Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 4 computations (60% saved)

sample539.0ms (44.7%)

Memory

-3.9MiB live, 554.9MiB allocated; 97ms collecting garbage

Samples

331.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 177.0ms

ival-hypot: 171.0ms (96.9% of total)

adjust: 3.0ms (1.7% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain78.0ms (6.5%)

Memory

4.7MiB live, 101.0MiB allocated; 24ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	2	(2.0508404249783888e-156)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	68	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	68
↳	`(*.f64 x x)`	overflow	136
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	68	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	68
↳	`(*.f64 x x)`	underflow	136

Confusion

	Predicted +	Predicted -
+	136	2
-	0	118

Precision

1.0

Recall

0.9855072463768116

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	2
-	0	0	118

Precision?

1.0

Recall?

0.9855072463768116

Freqs

test

number	freq
0	120
1	136

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

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

ival-hypot: 9.0ms (59.4% of total)

ival-mult: 4.0ms (26.4% of total)

ival-add: 2.0ms (13.2% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess242.0ms (20.1%)

Memory

-12.8MiB live, 176.5MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	29	19
2	84	19
3	144	19
4	298	19
5	663	19
6	1542	19
7	3518	19
0	4	8
0	7	6
1	17	6
2	54	6
3	135	6
4	264	6
5	612	6
6	1430	6
7	5304	6
0	8068	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 4 computations (50% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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
▶	50.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 8 to 4 computations (50% saved)

series4.0ms (0.3%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite92.0ms (7.6%)

Memory

-4.9MiB live, 41.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	70
0	23	59
1	60	35
0	352	35

Stop Event

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

Counts

9 → 35

Calls

Call 1

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

eval5.0ms (0.5%)

Memory: 7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 546 to 150 computations (72.5% saved)

prune11.0ms (0.9%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Accuracy

99.8%

Counts

59 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
	16.6%	(/.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)))))
	99.5%	(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	50.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 35 to 28 computations (20% saved)

series2.0ms (0.1%)

Memory

1.7MiB live, 1.7MiB allocated; 0ms collecting garbage

Counts

5 → 3

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(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) (fabs x)) (sqrt 2) 2 (fabs x) x)
0.0ms	x	@	inf	((* (sqrt 2) (fabs x)) (sqrt 2) 2 (fabs x) x)
0.0ms	x	@	0	((* (sqrt 2) (fabs x)) (sqrt 2) 2 (fabs x) x)

rewrite19.0ms (1.6%)

Memory

19.6MiB live, 19.6MiB allocated; 0ms 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
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(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 (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 (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 (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)

eval4.0ms (0.3%)

Memory: -42.9MiB live, 2.9MiB allocated; 4ms collecting garbage
Compiler: Compiled 128 to 45 computations (64.8% saved)

prune5.0ms (0.4%)

Memory

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

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	19	4	23

Accuracy

100.0%

Counts

23 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
▶	99.1%	(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	50.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 32 to 23 computations (28.1% saved)

series1.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Counts

7 → 3

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 x))
(*.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 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(fabs.f64 x)
x

Outputs
#s(approx (* (* (pow 2 1/4) (pow 2 1/4)) (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
0.0ms	x	@	-inf	((* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 (fabs x) x)
0.0ms	x	@	inf	((* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 (fabs x) x)
0.0ms	x	@	0	((* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 (fabs x) x)

Time

Variable

Point

Expression

0.0ms

-inf

((* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 (fabs x) x)

0.0ms

inf

((* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 (fabs x) x)

0.0ms

((* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (* (pow 2 1/4) (pow 2 1/4)) (pow 2 1/4) 2 1/4 (fabs x) x)

rewrite18.0ms (1.5%)

Memory

23.4MiB live, 23.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
0	20	34
0	49	34

Stop Event

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

Counts

10 → 22

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 x))
(*.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 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(fabs.f64 x)
x
#s(approx (* (* (pow 2 1/4) (pow 2 1/4)) (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 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x)))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 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 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(sqrt.f64 (*.f64 x x))
(fabs.f64 (neg.f64 x))
(fabs.f64 x)
x
#s(approx (* (* (pow 2 1/4) (pow 2 1/4)) (fabs x)) (*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (fabs x) (fabs.f64 x))
#s(approx x x)

eval2.0ms (0.2%)

Memory: 4.1MiB live, 4.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 275 to 58 computations (78.9% saved)

prune4.0ms (0.4%)

Memory

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

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	26	5	31

Accuracy

100.0%

Counts

31 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
▶	99.3%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x)))
✓	99.1%	(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
✓	50.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

series72.0ms (6%)

Memory

-51.2MiB live, 55.4MiB allocated; 31ms collecting garbage

Counts

7 → 4

Calls

Call 1

Inputs
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x))
(fabs.f64 x)
x

Outputs
#s(approx (* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) #s(hole binary64 (* (fabs x) (sqrt 2))))
#s(approx (* (pow 2 1/4) (fabs x)) #s(hole binary64 (* (pow 2 1/4) (fabs x))))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx x #s(hole binary64 x))

Calls

3 calls:

Time	Variable		Point	Expression
54.0ms	x	@	0	((* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) (fabs x)) (fabs x) x)
11.0ms	x	@	-inf	((* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) (fabs x)) (fabs x) x)
6.0ms	x	@	inf	((* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) (fabs x)) (fabs x) x)

Time

Variable

Point

Expression

54.0ms

((* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) (fabs x)) (fabs x) x)

11.0ms

-inf

((* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) (fabs x)) (fabs x) x)

6.0ms

inf

((* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) (pow 2 1/4) 2 1/4 (* (pow 2 1/4) (fabs x)) (fabs x) x)

rewrite24.0ms (2%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	23	61
1	43	51
0	121	51

Stop Event

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

Counts

11 → 34

Calls

Call 1

Inputs
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x))
(fabs.f64 x)
x
#s(approx (* (pow 2 1/4) (* (pow 2 1/4) (fabs x))) #s(hole binary64 (* (fabs x) (sqrt 2))))
#s(approx (* (pow 2 1/4) (fabs x)) #s(hole binary64 (* (pow 2 1/4) (fabs x))))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx x #s(hole binary64 x))

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

eval4.0ms (0.3%)

Memory: 5.5MiB live, 5.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 537 to 106 computations (80.3% saved)

prune15.0ms (1.3%)

Memory

14.7MiB live, 14.7MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	45	5	50

Accuracy

100.0%

Counts

50 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
✓	99.3%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x)))
	99.5%	(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (fabs.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))))
✓	99.1%	(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))

Compiler

Compiled 117 to 71 computations (39.3% saved)

regimes14.0ms (1.1%)

Memory

-25.7MiB live, 19.7MiB allocated; 4ms collecting garbage

Accuracy

Total -53.2b remaining (-17465%)

Threshold costs -53.2b (-17465%)

Counts

7 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 x))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fabs.f64 x)))
(/.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)))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (fabs.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))))

Outputs
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))

Calls

4 calls:

6.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

simplify37.0ms (3.1%)

Memory

-1.2MiB live, 43.2MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
2	12	9
3	18	9
4	50	9
5	372	9
6	3463	9

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))

Outputs
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))

derivations2.0ms (0.2%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 9 to 7 computations (22.2% saved)

preprocess11.0ms (0.9%)

Memory: 19.9MiB live, 19.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 52 to 36 computations (30.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample539.0ms (44.7%)

explain78.0ms (6.5%)

preprocess242.0ms (20.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite92.0ms (7.6%)

eval5.0ms (0.5%)

prune11.0ms (0.9%)

series2.0ms (0.1%)

rewrite19.0ms (1.6%)

eval4.0ms (0.3%)

prune5.0ms (0.4%)

series1.0ms (0.1%)

rewrite18.0ms (1.5%)

eval2.0ms (0.2%)

prune4.0ms (0.4%)

series72.0ms (6%)

rewrite24.0ms (2%)

eval4.0ms (0.3%)

prune15.0ms (1.3%)

regimes14.0ms (1.1%)

simplify37.0ms (3.1%)

derivations2.0ms (0.2%)

preprocess11.0ms (0.9%)

end0.0ms (0%)

Profiling