Metrics for Linear.V2:$cdot from linear-1.19.1.3, A

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
100%	99.8%	0%	0.2%	0%	0%	0%	1

Compiler

Compiled 9 to 9 computations (0% saved)

sample748.0ms (39.8%)

Memory

11.8MiB live, 1 536.5MiB allocated; 296ms collecting garbage

Samples

425.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-mult!: 99.0ms (84.4% of total)

ival-add!: 17.0ms (14.5% of total)

adjust: 2.0ms (1.7% of total)

Bogosity

preprocess19.0ms (1%)

Memory

4.6MiB live, 51.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	109
1	99	105
2	218	105
3	330	105
4	330	105

Stop Event

1×

saturated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(+.f64 (.f64 x y) (.f64 z t))

Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 14 to 14 computations (0% saved)

series17.0ms (0.9%)

Memory

-1.9MiB live, 44.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	190

Stop Event

1×	iter-limit

Counts

7 → 15

Calls

Call 1

Inputs
(+.f64 (.f64 x y) (.f64 z t))
(*.f64 x y)
x
y
(*.f64 z t)
z
t

Outputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))
#s(approx (+ (* x y) (* z t)) (fma.f64 t z (*.f64 x y)))
#s(approx (* x y) (*.f64 x y))
#s(approx x x)
#s(approx (+ (* x y) (* z t)) (.f64 x (+.f64 y (/.f64 (.f64 t z) x))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 x (fma.f64 #s(literal -1 binary64) y (.f64 #s(literal -1 binary64) (/.f64 (.f64 t z) x))))))
#s(approx y y)
#s(approx (+ (* x y) (* z t)) (.f64 y (+.f64 x (/.f64 (.f64 t z) y))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 y (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (/.f64 (.f64 t z) y))))))
#s(approx z z)
#s(approx (+ (* x y) (* z t)) (.f64 z (+.f64 t (/.f64 (.f64 x y) z))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 z (fma.f64 #s(literal -1 binary64) t (.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) z))))))
#s(approx t t)
#s(approx (+ (* x y) (* z t)) (.f64 t (+.f64 z (/.f64 (.f64 x y) t))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 t (fma.f64 #s(literal -1 binary64) z (.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) t))))))

Calls

12 calls:

Time	Variable	Point
4.0ms	z	-inf
1.0ms	x	-inf
1.0ms	x	inf
1.0ms	y	-inf
1.0ms	t	-inf

rewrite237.0ms (12.6%)

Memory

2.9MiB live, 185.5MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
0	10	17
1	35	17
2	102	17
3	237	17
4	404	17
5	731	17
6	3411	17
0	4565	16

Stop Event

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

Counts

7 → 39

Calls

Call 1

Inputs
(+.f64 (.f64 x y) (.f64 z t))
(*.f64 x y)
x
y
(*.f64 z t)
z
t

Outputs
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 x) y) (.f64 t z))) (.f64 t z))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y x) (.f64 t z))) (.f64 t z))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 z) t) (.f64 y x))) (.f64 y x))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 t z) (.f64 y x))) (.f64 y x))
(/.f64 (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 (neg.f64 x) y) (.f64 (neg.f64 x) y))) (+.f64 (.f64 t z) (.f64 (neg.f64 x) y)))
(/.f64 (-.f64 (pow.f64 (.f64 t z) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 x) y) #s(literal 3 binary64))) (fma.f64 (.f64 t z) (.f64 t z) (fma.f64 (.f64 (neg.f64 x) y) (.f64 (neg.f64 x) y) (.f64 (.f64 t z) (*.f64 (neg.f64 x) y)))))
(/.f64 (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 y x))) (-.f64 (.f64 t z) (.f64 y x)))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 (neg.f64 z) t) (.f64 (neg.f64 z) t))) (+.f64 (.f64 y x) (.f64 (neg.f64 z) t)))
(/.f64 (+.f64 (pow.f64 (.f64 t z) #s(literal 3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (.f64 t z) (.f64 t z) (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 t z) (.f64 y x)))))
(/.f64 (-.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 z) t) #s(literal 3 binary64))) (fma.f64 (.f64 y x) (.f64 y x) (fma.f64 (.f64 (neg.f64 z) t) (.f64 (neg.f64 z) t) (.f64 (.f64 y x) (*.f64 (neg.f64 z) t)))))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 t z) (.f64 t z))) (-.f64 (.f64 y x) (.f64 t z)))
(/.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) (pow.f64 (.f64 t z) #s(literal 3 binary64))) (fma.f64 (.f64 y x) (.f64 y x) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z)))))
(neg.f64 (neg.f64 (fma.f64 t z (*.f64 y x))))
(fma.f64 (neg.f64 y) (neg.f64 x) (*.f64 t z))
(fma.f64 (neg.f64 x) (neg.f64 y) (*.f64 t z))
(fma.f64 (neg.f64 t) (neg.f64 z) (*.f64 y x))
(fma.f64 (neg.f64 z) (neg.f64 t) (*.f64 y x))
(fma.f64 t z (*.f64 y x))
(fma.f64 z t (*.f64 y x))
(fma.f64 y x (*.f64 t z))
(fma.f64 x y (*.f64 t z))
(-.f64 (.f64 t z) (.f64 (neg.f64 x) y))
(-.f64 (.f64 y x) (.f64 (neg.f64 z) t))
(+.f64 (.f64 t z) (.f64 y x))
(+.f64 (.f64 y x) (.f64 t z))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 y x)
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))
x
y
(*.f64 (neg.f64 t) (neg.f64 z))
(*.f64 (neg.f64 z) (neg.f64 t))
(*.f64 t z)
(*.f64 z t)
(neg.f64 (*.f64 (neg.f64 z) t))
z
t

eval5.0ms (0.2%)

Memory: 14.1MiB live, 14.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 684 to 153 computations (77.6% saved)

prune2.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	2	49

Accuracy

100.0%

Counts

49 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(fma.f64 z t (*.f64 y x))
▶	55.1%	#s(approx (+ (* x y) (* z t)) (*.f64 t z))

Compiler

Compiled 17 to 15 computations (11.8% saved)

series42.0ms (2.2%)

Memory

-15.0MiB live, 21.2MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	190

Stop Event

1×	iter-limit

Counts

8 → 15

Calls

Call 1

Inputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))
(*.f64 t z)
t
z
(fma.f64 z t (*.f64 y x))
(*.f64 y x)
y
x

Outputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))
#s(approx (+ (* x y) (* z t)) (fma.f64 t z (*.f64 x y)))
#s(approx (* y x) (*.f64 x y))
#s(approx x x)
#s(approx (+ (* x y) (* z t)) (.f64 x (+.f64 y (/.f64 (.f64 t z) x))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 x (fma.f64 #s(literal -1 binary64) y (.f64 #s(literal -1 binary64) (/.f64 (.f64 t z) x))))))
#s(approx y y)
#s(approx (+ (* x y) (* z t)) (.f64 y (+.f64 x (/.f64 (.f64 t z) y))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 y (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (/.f64 (.f64 t z) y))))))
#s(approx z z)
#s(approx (+ (* x y) (* z t)) (.f64 z (+.f64 t (/.f64 (.f64 x y) z))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 z (fma.f64 #s(literal -1 binary64) t (.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) z))))))
#s(approx t t)
#s(approx (+ (* x y) (* z t)) (.f64 t (+.f64 z (/.f64 (.f64 x y) t))))
#s(approx (+ (* x y) (* z t)) (.f64 #s(literal -1 binary64) (.f64 t (fma.f64 #s(literal -1 binary64) z (.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) t))))))

Calls

12 calls:

Time	Variable	Point
35.0ms	y	-inf
1.0ms	x	-inf
1.0ms	z	-inf
1.0ms	t	-inf
0.0ms	z	inf

rewrite746.0ms (39.6%)

Memory

-123.4MiB live, 283.0MiB allocated; 924ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
0	14	26
1	64	26
2	157	26
3	285	26
4	390	26
5	706	26
6	3386	26
0	4540	26

Stop Event

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

Counts

8 → 40

Calls

Call 1

Inputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))
(*.f64 t z)
t
z
(fma.f64 z t (*.f64 y x))
(*.f64 y x)
y
x

Outputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))
(*.f64 (neg.f64 t) (neg.f64 z))
(*.f64 (neg.f64 z) (neg.f64 t))
(*.f64 t z)
(*.f64 z t)
(neg.f64 (*.f64 (neg.f64 z) t))
t
z
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 y) x) (.f64 t z))) (.f64 t z))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 z) t) (.f64 y x))) (.f64 y x))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 t z) (.f64 y x))) (.f64 y x))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y x) (.f64 t z))) (.f64 t z))
(/.f64 (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 (neg.f64 y) x) (.f64 (neg.f64 y) x))) (+.f64 (.f64 t z) (.f64 (neg.f64 y) x)))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 (neg.f64 z) t) (.f64 (neg.f64 z) t))) (+.f64 (.f64 y x) (.f64 (neg.f64 z) t)))
(/.f64 (-.f64 (pow.f64 (.f64 t z) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 y) x) #s(literal 3 binary64))) (fma.f64 (.f64 t z) (.f64 t z) (fma.f64 (.f64 (neg.f64 y) x) (.f64 (neg.f64 y) x) (.f64 (.f64 t z) (*.f64 (neg.f64 y) x)))))
(/.f64 (-.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 z) t) #s(literal 3 binary64))) (fma.f64 (.f64 y x) (.f64 y x) (fma.f64 (.f64 (neg.f64 z) t) (.f64 (neg.f64 z) t) (.f64 (.f64 y x) (*.f64 (neg.f64 z) t)))))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 t z) (.f64 t z))) (-.f64 (.f64 y x) (.f64 t z)))
(/.f64 (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 y x))) (-.f64 (.f64 t z) (.f64 y x)))
(/.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) (pow.f64 (.f64 t z) #s(literal 3 binary64))) (fma.f64 (.f64 y x) (.f64 y x) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z)))))
(/.f64 (+.f64 (pow.f64 (.f64 t z) #s(literal 3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (.f64 t z) (.f64 t z) (-.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 (.f64 t z) (.f64 y x)))))
(neg.f64 (neg.f64 (fma.f64 t z (*.f64 y x))))
(fma.f64 (neg.f64 x) (neg.f64 y) (*.f64 t z))
(fma.f64 (neg.f64 t) (neg.f64 z) (*.f64 y x))
(fma.f64 (neg.f64 z) (neg.f64 t) (*.f64 y x))
(fma.f64 (neg.f64 y) (neg.f64 x) (*.f64 t z))
(fma.f64 t z (*.f64 y x))
(fma.f64 z t (*.f64 y x))
(fma.f64 y x (*.f64 t z))
(fma.f64 x y (*.f64 t z))
(-.f64 (.f64 t z) (.f64 (neg.f64 y) x))
(-.f64 (.f64 y x) (.f64 (neg.f64 z) t))
(+.f64 (.f64 t z) (.f64 y x))
(+.f64 (.f64 y x) (.f64 t z))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 y x)
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 y) x))
y
x

eval5.0ms (0.2%)

Memory: 10.2MiB live, 10.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 700 to 154 computations (78% saved)

prune2.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	48	2	50

Accuracy

100.0%

Counts

50 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(fma.f64 z t (*.f64 y x))
✓	55.1%	#s(approx (+ (* x y) (* z t)) (*.f64 t z))

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes20.0ms (1%)

Memory

-4.1MiB live, 42.8MiB allocated; 3ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

3 → 1

Calls

Call 1

Inputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))

Outputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))

Call 2

Inputs
#s(approx (+ (* x y) (* z t)) (*.f64 t z))
(fma.f64 z t (*.f64 y x))
(+.f64 (.f64 x y) (.f64 z t))

Outputs
(fma.f64 z t (*.f64 y x))

Calls

14 calls:

3.0ms	(*.f64 z t)
1.0ms	t
1.0ms	y
1.0ms	z
1.0ms	x

Results

Accuracy	Segments	Branch
55.1%	1	`(*.f64 z t)`
55.1%	1	`(*.f64 x y)`
55.1%	1	`(+.f64 (.f64 x y) (.f64 z t))`
55.1%	1	`x`
55.1%	1	`y`
55.1%	1	`z`
55.1%	1	`t`
99.6%	1	`(*.f64 z t)`
99.6%	1	`(*.f64 x y)`
99.6%	1	`(+.f64 (.f64 x y) (.f64 z t))`
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`z`
99.6%	1	`t`

Compiler

Compiled 58 to 80 computations (-37.9% saved)

derivations20.0ms (1.1%)

Memory

18.6MiB live, 18.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 17 to 11 computations (35.3% saved)

preprocess18.0ms (1%)

Memory

-15.8MiB live, 31.0MiB allocated; 3ms collecting garbage

Remove

(sort z t)

(sort x y)

Compiler

Compiled 92 to 78 computations (15.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample748.0ms (39.8%)

preprocess19.0ms (1%)

series17.0ms (0.9%)

rewrite237.0ms (12.6%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

series42.0ms (2.2%)

rewrite746.0ms (39.6%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

regimes20.0ms (1%)

derivations20.0ms (1.1%)

preprocess18.0ms (1%)

end0.0ms (0%)

Profiling