Metrics for Octave 3.8, oct_fill

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze16.0ms (0.2%)

Memory

-8.8MiB live, 30.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
66.7%	25%	12.5%	0.1%	0%	62.4%	0%	6
66.7%	25%	12.5%	0.1%	0%	62.4%	0%	7
80%	25%	6.2%	0.1%	0%	68.7%	0%	8
80%	25%	6.2%	0.1%	0%	68.7%	0%	9
88.9%	25%	3.1%	0.1%	0%	71.8%	0%	10
88.9%	25%	3.1%	0.1%	0%	71.8%	0%	11
94.1%	25%	1.6%	0.1%	0%	73.4%	0%	12

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.1s (12.4%)

Memory

57.5MiB live, 1 931.4MiB allocated

Samples

698.0ms	8 256×	0	valid
45.0ms	518×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 514.0ms

ival-mult: 173.0ms (33.7% of total)

ival-div: 149.0ms (29% of total)

ival-sqrt: 70.0ms (13.6% of total)

ival-sub: 52.0ms (10.1% of total)

ival-add: 47.0ms (9.1% of total)

exact: 12.0ms (2.3% of total)

ival-true: 7.0ms (1.4% of total)

ival-assert: 4.0ms (0.8% of total)

Bogosity

explain175.0ms (2%)

Memory

-25.7MiB live, 345.8MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand))`
-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))))`
-	-	`a`
-	-	`rand`
-	-	`#s(literal 3 binary64)`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 9 binary64)`
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))`
-	-	`(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))`
-	-	`(sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))`
-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)`
-	-	`(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`
-	-	`(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

42.0ms	482×	0	valid
3.0ms	6×	5	exit
3.0ms	16×	1	valid
2.0ms	8×	2	valid

Compiler

Compiled 194 to 43 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 11.0ms (35.8% of total)

ival-div: 8.0ms (26.1% of total)

ival-sqrt: 4.0ms (13% of total)

ival-sub: 3.0ms (9.8% of total)

ival-add: 3.0ms (9.8% of total)

adjust: 1.0ms (3.3% of total)

exact: 1.0ms (3.3% of total)

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

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

preprocess262.0ms (3%)

Memory

13.4MiB live, 128.5MiB allocated

Algorithm

1×	egg-herbie

Rules

2 560×	`lower-fma.f64`
2 560×	`lower-fma.f32`
1 326×	`unsub-neg`
910×	`sub-neg`
784×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	88
1	94	76
2	330	70
3	1191	70
4	3285	70
5	4976	70
6	6491	70
7	6874	70
8	7097	70
9	7245	70
10	7252	70
11	7487	70
12	7531	70
13	7781	70
0	13	16
0	22	16
1	39	14
2	86	14
3	186	14
4	378	14
5	601	14
6	837	14
7	1420	14
8	2472	14
9	2925	14
10	3080	14
11	3233	14
12	3328	14
13	3334	14
0	3334	13

Stop Event

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

Calls

Call 1

Inputs

(*.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

Outputs

(*.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))))

Samples

0.0ms	1×	2	valid
0.0ms	1×	0	valid

Compiler

Compiled 75 to 44 computations (41.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0% of total)

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

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

const: 0.0ms (0% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

Status

Accuracy

Program

▶

99.8%

(*.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

Compiler

Compiled 22 to 13 computations (40.9% saved)

simplify516.0ms (5.9%)

Memory

-1.4MiB live, 857.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))
cost-diff	128	(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)
cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))

Rules

2 560×	`lower-fma.f64`
2 560×	`lower-fma.f32`
768×	`lower-*.f32`
762×	`lower-*.f64`
614×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
0	22	66
1	39	60
2	86	60
3	186	60
4	378	60
5	601	60
6	837	60
7	1420	60
8	2472	60
9	2925	60
10	3080	60
11	3233	60
12	3328	60
13	3334	60
0	3334	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))
(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
a
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 3 binary64)
(+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))))
(sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))
(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))
#s(literal 9 binary64)
rand

Outputs
(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))
(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))))
(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
(+.f64 a #s(literal -1/3 binary64))
a
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(literal 3 binary64)
(+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand))
(+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)
(/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))
(sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))
(sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))
(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))
(fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))
#s(literal 9 binary64)
rand

Samples

77.0ms	2 520×	0	valid
66.0ms	965×	0	invalid
2.0ms	9×	2	valid
0.0ms	3×	1	valid

Compiler

Compiled 26 903 to 25 742 computations (4.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-add: 29.0ms (37.8% of total)

ival-mult: 14.0ms (18.3% of total)

const: 12.0ms (15.6% of total)

ival-sqrt: 9.0ms (11.7% of total)

ival-div: 4.0ms (5.2% of total)

ival-true: 3.0ms (3.9% of total)

exact: 3.0ms (3.9% of total)

ival-assert: 1.0ms (1.3% of total)

ival-sub: 1.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

localize39.0ms (0.5%)

Memory

33.4MiB live, 72.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))
accuracy	0.09765625	(sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))
accuracy	0.22265625	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))))

Samples

20.0ms	241×	0	valid
1.0ms	3×	5	exit
1.0ms	8×	1	valid
1.0ms	4×	2	valid

Compiler

Compiled 86 to 15 computations (82.6% saved)

Precisions

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

ival-mult: 5.0ms (33.8% of total)

ival-div: 4.0ms (27% of total)

ival-sqrt: 2.0ms (13.5% of total)

adjust: 1.0ms (6.8% of total)

ival-sub: 1.0ms (6.8% of total)

ival-add: 1.0ms (6.8% of total)

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

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

exact: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory

-6.7MiB live, 32.0MiB allocated

Counts

6 → 84

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))) (patch (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand))) (patch (.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))) (patch (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 (* rand (sqrt -3))) (taylor 0 a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (+ (* -3/2 (/ (* a rand) (sqrt -3))) (* 1/3 (* rand (sqrt -3)))) (taylor 0 a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* -1/6 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3)))))) (taylor 0 a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* a (+ (* -1/6 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3)))))))) (taylor 0 a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (* (sqrt (/ 1 a)) rand)) (taylor inf a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))) (taylor inf a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (taylor inf a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (taylor inf a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))) (taylor -inf a) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1)))))))) (taylor -inf a) (#s(alt (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))) (patch (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	a	@	0	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
2.0ms	rand	@	0	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
1.0ms	a	@	inf	(/ 1 (sqrt (* 9 (- a (/ 1 3)))))
1.0ms	a	@	-inf	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
1.0ms	a	@	inf	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)

simplify6.6s (75.7%)

Memory

45.9MiB live, 11 080.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 334×	`lower-fma.f64`
13 334×	`lower-fma.f32`
5 788×	`lower-*.f64`
5 788×	`lower-*.f32`
5 386×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	333	1781
1	1013	1561
2	3378	1491
3	7925	1491
0	8321	1388

Stop Event

1×	iter limit
1×	node limit

Samples

1.6s	13 218×	0	valid
1.1s	8 227×	0	invalid
5.0ms	81×	1	valid
3.0ms	37×	2	valid

Compiler

Compiled 468 749 to 354 662 computations (24.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.1s

const: 725.0ms (34.7% of total)

ival-mult: 519.0ms (24.8% of total)

ival-sqrt: 282.0ms (13.5% of total)

ival-div: 239.0ms (11.4% of total)

ival-add: 200.0ms (9.6% of total)

ival-pow: 56.0ms (2.7% of total)

exact: 22.0ms (1.1% of total)

ival-true: 18.0ms (0.9% of total)

ival-sub: 10.0ms (0.5% of total)

ival-assert: 9.0ms (0.4% of total)

ival-neg: 8.0ms (0.4% of total)

adjust: 2.0ms (0.1% of total)

end0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

Octave 3.8, oct_fill_randg

start0.0ms (0%)

analyze16.0ms (0.2%)

sample1.1s (12.4%)

explain175.0ms (2%)

preprocess262.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify516.0ms (5.9%)

localize39.0ms (0.5%)

series18.0ms (0.2%)

simplify6.6s (75.7%)

end0.0ms (0%)

Profiling