Metrics for math.cube on real

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

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 7 to 5 computations (28.6% saved)

sample389.0ms (3.7%)

Memory

28.8MiB live, 737.9MiB allocated

Samples

255.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 121.0ms

ival-mult: 112.0ms (92.9% of total)

ival-true: 5.0ms (4.1% of total)

ival-assert: 3.0ms (2.5% of total)

Bogosity

preprocess40.0ms (0.4%)

Memory

-19.1MiB live, 19.8MiB allocated

Algorithm

2×	egg-herbie

Rules

18×	`distribute-lft-neg-in`
18×	`associate-r`
16×	`unsub-neg`
14×	`distribute-rgt-neg-in`
14×	`neg-sub0`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	25	10
2	61	10
3	123	10
4	143	10
5	151	10
0	3	5
1	4	3
2	6	3
0	6	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (* x x) x)

Outputs
(* (* x x) x)
(.f64 x (.f64 x x))

Call 2

Inputs
(* (* x x) x)
(* (* (neg x) (neg x)) (neg x))
(neg (* (* (neg x) (neg x)) (neg x)))

Outputs
(* (* x x) x)
(pow x 3)
(* (* (neg x) (neg x)) (neg x))
(pow (neg x) 3)
(neg (* (* (neg x) (neg x)) (neg x)))
(pow x 3)

Symmetry

(negabs x)

explain39.0ms (0.4%)

Memory

34.0MiB live, 76.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f64 (.f64 x x) x)`
-	-	`(*.f64 x x)`
-	-	`x`

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

16.0ms

512×

valid

Compiler

Compiled 34 to 16 computations (52.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 6.0ms (87.4% of total)

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

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

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 6 to 3 computations (50% saved)

prune2.0ms (0%)

Memory

-37.1MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 6 to 3 computations (50% saved)

simplify3.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) x)

Rules

6×	`-lowering-.f32`
6×	`-lowering-.f64`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`
2×	`cube-unmult`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3	9
1	4	7
2	6	7
0	6	7

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (* x x) x)
(* x x)
x

Outputs
(* (* x x) x)
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
x

localize12.0ms (0.1%)

Memory

28.0MiB live, 28.0MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 (.f64 x x) x)

Samples

8.0ms

256×

valid

Compiler

Compiled 11 to 5 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 3.0ms (88.4% of total)

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

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

series2.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (* (* x x) x)>
#<alt (* x x)>

Outputs
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* (* x x) x)
0.0ms	x	@	0	(* (* x x) x)
0.0ms	x	@	inf	(* (* x x) x)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	0	(* x x)

rewrite147.0ms (1.4%)

Memory

-26.8MiB live, 221.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 618×	`-lowering-.f32`
2 618×	`-lowering-.f64`
1 202×	`unpow-prod-down`
1 036×	`log-prod`
926×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	8	6
2	22	6
3	50	6
4	164	6
5	569	2
6	4062	2
7	4120	2
8	4359	2
9	6903	2
0	8620	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 4

Calls

Call 1

Inputs
(* (* x x) x)
(* x x)

Outputs
#s(literal 1 binary64)
x
#s(literal 1 binary64)
x

simplify5.0ms (0%)

Memory

16.0MiB live, 16.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-lowering-.f32`
6×	`-lowering-.f64`
4×	`pow-lowering-pow.f64`
4×	`pow-lowering-pow.f32`
2×	`cube-mult`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	8	72
2	10	72
3	12	72
0	12	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval8.0ms (0.1%)

Memory: -24.7MiB live, 17.2MiB allocated
Compiler: Compiled 129 to 6 computations (95.3% saved)

prune2.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Accuracy

99.9%

Counts

29 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)
▶	54.8%	(*.f64 x x)
▶	6.4%	x

Compiler

Compiled 12 to 6 computations (50% saved)

simplify3.0ms (0%)

Memory

9.1MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)

Rules

2×	`-lowering-.f32`
2×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	5
0	2	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* x x)
x

Outputs
x
(* x x)
(*.f64 x x)
x

localize12.0ms (0.1%)

Memory

-13.1MiB live, 24.6MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)

Samples

8.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 2.0ms (98.3% of total)

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

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

series0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* x x)>

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x x)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	-inf	(* x x)

rewrite117.0ms (1.1%)

Memory

25.1MiB live, 258.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 136×	`pow-lowering-pow.f64`
2 136×	`pow-lowering-pow.f32`
1 638×	`-lowering-.f32`
1 638×	`-lowering-.f64`
1 412×	`prod-exp`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	2	3
1	4	3
2	11	3
3	27	3
4	75	3
5	230	1
6	1483	1
7	1508	1
8	1631	1
9	2872	1
0	8317	1

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(* x x)

Outputs
#s(literal 1 binary64)
x

simplify6.0ms (0.1%)

Memory

-33.6MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`
2×	`-lowering-.f32`
2×	`-lowering-.f64`
2×	`unpow2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval1.0ms (0%)

Memory: 4.5MiB live, 4.5MiB allocated
Compiler: Compiled 39 to 3 computations (92.3% saved)

prune2.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	14	3	17

Accuracy

99.9%

Counts

17 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)
✓	54.8%	(*.f64 x x)
✓	6.4%	x

Compiler

Compiled 22 to 9 computations (59.1% saved)

regimes4.0ms (0%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(.f64 (.f64 x x) x)

Outputs
(.f64 (.f64 x x) x)

Calls

2 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 8 to 4 computations (50% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
54.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
6.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Memory

-20.1MiB live, 18.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	9
1	4	9

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(*.f64 x x)
x

Outputs
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(*.f64 x x)
x

soundness9.6s (91.9%)

Memory

-2.1MiB live, 215.7MiB allocated

Rules

2 618×	`-lowering-.f32`
2 618×	`-lowering-.f64`
1 202×	`unpow-prod-down`
1 036×	`log-prod`
926×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	8	6
2	22	6
3	50	6
4	164	6
5	569	2
6	4062	2
7	4120	2
8	4359	2
9	6903	2
0	8620	2

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 10 to 3 computations (70% saved)

preprocess38.0ms (0.4%)

Memory: -16.0MiB live, 99.3MiB allocated
Remove: (negabs x)
Compiler: Compiled 64 to 30 computations (53.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample389.0ms (3.7%)

preprocess40.0ms (0.4%)

explain39.0ms (0.4%)

eval0.0ms (0%)

prune2.0ms (0%)

simplify3.0ms (0%)

localize12.0ms (0.1%)

series2.0ms (0%)

rewrite147.0ms (1.4%)

simplify5.0ms (0%)

eval8.0ms (0.1%)

prune2.0ms (0%)

simplify3.0ms (0%)

localize12.0ms (0.1%)

series0.0ms (0%)

rewrite117.0ms (1.1%)

simplify6.0ms (0.1%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify8.0ms (0.1%)

soundness9.6s (91.9%)

preprocess38.0ms (0.4%)

end0.0ms (0%)

Profiling