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)

sample608.0ms (63.9%)

Memory

14.4MiB live, 719.7MiB allocated; 138ms collecting garbage

Samples

397.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 226.0ms

ival-mult!: 129.0ms (57.2% of total)

ival-sqrt: 95.0ms (42.1% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

explain58.0ms (6.1%)

Memory

-26.3MiB live, 111.3MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
128	-	2	(3.1361552740938455e-159)	`(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))`	oflow-rescue	68	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	overflow	68
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	uflow-rescue	58	0
↳	`(.f64 (.f64 #s(literal 2 binary64) 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

20.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult!: 5.0ms (55.3% of total)

ival-sqrt: 4.0ms (44.2% of total)

adjust: 0.0ms (0% of total)

preprocess80.0ms (8.4%)

Memory

-10.0MiB live, 42.3MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	25	19
2	62	19
3	196	19
4	333	19
5	1011	19
6	4908	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

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

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series4.0ms (0.4%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

5 → 5

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
#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 (* 2 x) #s(hole binary64 (* 2 x)))
#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
1.0ms	x	@	inf	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)
1.0ms	x	@	0	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)
1.0ms	x	@	-inf	((sqrt (* (* 2 x) x)) (* (* 2 x) x) (* 2 x) 2 x)

rewrite37.0ms (3.9%)

Memory

17.0MiB live, 63.8MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	48	60
0	150	51

Stop Event

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

Counts

10 → 58

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

eval5.0ms (0.5%)

Memory: 10.1MiB live, 10.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 477 to 133 computations (72.1% saved)

prune2.0ms (0.2%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Accuracy

100.0%

Counts

55 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	2.1%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 15 to 12 computations (20% saved)

series4.0ms (0.5%)

Memory

-40.1MiB live, 7.3MiB allocated; 2ms collecting garbage

Counts

7 → 7

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite50.0ms (5.3%)

Memory

17.5MiB live, 64.1MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	89
0	31	75
1	67	70
0	328	70

Stop Event

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

Counts

14 → 46

Calls

Call 1

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

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

eval3.0ms (0.3%)

Memory: 4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 399 to 110 computations (72.4% saved)

prune2.0ms (0.2%)

Memory

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

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	29	2	31

Accuracy

100.0%

Counts

31 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	2.1%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 36 to 26 computations (27.8% saved)

regimes4.0ms (0.5%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Accuracy

Total -62.6b remaining (-801698.2%)

Threshold costs -62.6b (-801698.2%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

3 calls:

2.0ms	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
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)

derivations2.0ms (0.2%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 3 to 2 computations (33.3% saved)

preprocess92.0ms (9.7%)

Memory: -29.2MiB live, 29.8MiB allocated; 109ms collecting garbage
Remove: (abs x)
Compiler: Compiled 24 to 18 computations (25% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample608.0ms (63.9%)

explain58.0ms (6.1%)

preprocess80.0ms (8.4%)

series4.0ms (0.4%)

rewrite37.0ms (3.9%)

eval5.0ms (0.5%)

prune2.0ms (0.2%)

series4.0ms (0.5%)

rewrite50.0ms (5.3%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

regimes4.0ms (0.5%)

derivations2.0ms (0.2%)

preprocess92.0ms (9.7%)

end0.0ms (0%)

Profiling