Metrics for sqrt B (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample733.0ms (33.9%)

Memory

7.2MiB live, 649.8MiB allocated; 112ms collecting garbage

Samples

518.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 291.0ms

ival-sqrt: 167.0ms (57.4% of total)

ival-mult: 110.0ms (37.8% of total)

ival-true: 5.0ms (1.7% of total)

exact: 5.0ms (1.7% of total)

ival-assert: 3.0ms (1% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

explain89.0ms (4.1%)

Memory

-15.1MiB live, 106.7MiB allocated; 65ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
126	-	2	(1.9632199916543745e-162)	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	uflow-rescue	63	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	underflow	63
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	oflow-rescue	61	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	overflow	61

Confusion

	Predicted +	Predicted -
+	124	2
-	0	130

Precision

1.0

Recall

0.9841269841269841

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	124	0	2
-	0	0	130

Precision?

1.0

Recall?

0.9841269841269841

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-sqrt: 39.0ms (82.1% of total)

ival-mult: 7.0ms (14.7% 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)

preprocess28.0ms (1.3%)

Memory

3.8MiB live, 48.1MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	18	13
2	49	13
3	102	13
4	147	13
5	235	13
6	255	13
7	275	13
0	5	6
0	8	6
1	15	6
2	23	6
3	54	6
4	120	6
5	184	6
6	220	6
7	240	6
8	260	6
0	260	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.3%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	15	16
2	23	16
3	54	16
4	120	16
5	184	16
6	220	16
7	240	16
8	260	16
0	260	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.9%)

Memory

-17.7MiB live, 26.9MiB allocated; 8ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 #s(literal 2 binary64) x) x)
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	29.21477555295001	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Samples

10.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (59.9% of total)

ival-sqrt: 2.0ms (39.9% 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)

series4.0ms (0.2%)

Memory

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

Counts

3 → 4

Calls

Call 1

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

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

Calls

3 calls:

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

simplify8.0ms (0.4%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	21	17
2	42	17
3	90	17
4	228	17
5	439	17
6	502	17
0	502	17

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 4

Calls

Call 1

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

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

rewrite39.0ms (1.8%)

Memory

9.9MiB live, 54.7MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	12
1	20	12
2	57	10
0	280	9

Stop Event

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

Counts

3 → 109

Calls

Call 1

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

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

eval7.0ms (0.3%)

Memory: 17.6MiB live, 17.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 644 to 172 computations (73.3% saved)

prune17.0ms (0.8%)

Memory

-31.0MiB live, 19.6MiB allocated; 23ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Accuracy

100.0%

Counts

81 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	30.8%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
▶	7.1%	(sqrt.f64 (+.f64 x x))
✓	54.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
▶	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 37 to 29 computations (21.6% saved)

simplify317.0ms (14.6%)

Memory

10.2MiB live, 277.1MiB allocated; 43ms collecting garbage

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(hypot.f64 x x)
cost-diff	1	(fma.f64 x x #s(literal 0 binary64))
cost-diff	2	(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
cost-diff	3	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
cost-diff	4	(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
cost-diff	0	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
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 (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	79
0	32	82
1	57	74
2	174	68
3	848	56
4	6176	56
0	8326	56

Stop Event

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

Calls

Call 1

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

Outputs
#s(approx (sqrt (* (* 2 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 x x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(+.f64 x x)
(*.f64 x #s(literal 2 binary64))
x
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
(hypot.f64 x x)
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 x x #s(literal 0 binary64))
(*.f64 x x)
#s(literal 0 binary64)
(hypot.f64 x x)
x

localize48.0ms (2.2%)

Memory

17.7MiB live, 63.2MiB allocated; 4ms collecting garbage

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.015625	(hypot.f64 x x)
accuracy	0.0078125	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	0.08984375	(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
accuracy	29.21477555295001	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
accuracy	40.41937789980474	(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(sqrt.f64 (+.f64 x x))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.35546875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

37.0ms

256×

valid

Compiler

Compiled 84 to 21 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 8.0ms (31.9% of total)

ival-sqrt: 6.0ms (24% of total)

ival-hypot: 4.0ms (16% of total)

ival-pow: 3.0ms (12% of total)

ival-add: 2.0ms (8% of total)

ival-div: 1.0ms (4% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.4%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Counts

11 → 9

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(* (sqrt x) (sqrt 2))
(* 2 x)
(* 2 (pow x 2))
(* 2 (pow x 4))
(pow x 2)
(* 2 (pow x 3))
(* -1 (* x (sqrt 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) (sqrt (+ x x)) (+ x x) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (* (* 2 (pow x 3)) x) (+ (* x x) 0) (sqrt (+ (* x x) (* x x))) (* 2 (pow x 3)))
2.0ms	x	@	inf	((sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) (sqrt (+ x x)) (+ x x) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (* (* 2 (pow x 3)) x) (+ (* x x) 0) (sqrt (+ (* x x) (* x x))) (* 2 (pow x 3)))
2.0ms	x	@	0	((sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) (sqrt (+ x x)) (+ x x) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (* (* 2 (pow x 3)) x) (+ (* x x) 0) (sqrt (+ (* x x) (* x x))) (* 2 (pow x 3)))

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify38.0ms (1.7%)

Memory

-34.5MiB live, 20.7MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	50	44
2	112	44
3	238	44
4	513	44
5	906	44
6	980	44
7	986	44
8	990	44
9	993	44
10	998	44
11	1021	44
12	1092	44
13	1178	44
0	1178	44

Stop Event

1×	iter limit
1×	saturated

Counts

9 → 9

Calls

Call 1

Inputs
(* x (sqrt 2))
(* (sqrt x) (sqrt 2))
(* 2 x)
(* 2 (pow x 2))
(* 2 (pow x 4))
(pow x 2)
(* 2 (pow x 3))
(* -1 (* x (sqrt 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* 2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))

rewrite41.0ms (1.9%)

Memory

5.9MiB live, 51.7MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	68
0	32	38
1	106	22
0	824	22

Stop Event

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

Counts

11 → 46

Calls

Call 1

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

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

eval4.0ms (0.2%)

Memory: 7.9MiB live, 7.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 707 to 182 computations (74.3% saved)

prune3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	47	6	53

Accuracy

100.0%

Counts

53 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	30.8%	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
✓	7.1%	(sqrt.f64 (+.f64 x x))
✓	54.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
✓	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	3.9%	#s(literal 0 binary64)

Compiler

Compiled 44 to 36 computations (18.2% saved)

simplify58.0ms (2.7%)

Memory

-4.8MiB live, 39.3MiB allocated; 14ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
cost-diff	1	(fma.f64 x x #s(literal 0 binary64))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	67
0	20	64
1	37	58
2	102	58
3	481	58
4	1355	58
5	2171	58
6	2371	58
7	2553	58
8	2595	58
9	2595	58
10	2595	58
11	2595	58
0	2595	58

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 0 binary64)
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 2 binary64)
(fma.f64 x x #s(literal 0 binary64))
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 2 binary64)
(fma.f64 x x #s(literal 0 binary64))
(*.f64 x x)
#s(literal 0 binary64)

localize38.0ms (1.8%)

Memory

7.1MiB live, 51.7MiB allocated; 9ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
accuracy	0.0	#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
accuracy	29.21477555295001	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
accuracy	40.41937789980474	(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))

Samples

30.0ms

256×

valid

Compiler

Compiled 54 to 16 computations (70.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 12.0ms (53.7% of total)

ival-pow: 5.0ms (22.4% of total)

ival-sqrt: 2.0ms (8.9% of total)

ival-div: 1.0ms (4.5% of total)

ival-add: 1.0ms (4.5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.2%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

Inputs
(fma.f64 x x #s(literal 0 binary64))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))

Outputs
(pow x 2)
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 4))
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((+ (* x x) 0) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2))

1.0ms

-inf

((+ (* x x) 0) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2))

1.0ms

((+ (* x x) 0) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2))

simplify9.0ms (0.4%)

Memory

12.7MiB live, 12.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	23	22
2	48	22
3	96	22
4	232	22
5	436	22
6	478	22
0	478	22

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 5

Calls

Call 1

Inputs
(pow x 2)
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 4))
(* -1 (* x (sqrt 2)))

Outputs
(pow x 2)
(*.f64 x x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(* 2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite190.0ms (8.8%)

Memory

-42.6MiB live, 119.6MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	59
0	20	56
1	73	49
2	442	20
3	4939	20
0	9384	20

Stop Event

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

Counts

5 → 284

Calls

Call 1

Inputs
(fma.f64 x x #s(literal 0 binary64))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))

Outputs
(*.f64 (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 5/2 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -8 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 6 binary64)))
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(fma.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64)) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 0 binary64) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(fma.f64 (.f64 x x) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 x x) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(fma.f64 (.f64 x x) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 0 binary64)))
(fma.f64 (.f64 x x) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(+.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(+.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(+.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(+.f64 (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 0 binary64)) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(+.f64 (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))))
(+.f64 (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 0 binary64)) (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x))
(+.f64 (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x) (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x) (.f64 #s(literal 0 binary64) (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(+.f64 (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 0 binary64)))
(+.f64 (/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64)) x) x) (.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) #s(literal 0 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 0 binary64)))
#s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64))
(neg.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) #s(literal 0 binary64))))
#s(literal 0 binary64)

eval28.0ms (1.3%)

Memory: 11.0MiB live, 55.0MiB allocated; 5ms collecting garbage
Compiler: Compiled 7 196 to 958 computations (86.7% saved)

prune6.0ms (0.3%)

Memory

20.4MiB live, 20.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	289	6	295

Accuracy

100.0%

Counts

295 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	30.8%	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
✓	7.1%	(sqrt.f64 (+.f64 x x))
✓	54.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
✓	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 43 to 35 computations (18.6% saved)

simplify35.0ms (1.6%)

Memory

-38.3MiB live, 16.7MiB allocated; 9ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
cost-diff	0	#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))
cost-diff	0	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	62
0	18	62
1	34	56
2	85	56
3	334	56
4	829	56
5	1136	56
6	1266	56
7	1350	56
8	1350	56
0	1350	56

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 2 binary64)
(*.f64 x x)

Outputs
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 2 binary64)
(*.f64 x x)

localize105.0ms (4.9%)

Memory

-2.0MiB live, 43.4MiB allocated; 5ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
accuracy	29.21477555295001	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
accuracy	40.41937789980474	(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))

Samples

97.0ms

256×

valid

Compiler

Compiled 46 to 14 computations (69.6% saved)

Precisions

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

ival-mult: 6.0ms (41.2% of total)

ival-pow: 5.0ms (34.3% of total)

ival-sqrt: 2.0ms (13.7% of total)

ival-div: 1.0ms (6.9% 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)

series3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(*.f64 x x)

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 4))
(pow x 2)
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((sqrt (/ (* (* 2 (pow x 3)) x) (* x x))) (/ (* (* 2 (pow x 3)) x) (* x x)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2) (* x x))

1.0ms

-inf

((sqrt (/ (* (* 2 (pow x 3)) x) (* x x))) (/ (* (* 2 (pow x 3)) x) (* x x)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2) (* x x))

1.0ms

((sqrt (/ (* (* 2 (pow x 3)) x) (* x x))) (/ (* (* 2 (pow x 3)) x) (* x x)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2) (* x x))

simplify9.0ms (0.4%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	23	22
2	48	22
3	97	22
4	232	22
5	432	22
6	481	22
0	481	22

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 5

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 4))
(pow x 2)
(* -1 (* x (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(* 2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite61.0ms (2.8%)

Memory

19.0MiB live, 19.0MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	56
0	18	58
1	54	51
2	213	18
3	1333	16
0	5807	16

Stop Event

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

Counts

5 → 51

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(*.f64 x x)

Outputs
(.f64 (.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 #s(approx ( (* 2 (pow x 3)) x) x) #s(literal 1/4 binary64)) x) (/.f64 (pow.f64 #s(approx (* (* 2 (pow x 3)) x) x) #s(literal 1/4 binary64)) x))
(.f64 (neg.f64 (neg.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)))))
(.f64 (neg.f64 (neg.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)))) (neg.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(approx ( (* 2 (pow x 3)) x) x) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(approx (* (* 2 (pow x 3)) x) x) #s(literal 1/4 binary64)) x))
(.f64 (neg.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))) (neg.f64 (neg.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)))))
(.f64 (neg.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))))
(.f64 (neg.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))) (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x)))
(pow.f64 (neg.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx ( (* 2 (pow x 3)) x) x)) x))) (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))) (.f64 (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx ( (* 2 (pow x 3)) x) x)) x))) (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))))) (-.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) (-.f64 (.f64 (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx ( (* 2 (pow x 3)) x) x)) x))) (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))) (.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx ( (* 2 (pow x 3)) x) x)) x))) (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) x))))) x)
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) x)))) x)
(/.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x) x)
(/.f64 (neg.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x))) x)
(/.f64 (sqrt.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) x))) x)
(/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)
(neg.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x))
(fabs.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))
(exp.f64 (-.f64 (.f64 (log.f64 #s(approx ( (* 2 (pow x 3)) x) x)) #s(literal 1/2 binary64)) (log.f64 x)))
(exp.f64 (fma.f64 (log.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x)) #s(literal 1/4 binary64) (.f64 (log.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) x) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))
(+.f64 (neg.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))) (neg.f64 (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)))))
(+.f64 (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))))
(+.f64 (cosh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))) (sinh.f64 (log.f64 (/.f64 (sqrt.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x))))
(/.f64 (exp.f64 (log.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) x)))) x)
(/.f64 (exp.f64 (log.f64 #s(approx (* (* 2 (pow x 3)) x) x))) x)
(/.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) x)) x)
(/.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x) x)
(/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x)
(neg.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x))
(exp.f64 (log.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x)))
(+.f64 (cosh.f64 (log.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x))) (sinh.f64 (log.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) x) x))))
#s(approx (* (* 2 (pow x 3)) x) x)
(neg.f64 (neg.f64 #s(approx (* (* 2 (pow x 3)) x) x)))
x
#s(literal 0 binary64)
x
#s(literal 0 binary64)

eval5.0ms (0.3%)

Memory: 5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 245 to 146 computations (88.3% saved)

prune4.0ms (0.2%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	54	6	60

Accuracy

100.0%

Counts

60 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	30.8%	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
✓	7.1%	(sqrt.f64 (+.f64 x x))
✓	54.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
✓	99.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 118 to 71 computations (39.8% saved)

regimes17.0ms (0.8%)

Memory

-21.6MiB live, 22.9MiB allocated; 6ms collecting garbage

Counts

8 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(sqrt.f64 (+.f64 x x))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(hypot.f64 x x)
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))

Outputs
(hypot.f64 x x)

Calls

3 calls:

11.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
3.0ms	x
3.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes6.0ms (0.3%)

Memory

12.6MiB live, 12.6MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(sqrt.f64 (+.f64 x x))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes4.0ms (0.2%)

Memory

10.0MiB live, 10.0MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(sqrt.f64 (+.f64 x x))

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

Calls

3 calls:

1.0ms	x
1.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)
1.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Results

Accuracy	Segments	Branch
7.1%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
7.1%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
7.1%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes3.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

3 calls:

1.0ms	x
1.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
1.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

Accuracy	Segments	Branch
3.9%	1	`x`
3.9%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
3.9%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify45.0ms (2.1%)

Memory

-43.5MiB live, 52.4MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	19	19
2	26	19
3	60	19
4	137	19
5	223	19
6	421	19
7	2074	19
8	3272	19

Stop Event

1×	node limit

Calls

Call 1

Inputs
(hypot.f64 x x)
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (+.f64 x x))
#s(literal 0 binary64)

Outputs
(hypot.f64 x x)
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (+.f64 x x))
#s(literal 0 binary64)

derivations108.0ms (5%)

Memory

18.1MiB live, 110.0MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	21	17
2	42	17
3	90	17
4	228	17
5	439	17
6	502	17
0	502	17
0	5	14
0	8	12
1	20	12
2	57	10
0	280	9
0	19	68
0	32	38
1	106	22
0	824	22

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated

Compiler

Compiled 19 to 13 computations (31.6% saved)

preprocess17.0ms (0.8%)

Memory: 28.6MiB live, 28.6MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 56 to 40 computations (28.6% saved)

end0.0ms (0%)

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

Iter	Nodes	Cost
0	7	17
1	18	13
2	49	13
3	102	13
4	147	13
5	235	13
6	255	13
7	275	13
0	5	6
0	8	6
1	15	6
2	23	6
3	54	6
4	120	6
5	184	6
6	220	6
7	240	6
8	260	6
0	260	3

Iter	Nodes	Cost
0	9	17
1	21	17
2	42	17
3	90	17
4	228	17
5	439	17
6	502	17
0	502	17
0	5	14
0	8	12
1	20	12
2	57	10
0	280	9
0	19	68
0	32	38
1	106	22
0	824	22

Iter	Nodes	Cost
0	7	17
1	18	13
2	49	13
3	102	13
4	147	13
5	235	13
6	255	13
7	275	13
0	5	6
0	8	6
1	15	6
2	23	6
3	54	6
4	120	6
5	184	6
6	220	6
7	240	6
8	260	6
0	260	3

Iter	Nodes	Cost
0	9	17
1	21	17
2	42	17
3	90	17
4	228	17
5	439	17
6	502	17
0	502	17
0	5	14
0	8	12
1	20	12
2	57	10
0	280	9
0	19	68
0	32	38
1	106	22
0	824	22

start0.0ms (0%)

analyze0.0ms (0%)

sample733.0ms (33.9%)

explain89.0ms (4.1%)

preprocess28.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.3%)

localize20.0ms (0.9%)

series4.0ms (0.2%)

simplify8.0ms (0.4%)

rewrite39.0ms (1.8%)

eval7.0ms (0.3%)

prune17.0ms (0.8%)

simplify317.0ms (14.6%)

localize48.0ms (2.2%)

series8.0ms (0.4%)

simplify38.0ms (1.7%)

rewrite41.0ms (1.9%)

eval4.0ms (0.2%)

prune3.0ms (0.1%)

simplify58.0ms (2.7%)

localize38.0ms (1.8%)

series3.0ms (0.2%)

simplify9.0ms (0.4%)

rewrite190.0ms (8.8%)

eval28.0ms (1.3%)

prune6.0ms (0.3%)

simplify35.0ms (1.6%)

localize105.0ms (4.9%)

series3.0ms (0.1%)

simplify9.0ms (0.4%)

rewrite61.0ms (2.8%)

eval5.0ms (0.3%)

prune4.0ms (0.2%)

regimes17.0ms (0.8%)

regimes6.0ms (0.3%)

regimes4.0ms (0.2%)

regimes3.0ms (0.1%)

simplify45.0ms (2.1%)

derivations108.0ms (5%)

preprocess17.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	17
1	18	13
2	49	13
3	102	13
4	147	13
5	235	13
6	255	13
7	275	13
0	5	6
0	8	6
1	15	6
2	23	6
3	54	6
4	120	6
5	184	6
6	220	6
7	240	6
8	260	6
0	260	3

Iter	Nodes	Cost
0	9	17
1	21	17
2	42	17
3	90	17
4	228	17
5	439	17
6	502	17
0	502	17
0	5	14
0	8	12
1	20	12
2	57	10
0	280	9
0	19	68
0	32	38
1	106	22
0	824	22