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

0.5MiB 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)

sample842.0ms (52.7%)

Memory

58.3MiB live, 611.6MiB allocated; 689ms collecting garbage

Samples

349.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 187.0ms

ival-mult: 114.0ms (60.8% of total)

ival-sqrt: 62.0ms (33.1% of total)

exact: 6.0ms (3.2% of total)

adjust: 3.0ms (1.6% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain62.0ms (3.9%)

Memory

-17.3MiB live, 74.8MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
123	-	2	(9.816483101969648e-157)	`(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)))`	uflow-rescue	62	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	62
↳	`(*.f64 x x)`	underflow	62
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	59	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	59
↳	`(*.f64 x x)`	overflow	59

Confusion

	Predicted +	Predicted -
+	121	2
-	0	133

Precision

1.0

Recall

0.983739837398374

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	0	2
-	0	0	133

Precision?

1.0

Recall?

0.983739837398374

Freqs

test

number	freq
0	135
1	121

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

29.0ms

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 (61.5% of total)

ival-sqrt: 3.0ms (26.4% 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)

preprocess321.0ms (20.1%)

Memory

-5.8MiB live, 189.3MiB allocated; 85ms 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
0	5	6
0	8	6
1	18	6
2	61	6
3	182	6
4	501	6
5	1234	6
6	4730	6
7	7915	6
0	8495	3

Stop Event

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

Calls

Call 1

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

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

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series4.0ms (0.3%)

Memory

6.7MiB live, 6.7MiB 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)

rewrite59.0ms (3.7%)

Memory

15.6MiB live, 67.0MiB allocated; 6ms 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)))

eval11.0ms (0.7%)

Memory: -30.1MiB live, 13.5MiB allocated; 8ms collecting garbage
Compiler: Compiled 563 to 158 computations (71.9% saved)

prune14.0ms (0.9%)

Memory

24.1MiB live, 24.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	2	68

Accuracy

100.0%

Counts

68 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
▶	99.5%	(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 16 to 11 computations (31.3% saved)

series5.0ms (0.3%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Counts

7 → 8

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((* (pow (* x 2) 1/2) (pow x 1/2)) (pow (* x 2) 1/2) (* x 2) x 2 1/2 (pow x 1/2))
1.0ms	x	@	0	((* (pow (* x 2) 1/2) (pow x 1/2)) (pow (* x 2) 1/2) (* x 2) x 2 1/2 (pow x 1/2))
1.0ms	x	@	inf	((* (pow (* x 2) 1/2) (pow x 1/2)) (pow (* x 2) 1/2) (* x 2) x 2 1/2 (pow x 1/2))

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

rewrite26.0ms (1.6%)

Memory

-24.0MiB live, 20.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	112
0	41	86
0	104	86

Stop Event

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

Counts

15 → 28

Calls

Call 1

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

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

eval3.0ms (0.2%)

Memory: 5.0MiB live, 5.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 327 to 78 computations (76.1% saved)

prune5.0ms (0.3%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	31	2	33

Accuracy

100.0%

Counts

33 → 2

Alt Table

Click to see full alt table

Status

Accuracy

Program

100.0%

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

▶

99.1%

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

Compiler

Compiled 20 to 13 computations (35% saved)

series54.0ms (3.4%)

Memory

17.3MiB live, 62.7MiB allocated; 6ms collecting garbage

Counts

9 → 10

Calls

Call 1

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

Outputs
#s(approx (* (pow (* x 2) 1/2) (* (pow x 1/4) (pow x 1/4))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (pow (* x 2) 1/2) #s(hole binary64 (* (sqrt x) (sqrt 2))))
#s(approx (* x 2) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (pow x 1/4) (pow x 1/4)) #s(hole binary64 (sqrt x)))
#s(approx (pow x 1/4) #s(hole binary64 (pow (* 1 x) 1/4)))
#s(approx (* (pow (* x 2) 1/2) (* (pow x 1/4) (pow x 1/4))) #s(hole binary64 (* -1 (* x (* (sqrt -2) (sqrt -1))))))
#s(approx (pow (* x 2) 1/2) #s(hole binary64 (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))))
#s(approx (* (pow x 1/4) (pow x 1/4)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (pow x 1/4) #s(hole binary64 (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))

Calls

3 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	((* (pow (* x 2) 1/2) (* (pow x 1/4) (pow x 1/4))) (pow (* x 2) 1/2) (* x 2) x 2 1/2 (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)
18.0ms	x	@	-inf	((* (pow (* x 2) 1/2) (* (pow x 1/4) (pow x 1/4))) (pow (* x 2) 1/2) (* x 2) x 2 1/2 (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)
7.0ms	x	@	inf	((* (pow (* x 2) 1/2) (* (pow x 1/4) (pow x 1/4))) (pow (* x 2) 1/2) (* x 2) x 2 1/2 (* (pow x 1/4) (pow x 1/4)) (pow x 1/4) 1/4)

Time

Variable

Point

Expression

28.0ms

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

18.0ms

-inf

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

7.0ms

inf

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

rewrite31.0ms (2%)

Memory

-30.9MiB live, 20.8MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	165
0	59	112
0	180	112

Stop Event

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

Counts

19 → 38

Calls

Call 1

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

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

eval4.0ms (0.3%)

Memory: 5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 718 to 127 computations (82.3% saved)

prune8.0ms (0.5%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	49	2	51

Accuracy

100.0%

Counts

51 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
✓	99.1%	(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))

Status

Accuracy

Program

▶

100.0%

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

✓

99.1%

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

Compiler

Compiled 20 to 13 computations (35% saved)

series2.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

rewrite49.0ms (3.1%)

Memory

24.7MiB live, 24.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	53
0	25	35
1	68	32
0	333	32

Stop Event

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

Counts

9 → 21

Calls

Call 1

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

eval23.0ms (1.5%)

Memory: -39.2MiB live, 6.9MiB allocated; 4ms collecting garbage
Compiler: Compiled 204 to 66 computations (67.6% saved)

prune5.0ms (0.3%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	25	2	27

Accuracy

100.0%

Counts

27 → 2

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

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

✓

99.1%

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

Compiler

Compiled 55 to 30 computations (45.5% saved)

regimes7.0ms (0.4%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Accuracy

Total -28.8b remaining (-368173.7%)

Threshold costs -28.8b (-368173.7%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 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)

simplify51.0ms (3.2%)

Memory

-13.2MiB live, 32.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3
1	14	3
2	19	3
3	28	3
4	44	3
5	56	3
6	61	3
7	63	3
8	65	3
9	81	3
10	264	3
11	3073	3

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 x x)

derivations2.0ms (0.1%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 3 to 2 computations (33.3% saved)

preprocess10.0ms (0.6%)

Memory: 11.3MiB live, 11.3MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 30 to 22 computations (26.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample842.0ms (52.7%)

explain62.0ms (3.9%)

preprocess321.0ms (20.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite59.0ms (3.7%)

eval11.0ms (0.7%)

prune14.0ms (0.9%)

series5.0ms (0.3%)

rewrite26.0ms (1.6%)

eval3.0ms (0.2%)

prune5.0ms (0.3%)

series54.0ms (3.4%)

rewrite31.0ms (2%)

eval4.0ms (0.3%)

prune8.0ms (0.5%)

series2.0ms (0.1%)

rewrite49.0ms (3.1%)

eval23.0ms (1.5%)

prune5.0ms (0.3%)

regimes7.0ms (0.4%)

simplify51.0ms (3.2%)

derivations2.0ms (0.1%)

preprocess10.0ms (0.6%)

end0.0ms (0%)

Profiling