
0	25	51
1	33	51
2	34	51
0	34	51

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize105.0ms (4.2%)

Memory

-5.8MiB live, 48.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.015625	(hypot.f64 x x)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.3515625	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	29.53952379132468	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.4609375	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

29.0ms

256×

valid

Compiler

Compiled 120 to 30 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 7.0ms (40.3% of total)

ival-sqrt: 6.0ms (34.5% of total)

ival-hypot: 4.0ms (23% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.5%)

Memory

-30.0MiB live, 7.7MiB allocated

Counts

11 → 10

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Calls

3 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x x) 2) (* x x) (sqrt (* (* x x) 2)) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))
3.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x x) 2) (* x x) (sqrt (* (* x x) 2)) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x x) 2) (* x x) (sqrt (* (* x x) 2)) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

8.0ms

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

3.0ms

-inf

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

1.0ms

inf

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

simplify132.0ms (5.3%)

Memory

9.4MiB live, 47.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	46
1	50	46
2	136	46
3	263	46
4	491	46
5	809	46
6	1420	46
7	1546	46
8	1601	46
9	1639	46
10	1822	46
11	2036	46
12	2080	46
13	2108	46
14	2112	46
15	2112	46
16	2253	46
17	2437	46
18	3518	46
19	3636	46
20	3660	46
21	3668	46
22	3672	46
23	3676	46
24	3788	46
25	3836	46
26	3836	46
27	4001	46
0	4001	46

Stop Event

1×	iter limit
1×	saturated

Counts

10 → 10

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

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

rewrite29.0ms (1.2%)

Memory

1.7MiB live, 39.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
0	25	40
1	53	38
0	203	38

Stop Event

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

Counts

11 → 83

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* 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)))
(*.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 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 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 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 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 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) (-.f64 x x))
(+.f64 x x)
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 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 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))

eval6.0ms (0.2%)

Memory: 15.4MiB live, 15.3MiB allocated
Compiler: Compiled 584 to 173 computations (70.4% saved)

prune3.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	62	5	67

Accuracy

100.0%

Counts

67 → 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)))
✓	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 45 to 31 computations (31.1% saved)

simplify15.0ms (0.6%)

Memory

-36.8MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
0	23	46
1	32	43
2	40	43
0	40	40

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize83.0ms (3.3%)

Memory

6.2MiB live, 43.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.3515625	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.4609375	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

26.0ms

256×

valid

Compiler

Compiled 102 to 29 computations (71.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 4.0ms (21.9% of total)

ival-hypot: 4.0ms (21.9% of total)

ival-log: 3.0ms (16.4% of total)

ival-sqrt: 3.0ms (16.4% of total)

ival-exp: 2.0ms (11% of total)

ival-add: 1.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

9 → 8

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify88.0ms (3.5%)

Memory

16.3MiB live, 54.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	46	38
2	130	38
3	257	38
4	492	38
5	806	38
6	1407	38
7	1535	38
8	1587	38
9	1611	38
10	1730	38
11	1921	38
12	1961	38
13	1989	38
14	1993	38
15	1993	38
16	2177	38
17	2281	38
18	2883	38
19	3229	38
20	3241	38
0	3241	38

Stop Event

1×	iter limit
1×	saturated

Counts

8 → 8

Calls

Call 1

Inputs
(* x (sqrt 2))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

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

rewrite48.0ms (1.9%)

Memory

-10.2MiB live, 28.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	23	39
1	52	34
0	261	31

Stop Event

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

Counts

9 → 71

Calls

Call 1

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

Outputs
(*.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 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (hypot.f64 x x) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (hypot.f64 x x))
(.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)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 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 (*.f64 x #s(literal 2 binary64)))
(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)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (hypot.f64 x x) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (hypot.f64 x x))
(.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)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 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 (*.f64 x #s(literal 2 binary64)))
(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)) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (.f64 x (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(+.f64 x x)
(log.f64 #s(literal 2 binary64))

eval6.0ms (0.3%)

Memory: 10.8MiB live, 10.8MiB allocated
Compiler: Compiled 695 to 190 computations (72.7% saved)

prune3.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	0	0
Picked	1	1	2
Done	0	3	3
Total	62	5	67

Accuracy

100.0%

Counts

67 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	32.1%	(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify143.0ms (5.7%)

Memory

10.4MiB live, 127.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	7488	(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	53
0	19	49
1	28	49
2	61	31
3	154	31
4	479	31
5	1857	31
6	2833	31
7	3822	31
8	4419	31
9	5290	31
10	5657	31
11	5819	31
12	5949	31
13	6804	31
14	7055	31
0	8142	31

Stop Event

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

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
(sqrt.f64 x)
x
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(fma.f64 x x #s(literal 0 binary64))
#s(literal 0 binary64)

Outputs
(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(sqrt.f64 x)
x
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(fma.f64 x x #s(literal 0 binary64))
(*.f64 x x)
#s(literal 0 binary64)

localize44.0ms (1.8%)

Memory

-11.5MiB live, 71.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64))))
accuracy	0	(sqrt.f64 x)
accuracy	0.3515625	(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
accuracy	41.99573326169967	(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))

Samples

36.0ms

256×

valid

Compiler

Compiled 112 to 25 computations (77.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sqrt: 8.0ms (44.5% of total)

ival-mult: 4.0ms (22.2% of total)

ival-pow: 3.0ms (16.7% of total)

ival-div: 1.0ms (5.6% of total)

ival-add: 1.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Counts

5 → 8

Calls

Call 1

Inputs
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 x x #s(literal 0 binary64))
(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
(sqrt.f64 x)
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64))))

Outputs
(* 2 x)
(pow x 2)
(* x (sqrt 2))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

((/ (* 2 (pow x 3)) (+ (* x x) 0)) (+ (* x x) 0) (* (sqrt x) (sqrt (/ (* 2 (pow x 3)) (+ (* x x) 0)))) (sqrt x) (sqrt (/ (* 2 (pow x 3)) (+ (* x x) 0))))

1.0ms

inf

((/ (* 2 (pow x 3)) (+ (* x x) 0)) (+ (* x x) 0) (* (sqrt x) (sqrt (/ (* 2 (pow x 3)) (+ (* x x) 0)))) (sqrt x) (sqrt (/ (* 2 (pow x 3)) (+ (* x x) 0))))

1.0ms

((/ (* 2 (pow x 3)) (+ (* x x) 0)) (+ (* x x) 0) (* (sqrt x) (sqrt (/ (* 2 (pow x 3)) (+ (* x x) 0)))) (sqrt x) (sqrt (/ (* 2 (pow x 3)) (+ (* x x) 0))))

simplify94.0ms (3.7%)

Memory

-10.2MiB live, 27.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	44	36
2	118	36
3	244	36
4	476	36
5	794	36
6	1297	36
7	1418	36
8	1469	36
9	1509	36
10	1659	36
11	1856	36
12	1896	36
13	1924	36
14	1928	36
15	1928	36
16	2126	36
17	2262	36
18	3019	36
19	3322	36
20	3338	36
21	3338	36
0	3338	36

Stop Event

1×	iter limit
1×	saturated

Counts

8 → 8

Calls

Call 1

Inputs
(* 2 x)
(pow x 2)
(* x (sqrt 2))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

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

rewrite144.0ms (5.7%)

Memory

-11.0MiB live, 178.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	41
0	19	36
1	68	21
2	456	16
3	5369	16
0	8177	16

Stop Event

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

Counts

5 → 747

Calls

Call 1

Inputs
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 x x #s(literal 0 binary64))
(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
(sqrt.f64 x)
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64))))

Outputs
(.f64 (/.f64 (.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 x x) (pow.f64 x #s(literal -4 binary64))))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)) (neg.f64 (pow.f64 x #s(literal 4 binary64)))) (*.f64 (neg.f64 x) x))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (neg.f64 x) x))
(.f64 (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal -2 binary64)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) x) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal -4 binary64)))
(.f64 (.f64 (/.f64 #s(literal 2 binary64) x) x) x)
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -3 binary64))) (pow.f64 x #s(literal 3 binary64))) x)
(.f64 (.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -3 binary64))) x) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))) x)
(.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -2 binary64)))
(.f64 (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (/.f64 #s(literal -2 binary64) x))
(.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 2 binary64) (neg.f64 x)) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) x))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal -4 binary64))))
(.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 x (pow.f64 x #s(literal -4 binary64))))
(.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal -4 binary64))))
(.f64 (/.f64 (.f64 x x) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal -4 binary64))))
(.f64 (/.f64 x (pow.f64 x #s(literal 6 binary64))) (/.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) (pow.f64 x #s(literal -4 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)) (neg.f64 x)))
(*.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))
(*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal -4 binary64))))
(*.f64 (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) x) (/.f64 #s(literal 2 binary64) (neg.f64 x)))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal -2 binary64))))
(.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 3 binary64)))
(.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))))
(*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal -2 binary64))))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) x) (sqrt.f64 x))
(.f64 (/.f64 (.f64 x #s(literal 2 binary64)) x) x)
(.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(.f64 (pow.f64 x #s(literal -3 binary64)) (/.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))))
(*.f64 (pow.f64 x #s(literal -3 binary64)) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -4 binary64))))
(.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 2 binary64) x) (.f64 x x))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -3 binary64))) (pow.f64 x #s(literal 4 binary64)))
(.f64 (pow.f64 x #s(literal -4 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 5 binary64))))
(.f64 (pow.f64 x #s(literal -6 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)))
(.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))) (.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 x #s(literal -2 binary64)))))
(*.f64 #s(literal -2 binary64) (neg.f64 x))
(.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) x))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) (*.f64 x x)))
(*.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -2 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -3 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(.f64 (.f64 x x) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) x))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 (*.f64 x #s(literal 2 binary64))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(.f64 (sqrt.f64 x) (/.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) x))
(.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64)))
(.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -2 binary64) (neg.f64 (pow.f64 x #s(literal -2 binary64)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)))
(.f64 x (.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (pow.f64 x #s(literal -2 binary64))))
(.f64 x (.f64 (.f64 x x) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64))))
(.f64 x (/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (.f64 x x)))
(.f64 x (/.f64 (.f64 x #s(literal 2 binary64)) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(pow.f64 (.f64 (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))) (exp.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x #s(literal 2 binary64)) (exp.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (.f64 (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))) (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))
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(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(pow.f64 (.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1/4 binary64))
(pow.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal -1 binary64))) (.f64 x x))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal -3 binary64))) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal -2 binary64)))
(/.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 x x)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) x)
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 x))
(/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) x)
(/.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(neg.f64 (/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) x))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 x)))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))

eval353.0ms (14.1%)

Memory: -12.1MiB live, 139.9MiB allocated
Compiler: Compiled 13 234 to 2 553 computations (80.7% saved)

prune15.0ms (0.6%)

Memory

7.3MiB live, 44.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	752	2	754
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	753	6	759

Accuracy

100.0%

Counts

759 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	99.4%	(/.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)))
	99.3%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 135 to 75 computations (44.4% saved)

regimes17.0ms (0.7%)

Memory

-12.8MiB live, 25.4MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
(/.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)))
(hypot.f64 x x)
(.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))))
#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Outputs
(hypot.f64 x x)

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
4.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes11.0ms (0.4%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
3.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes251.0ms (10%)

Memory

-37.0MiB live, 11.5MiB allocated

Accuracy

Total -29.3b remaining (-6363.1%)

Threshold costs -29.3b (-6363.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

245.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 10 computations (47.4% saved)

simplify20.0ms (0.8%)

Memory

27.6MiB live, 27.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	15	23

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness50.0ms (2%)

Memory

-0.1MiB live, 37.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	8	17
1	15	17
2	32	17
3	37	17
4	41	17
5	53	17
6	65	17
7	76	17
8	96	17
9	101	17
0	101	17
0	16	47
0	25	40
1	53	38
0	203	38

Stop Event

1×	fuel
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 67 to 40 computations (40.3% saved)

preprocess32.0ms (1.3%)

Memory: -4.0MiB live, 33.4MiB allocated
Remove: (abs x)
Compiler: Compiled 74 to 42 computations (43.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	8	17
1	15	17
2	32	17
3	37	17
4	41	17
5	53	17
6	65	17
7	76	17
8	96	17
9	101	17
0	101	17
0	16	47
0	25	40
1	53	38
0	203	38

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	8	17
1	15	17
2	32	17
3	37	17
4	41	17
5	53	17
6	65	17
7	76	17
8	96	17
9	101	17
0	101	17
0	16	47
0	25	40
1	53	38
0	203	38

start0.0ms (0%)

analyze0.0ms (0%)

sample504.0ms (20.1%)

explain153.0ms (6.1%)

preprocess45.0ms (1.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize16.0ms (0.6%)

series3.0ms (0.1%)

simplify4.0ms (0.2%)

rewrite57.0ms (2.3%)

eval4.0ms (0.2%)

prune2.0ms (0.1%)

simplify3.0ms (0.1%)

localize105.0ms (4.2%)

series13.0ms (0.5%)

simplify132.0ms (5.3%)

rewrite29.0ms (1.2%)

eval6.0ms (0.2%)

prune3.0ms (0.1%)

simplify15.0ms (0.6%)

localize83.0ms (3.3%)

series3.0ms (0.1%)

simplify88.0ms (3.5%)

rewrite48.0ms (1.9%)

eval6.0ms (0.3%)

prune3.0ms (0.1%)

simplify143.0ms (5.7%)

localize44.0ms (1.8%)

series3.0ms (0.1%)

simplify94.0ms (3.7%)

rewrite144.0ms (5.7%)

eval353.0ms (14.1%)

prune15.0ms (0.6%)

regimes17.0ms (0.7%)

regimes11.0ms (0.4%)

regimes251.0ms (10%)

simplify20.0ms (0.8%)

soundness50.0ms (2%)

preprocess32.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	8	17
1	15	17
2	32	17
3	37	17
4	41	17
5	53	17
6	65	17
7	76	17
8	96	17
9	101	17
0	101	17
0	16	47
0	25	40
1	53	38
0	203	38