Metrics for Numeric.Log:$cexpm1 from log-domain-0.10.2.1, A

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 5 computations (28.6% 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)

sample713.0ms (16.9%)

Results

507.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-mult: 136.0ms (90.2% of total)

const: 11.0ms (7.3% of total)

backward-pass: 3.0ms (2% of total)

Bogosity

preprocess20.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

122×	`fnmadd-define`
120×	`fnmsub-define`
120×	`fmsub-define`
104×	`fma-define`
44×	`distribute-lft-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	27	15
2	68	12
3	169	12
4	266	12
5	412	12
6	500	12
0	4	5
1	7	5
2	10	4
3	11	4
0	11	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (* x 2) x)

Outputs
(* (* x 2) x)
(.f64 x (.f64 x #s(literal 2 binary64)))

Call 2

Inputs
(* (* x 2) x)
(* (* (neg x) 2) (neg x))
(neg (* (* (neg x) 2) (neg x)))

Outputs
(* (* x 2) x)
(* 2 (square x))
(* (* (neg x) 2) (neg x))
(* 2 (square x))
(neg (* (* (neg x) 2) (neg x)))
(* -2 (square x))

Symmetry

(abs x)

explain64.0ms (1.5%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x #s(literal 2 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`(.f64 (.f64 x #s(literal 2 binary64)) x)`

Results

48.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 25.0ms (96.1% of total)

const: 1.0ms (3.8% of total)

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

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 x #s(literal 2 binary64)) x)

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) x)

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
4×	`associate-l`
2×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	7	10
2	10	9
3	11	9
0	11	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (* x 2) x)
(* x 2)
x
2

Outputs
(* (* x 2) x)
(.f64 x (.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)

localize21.0ms (0.5%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 x #s(literal 2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))

Results

16.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

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

ival-mult: 4.0ms (94.2% 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 2) x)>
#<alt (* x 2)>

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(* (* x 2) x)
0.0ms	x	@	0	(* x 2)
0.0ms	x	@	inf	(* (* x 2) x)
0.0ms	x	@	-inf	(* x 2)
0.0ms	x	@	inf	(* x 2)

rewrite225.0ms (5.3%)

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: 7 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	7	10
2	10	8
3	12	8
4	19	8
5	36	8
6	94	8
7	288	2
8	1894	2
9	1926	2
10	2060	2
11	3374	2
0	8768	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
(* (* x 2) x)
(* x 2)

Outputs
#s(literal 2 binary64)
#s(literal 2 binary64)

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	96
1	8	84
2	11	84
0	11	84

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

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

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

eval2.0ms (0.1%)

Compiler: Compiled 125 to 6 computations (95.2% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Accuracy

100.0%

Counts

27 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 x #s(literal 2 binary64)) x)
▶	6.7%	(*.f64 #s(literal 2 binary64) x)
▶	4.3%	#s(literal 2 binary64)

Compiler

Compiled 12 to 9 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	4	6
0	4	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
2
(* 2 x)
2
x

Outputs
2
#s(literal 2 binary64)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x

localize45.0ms (1.1%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)

Results

40.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

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

ival-mult: 2.0ms (83.5% 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 (* 2 x)>

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

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* 2 x)
0.0ms	x	@	-inf	(* 2 x)
0.0ms	x	@	0	(* 2 x)

rewrite14.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 2 x)

Outputs
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

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
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)

eval1.0ms (0%)

Compiler: Compiled 43 to 4 computations (90.7% 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

100.0%

Counts

17 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 x #s(literal 2 binary64)) x)
✓	6.7%	(*.f64 #s(literal 2 binary64) x)
✓	4.3%	#s(literal 2 binary64)

Compiler

Compiled 22 to 14 computations (36.4% saved)

regimes9.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) x)
(.f64 (.f64 x #s(literal 2 binary64)) x)

Outputs
(.f64 (.f64 x #s(literal 2 binary64)) x)

Calls

2 calls:

7.0ms	x
2.0ms	(.f64 (.f64 x #s(literal 2 binary64)) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 (.f64 x #s(literal 2 binary64)) x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes8.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) x)

Outputs
(*.f64 #s(literal 2 binary64) x)

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
6.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)

Outputs
#s(literal 2 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
4.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	6	9

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 x #s(literal 2 binary64)) x)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)

Outputs
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 x (.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)

soundness3.0s (71.1%)

Rules

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

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	7	10
2	10	8
3	12	8
4	19	8
5	36	8
6	94	8
7	288	2
8	1894	2
9	1926	2
10	2060	2
11	3374	2
0	8768	2

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 10 to 4 computations (60% saved)

preprocess47.0ms (1.1%)

Remove: (abs x)
Compiler: Compiled 80 to 48 computations (40% saved)

Numeric.Log:$cexpm1 from log-domain-0.10.2.1, A

analyze0.0ms (0%)

sample713.0ms (16.9%)

preprocess20.0ms (0.5%)

explain64.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize21.0ms (0.5%)

series2.0ms (0%)

rewrite225.0ms (5.3%)

simplify23.0ms (0.5%)

eval2.0ms (0.1%)

prune2.0ms (0%)

simplify4.0ms (0.1%)

localize45.0ms (1.1%)

series0.0ms (0%)

rewrite14.0ms (0.3%)

simplify4.0ms (0.1%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes9.0ms (0.2%)

regimes8.0ms (0.2%)

regimes2.0ms (0%)

simplify7.0ms (0.2%)

soundness3.0s (71.1%)

preprocess47.0ms (1.1%)

end0.0ms (0%)

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