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)

sample536.0ms (60.7%)

Results

305.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-mult: 134.0ms (91.1% of total)

const: 10.0ms (6.8% of total)

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

Bogosity

preprocess14.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

44×	`distribute-lft-neg-in`
40×	`associate-r`
32×	`distribute-lft-in`
24×	`cancel-sign-sub-inv`
22×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	27	15
2	68	15
3	167	15
4	219	15
5	231	15
0	4	5
1	7	5
2	10	5
0	10	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (* x 2) x)

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

Call 2

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

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

Symmetry

(abs x)

explain47.0ms (5.3%)

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

31.0ms

512×

valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 13.0ms (94.1% of total)

const: 1.0ms (7.2% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0.1%)

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)

localize33.0ms (3.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 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)
✓	accuracy	100.0%	(.f64 (.f64 x #s(literal 2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	7	10
2	10	10
0	10	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

15.0ms

256×

valid

Compiler

Compiled 12 to 8 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 6.0ms (95.5% of total)

const: 1.0ms (15.9% of total)

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

series4.0ms (0.4%)

Counts

2 → 24

Calls

Call 1

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

Calls

6 calls:

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

rewrite149.0ms (16.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2136×	`pow-lowering-pow.f64`
2136×	`pow-lowering-pow.f32`
1588×	`-lowering-.f32`
1588×	`-lowering-.f64`
1412×	`prod-exp`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	7	6
2	10	6
3	11	6
4	18	6
5	34	6
6	90	6
7	279	2
8	1678	2
9	1703	2
10	1826	2
11	3043	2
0	8411	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

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

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

simplify6.0ms (0.7%)

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: 0 (0.0ms)

Iter	Nodes	Cost
0	5	96
1	8	96
2	10	96
0	10	96

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

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)
(* 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))

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)
(* 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))

eval7.0ms (0.7%)

Compiler: Compiled 125 to 65 computations (48% saved)

prune2.0ms (0.2%)

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)
▶	4.2%	#s(literal 2 binary64)

Compiler

Compiled 12 to 9 computations (25% saved)

localize22.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(*.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	5
1	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
2
(* 2 x)
x

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

Results

10.0ms

256×

valid

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

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

ival-mult: 3.0ms (86.1% of total)

const: 1.0ms (28.7% of total)

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

series1.0ms (0.1%)

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	@	0	(* 2 x)
0.0ms	x	@	-inf	(* 2 x)

rewrite8.0ms (0.9%)

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))

simplify6.0ms (0.6%)

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)

eval2.0ms (0.2%)

Compiler: Compiled 43 to 29 computations (32.6% saved)

prune2.0ms (0.2%)

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)
✓	4.2%	#s(literal 2 binary64)

Compiler

Compiled 22 to 16 computations (27.3% saved)

regimes3.0ms (0.4%)

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:

2.0ms	x
1.0ms	(.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)

regimes2.0ms (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:

1.0ms

Results

Accuracy	Segments	Branch
6.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0.1%)

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:

0.0ms

Results

Accuracy	Segments	Branch
4.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

soundness1.0ms (0.2%)

Stop Event

1×

done

Compiler

Compiled 10 to 7 computations (30% saved)

preprocess39.0ms (4.4%)

Remove: (abs x)
Compiler: Compiled 92 to 62 computations (32.6% saved)

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

analyze0.0ms (0%)

sample536.0ms (60.7%)

preprocess14.0ms (1.6%)

explain47.0ms (5.3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize33.0ms (3.7%)

series4.0ms (0.4%)

rewrite149.0ms (16.9%)

simplify6.0ms (0.7%)

eval7.0ms (0.7%)

prune2.0ms (0.2%)

localize22.0ms (2.5%)

series1.0ms (0.1%)

rewrite8.0ms (0.9%)

simplify6.0ms (0.6%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

regimes3.0ms (0.4%)

regimes2.0ms (0.2%)

regimes1.0ms (0.1%)

soundness1.0ms (0.2%)

preprocess39.0ms (4.4%)

end0.0ms (0%)

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