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

0.5MiB live, 0.5MiB 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)

sample634.0ms (56%)

Memory

11.5MiB live, 569.5MiB allocated; 102ms collecting garbage

Samples

378.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 194.0ms

ival-mult: 125.0ms (64.5% of total)

ival-sqrt: 57.0ms (29.4% of total)

exact: 6.0ms (3.1% of total)

ival-assert: 3.0ms (1.5% of total)

adjust: 2.0ms (1% of total)

Bogosity

explain62.0ms (5.4%)

Memory

-15.3MiB live, 87.0MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
124	-	1	(-2.213483507942375e-160)	`(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	70	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	overflow	70
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	uflow-rescue	53	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	underflow	53

Confusion

	Predicted +	Predicted -
+	123	1
-	0	132

Precision

1.0

Recall

0.9919354838709677

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	123	0	1
-	0	0	132

Precision?

1.0

Recall?

0.9919354838709677

Freqs

test

number	freq
0	133
1	123

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 7.0ms (62.3% of total)

ival-sqrt: 3.0ms (26.7% 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)

preprocess251.0ms (22.1%)

Memory

-2.9MiB live, 136.3MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (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
0	5	6
0	8	6
1	15	6
2	28	6
3	90	6
4	232	6
5	818	6
6	4263	6
0	8038	3

Stop Event

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

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

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.0%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series4.0ms (0.4%)

Memory

6.0MiB live, 6.0MiB 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
2.0ms	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)

rewrite35.0ms (3.1%)

Memory

36.3MiB live, 36.3MiB allocated; 0ms 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))))

eval26.0ms (2.3%)

Memory: -24.4MiB live, 22.8MiB allocated; 8ms collecting garbage
Compiler: Compiled 513 to 135 computations (73.7% saved)

prune12.0ms (1%)

Memory

20.2MiB live, 20.2MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	3	61

Accuracy

100.0%

Counts

61 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(hypot.f64 (neg.f64 x) (neg.f64 x))
✓	55.0%	(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 22 to 17 computations (22.7% saved)

series2.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

Counts

5 → 4

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

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

rewrite24.0ms (2.1%)

Memory

-21.3MiB live, 23.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	55
0	20	54
1	38	54
0	100	45

Stop Event

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

Counts

9 → 13

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

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

eval2.0ms (0.1%)

Memory: 2.2MiB live, 2.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 149 to 35 computations (76.5% saved)

prune2.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	12	0	12
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	12	3	15

Accuracy

100.0%

Counts

15 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 (neg.f64 x) (neg.f64 x))
✓	55.0%	(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 22 to 17 computations (22.7% saved)

series2.0ms (0.2%)

Memory

3.3MiB live, 3.3MiB allocated; 0ms collecting garbage

Counts

3 → 4

Calls

Call 1

Inputs
(hypot.f64 (neg.f64 x) (neg.f64 x))
(neg.f64 x)
x

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

Calls

3 calls:

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

rewrite57.0ms (5%)

Memory

1.3MiB live, 47.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	39
0	18	37
1	54	28
0	413	28

Stop Event

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

Counts

7 → 19

Calls

Call 1

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

eval2.0ms (0.2%)

Memory: 3.5MiB live, 3.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 182 to 60 computations (67% saved)

prune4.0ms (0.3%)

Memory

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

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	25	3	28

Accuracy

100.0%

Counts

28 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 (neg.f64 x) (neg.f64 x))
✓	55.0%	(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 44 to 34 computations (22.7% saved)

derivations2.0ms (0.2%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 5 to 3 computations (40% saved)

preprocess13.0ms (1.1%)

Memory: -32.7MiB live, 14.2MiB allocated; 2ms collecting garbage
Remove: (abs x)
Compiler: Compiled 32 to 22 computations (31.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample634.0ms (56%)

explain62.0ms (5.4%)

preprocess251.0ms (22.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.4%)

rewrite35.0ms (3.1%)

eval26.0ms (2.3%)

prune12.0ms (1%)

series2.0ms (0.1%)

rewrite24.0ms (2.1%)

eval2.0ms (0.1%)

prune2.0ms (0.2%)

series2.0ms (0.2%)

rewrite57.0ms (5%)

eval2.0ms (0.2%)

prune4.0ms (0.3%)

derivations2.0ms (0.2%)

preprocess13.0ms (1.1%)

end0.0ms (0%)

Profiling