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)

sample3.8s (24.5%)

Results

3.5s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

ival-mult: 3.4s (99.7% of total)

const: 6.0ms (0.2% of total)

backward-pass: 3.0ms (0.1% of total)

Bogosity

preprocess24.0ms (0.2%)

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	16
1	25	10
2	61	10
3	123	10
4	181	10
5	271	10
6	319	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)

explain34.0ms (0.2%)

FPErrors

Click to see full error table

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

Results

22.0ms

512×

valid

Compiler

Compiled 28 to 11 computations (60.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 9.0ms (91.1% 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
▶	99.8%	(.f64 (.f64 x x) x)

Compiler

Compiled 6 to 3 computations (50% saved)

simplify7.0ms (0%)

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

localize14.0ms (0.1%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 (.f64 x x) x)

Results

10.0ms

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 (97.5% 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)

rewrite168.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2652×	`-lowering-.f32`
2652×	`-lowering-.f64`
1150×	`unpow-prod-down`
1038×	`log-prod`
950×	`pow-lowering-pow.f64`

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	574	2
6	4531	2
7	4593	2
8	4837	2
9	7415	2
0	8374	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%)

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)

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

99.8%

Counts

29 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(.f64 (.f64 x x) x)
▶	52.6%	(*.f64 x x)
▶	6.2%	x

Compiler

Compiled 12 to 6 computations (50% saved)

simplify3.0ms (0%)

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

localize43.0ms (0.3%)

Localize:

Found 1 expressions of interest:

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

Results

39.0ms

256×

valid

Compiler

Compiled 7 to 3 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 32.0ms (98.4% 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)

rewrite134.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1432×	`prod-exp`
1304×	`-lowering-.f32`
1304×	`-lowering-.f64`

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	234	1
6	1655	1
7	1684	1
8	1814	1
9	3107	1
0	8343	1

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(* x x)

Outputs
#s(literal 1 binary64)
x

simplify4.0ms (0%)

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%)

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

99.8%

Counts

17 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(.f64 (.f64 x x) x)
✓	52.6%	(*.f64 x x)
✓	6.2%	x

Compiler

Compiled 22 to 9 computations (59.1% saved)

regimes5.0ms (0%)

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
99.8%	1	`x`
99.8%	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
52.6%	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
6.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0%)

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

soundness11.2s (72.3%)

Rules

2652×	`-lowering-.f32`
2652×	`-lowering-.f64`
1150×	`unpow-prod-down`
1038×	`log-prod`
950×	`pow-lowering-pow.f64`

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	574	2
6	4531	2
7	4593	2
8	4837	2
9	7415	2
0	8374	2

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 10 to 3 computations (70% saved)

preprocess35.0ms (0.2%)

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

math.cube on real

analyze0.0ms (0%)

sample3.8s (24.5%)

preprocess24.0ms (0.2%)

explain34.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0%)

localize14.0ms (0.1%)

series2.0ms (0%)

rewrite168.0ms (1.1%)

simplify5.0ms (0%)

eval2.0ms (0%)

prune2.0ms (0%)

simplify3.0ms (0%)

localize43.0ms (0.3%)

series0.0ms (0%)

rewrite134.0ms (0.9%)

simplify4.0ms (0%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify6.0ms (0%)

soundness11.2s (72.3%)

preprocess35.0ms (0.2%)

end0.0ms (0%)

Profiling