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)

sample597.0ms (61.7%)

Results

434.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-mult: 168.0ms (94.5% of total)

const: 7.0ms (3.9% of total)

backward-pass: 3.0ms (1.7% of total)

Bogosity

preprocess45.0ms (4.7%)

Algorithm

2×	egg-herbie

Rules

74×	`fnmadd-define`
72×	`fnmsub-define`
72×	`fmsub-define`
66×	`fma-define`
28×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	27	10
2	61	10
3	132	10
4	190	10
5	280	10
6	328	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)

explain72.0ms (7.4%)

FPErrors

Click to see full error table

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

Results

54.0ms

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: 7.0ms (85.9% 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 (0.1%)

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)

simplify4.0ms (0.4%)

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

localize18.0ms (1.9%)

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

13.0ms

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 (96.3% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.2%)

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)

rewrite55.0ms (5.7%)

Algorithm

1×	batch-egg-rewrite

Rules

14×	`prod-exp`
14×	`-lowering-.f32`
14×	`-lowering-.f64`
12×	`exp-prod`
12×	`pow-to-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	9	5
2	16	5
3	24	5
4	37	5
5	52	5
6	65	5
0	65	5

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 9

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)

simplify5.0ms (0.5%)

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)

eval3.0ms (0.3%)

Compiler: Compiled 168 to 20 computations (88.1% saved)

prune2.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	2	34

Accuracy

100.0%

Counts

34 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal 3 binary64))
✓	99.8%	(.f64 (.f64 x x) x)

Compiler

Compiled 10 to 6 computations (40% saved)

simplify5.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6208	(pow.f64 x #s(literal 3 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	6	5
2	7	5
0	7	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(pow x 3)
x
3

Outputs
(pow x 3)
(.f64 x (.f64 x x))
x
3
#s(literal 3 binary64)

localize19.0ms (2%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 3 binary64))

Results

14.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

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

ival-pow: 3.0ms (78.4% 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 (pow x 3)>

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)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(pow x 3)
0.0ms	x	@	-inf	(pow x 3)
0.0ms	x	@	0	(pow x 3)

rewrite19.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

14×	`prod-exp`
14×	`-lowering-.f32`
14×	`-lowering-.f64`
10×	`exp-lowering-exp.f32`
10×	`exp-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	9	3
2	15	3
3	27	3
4	39	3
5	50	3
6	56	3
7	64	3
0	64	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 5

Calls

Call 1

Inputs
(pow x 3)

Outputs
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)

simplify5.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	6	36
2	7	36
0	7	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

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)

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))

eval2.0ms (0.2%)

Compiler: Compiled 84 to 11 computations (86.9% saved)

prune2.0ms (0.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	17	2	19

Accuracy

100.0%

Counts

19 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal 3 binary64))
✓	99.8%	(.f64 (.f64 x x) x)

Compiler

Compiled 19 to 11 computations (42.1% saved)

regimes3.0ms (0.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(pow.f64 x #s(literal 3 binary64))

Outputs
(pow.f64 x #s(literal 3 binary64))

Calls

2 calls:

1.0ms	x
1.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 8 to 4 computations (50% saved)

regimes4.0ms (0.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	x
1.0ms	(.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)

simplify7.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	6	8

Stop Event

1×

saturated

Calls

Call 1

Inputs
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 x x) x)

Outputs
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))

soundness55.0ms (5.7%)

Rules

14×	`prod-exp`
14×	`-lowering-.f32`
14×	`-lowering-.f64`
12×	`exp-prod`
12×	`pow-to-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	9	5
2	16	5
3	24	5
4	37	5
5	52	5
6	65	5
0	65	5

Stop Event

1×	done
1×	iter limit
1×	saturated

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess42.0ms (4.3%)

Remove: (negabs x)
Compiler: Compiled 54 to 34 computations (37% saved)

math.cube on real

analyze0.0ms (0%)

sample597.0ms (61.7%)

preprocess45.0ms (4.7%)

explain72.0ms (7.4%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify4.0ms (0.4%)

localize18.0ms (1.9%)

series2.0ms (0.2%)

rewrite55.0ms (5.7%)

simplify5.0ms (0.5%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

simplify5.0ms (0.5%)

localize19.0ms (2%)

series0.0ms (0%)

rewrite19.0ms (2%)

simplify5.0ms (0.5%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

regimes3.0ms (0.3%)

regimes4.0ms (0.4%)

simplify7.0ms (0.7%)

soundness55.0ms (5.7%)

preprocess42.0ms (4.3%)

end0.0ms (0%)

Profiling