Metrics for math.cube on real

analyze0.0ms (0%)

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 4 computations (42.9% saved)

Precisions

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample601.0ms (11.1%)

Results

458.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

ival-mult: 197.0ms (95.1% of total)

const: 7.0ms (3.4% of total)

backward-pass: 3.0ms (1.4% of total)

Bogosity

preprocess20.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

76×	`fnmadd-define`
72×	`fnmsub-define`
72×	`fmsub-define`
64×	`fma-define`
28×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	27	10
2	63	10
3	131	10
4	189	10
5	279	10
6	327	10
0	3	4
1	5	3
2	7	3
0	7	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)

explain43.0ms (0.8%)

FPErrors

Click to see full error table

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

Results

29.0ms

512×

valid

Compiler

Compiled 28 to 11 computations (60.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 8.0ms (98.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 3 computations (50% saved)

prune1.0ms (0%)

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)

simplify4.0ms (0.1%)

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	7
1	5	6
2	7	6
0	7	6

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

localize40.0ms (0.7%)

Localize:

Found 2 expressions of interest:

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

Results

35.0ms

256×

valid

Compiler

Compiled 11 to 4 computations (63.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 4.0ms (90.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0%)

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)

rewrite167.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2652×	`-lowering-.f32`
2652×	`-lowering-.f64`
1140×	`unpow-prod-down`
1030×	`log-prod`
950×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	9	6
2	23	6
3	53	6
4	170	6
5	588	2
6	4525	2
7	4593	2
8	4849	2
9	7461	2
0	8522	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 (0.1%)

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: 1 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	8	60
2	11	60
3	13	60
0	13	60

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)

eval2.0ms (0%)

Compiler: Compiled 129 to 6 computations (95.3% saved)

prune2.0ms (0%)

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)
▶	51.0%	(*.f64 x x)
▶	6.1%	x

Compiler

Compiled 12 to 6 computations (50% saved)

simplify5.0ms (0.1%)

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`
2×	`square-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	4
1	3	4
0	3	4

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
x
(* x x)
x

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

localize15.0ms (0.3%)

Localize:

Found 1 expressions of interest:

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

Results

11.0ms

256×

valid

Compiler

Compiled 7 to 3 computations (57.1% saved)

Precisions

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

ival-mult: 2.0ms (79.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

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)

rewrite154.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1438×	`prod-exp`
1304×	`-lowering-.f32`
1304×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	5	2
2	12	2
3	29	2
4	79	2
5	239	1
6	1690	1
7	1722	1
8	1856	1
9	3127	1
0	8463	1

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(* x x)

Outputs
#s(literal 1 binary64)
x

simplify5.0ms (0.1%)

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: 1 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	24
2	5	24
0	5	24

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%)

Compiler: Compiled 39 to 3 computations (92.3% saved)

prune2.0ms (0%)

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)
✓	51.0%	(*.f64 x x)
✓	6.1%	x

Compiler

Compiled 22 to 9 computations (59.1% saved)

regimes4.0ms (0.1%)

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%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
51.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

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
6.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

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

soundness4.3s (79.4%)

Rules

2652×	`-lowering-.f32`
2652×	`-lowering-.f64`
1140×	`unpow-prod-down`
1030×	`log-prod`
950×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	9	6
2	23	6
3	53	6
4	170	6
5	588	2
6	4525	2
7	4593	2
8	4849	2
9	7461	2
0	8522	2

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 16 to 6 computations (62.5% saved)

preprocess33.0ms (0.6%)

Remove: (negabs x)
Compiler: Compiled 64 to 30 computations (53.1% saved)

math.cube on real

analyze0.0ms (0%)

sample601.0ms (11.1%)

preprocess20.0ms (0.4%)

explain43.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize40.0ms (0.7%)

series2.0ms (0%)

rewrite167.0ms (3.1%)

simplify5.0ms (0.1%)

eval2.0ms (0%)

prune2.0ms (0%)

simplify5.0ms (0.1%)

localize15.0ms (0.3%)

series0.0ms (0%)

rewrite154.0ms (2.8%)

simplify5.0ms (0.1%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify8.0ms (0.1%)

soundness4.3s (79.4%)

preprocess33.0ms (0.6%)

end0.0ms (0%)

Profiling