Metrics for sqrt C (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)

sample583.0ms (58.4%)

Memory

2.7MiB live, 614.0MiB allocated; 166ms collecting garbage

Samples

408.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-mult!: 81.0ms (50.3% of total)

ival-sqrt: 79.0ms (49% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

explain82.0ms (8.2%)

Memory

-26.3MiB live, 73.7MiB allocated; 31ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
128	-	2	(3.1361552740938455e-159)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	68	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	68
↳	`(*.f64 x x)`	overflow	68
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	58	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	58
↳	`(*.f64 x x)`	underflow	58

Confusion

	Predicted +	Predicted -
+	126	2
-	0	128

Precision

1.0

Recall

0.984375

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	126	0	2
-	0	0	128

Precision?

1.0

Recall?

0.984375

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

41.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-sqrt: 25.0ms (82% of total)

ival-mult!: 5.0ms (16.4% of total)

adjust: 0.0ms (0% of total)

preprocess79.0ms (7.9%)

Memory

-7.9MiB live, 38.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	28	19
2	90	19
3	185	19
4	578	19
5	1314	19
6	4975	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series4.0ms (0.4%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)
1.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)

rewrite70.0ms (7%)

Memory

-3.2MiB live, 40.4MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	50	54
0	171	49

Stop Event

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

Counts

10 → 65

Calls

Call 1

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

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

eval7.0ms (0.7%)

Memory: 14.7MiB live, 14.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 527 to 156 computations (70.4% saved)

prune2.0ms (0.2%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	2	62

Accuracy

100.0%

Counts

62 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
✓	53.8%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0.1%)

Memory

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

Counts

2 → 3

Calls

Call 1

Inputs
(hypot.f64 x x)
x

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

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) x)
0.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) x)
0.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) x)

rewrite51.0ms (5.1%)

Memory

-2.2MiB live, 40.0MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	25
0	13	24
1	42	21
0	294	21

Stop Event

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

Counts

5 → 15

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 3.2MiB live, 3.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 101 to 46 computations (54.5% saved)

prune1.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	13	3	16

Accuracy

100.0%

Counts

16 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
▶	5.2%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 10 to 10 computations (0% saved)

series2.0ms (0.2%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Counts

5 → 3

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((sqrt 2) 2 (* (sqrt 2) (fabs x)) (fabs x) x)
0.0ms	x	@	inf	((sqrt 2) 2 (* (sqrt 2) (fabs x)) (fabs x) x)
0.0ms	x	@	0	((sqrt 2) 2 (* (sqrt 2) (fabs x)) (fabs x) x)

rewrite72.0ms (7.3%)

Memory

-42.3MiB live, 22.0MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
0	16	30
1	25	30
0	55	30

Stop Event

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

Counts

8 → 19

Calls

Call 1

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

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

eval8.0ms (0.8%)

Memory: 8.0MiB live, 8.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 118 to 44 computations (62.7% saved)

prune2.0ms (0.2%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	17	3	20

Accuracy

100.0%

Counts

20 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	5.2%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 26 to 19 computations (26.9% saved)

regimes7.0ms (0.7%)

Memory

12.9MiB live, 12.9MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
1.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
1.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes4.0ms (0.4%)

Memory

9.6MiB live, 9.6MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.2%	1	`(*.f64 x x)`
5.2%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
5.2%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
5.2%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

derivations3.0ms (0.3%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 5 to 4 computations (20% saved)

preprocess17.0ms (1.7%)

Memory: -14.7MiB live, 34.1MiB allocated; 5ms collecting garbage
Remove: (abs x)
Compiler: Compiled 32 to 28 computations (12.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample583.0ms (58.4%)

explain82.0ms (8.2%)

preprocess79.0ms (7.9%)

series4.0ms (0.4%)

rewrite70.0ms (7%)

eval7.0ms (0.7%)

prune2.0ms (0.2%)

series1.0ms (0.1%)

rewrite51.0ms (5.1%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

series2.0ms (0.2%)

rewrite72.0ms (7.3%)

eval8.0ms (0.8%)

prune2.0ms (0.2%)

regimes7.0ms (0.7%)

regimes4.0ms (0.4%)

derivations3.0ms (0.3%)

preprocess17.0ms (1.7%)

end0.0ms (0%)

Profiling