Metrics for Expanding a square

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 11 to 9 computations (18.2% saved)

sample833.0ms (45.1%)

Results

281.0ms	2059×	body	1024	valid
212.0ms	2927×	body	256	valid
176.0ms	2032×	body	256	infinite
111.0ms	1012×	body	512	valid
38.0ms	226×	body	2048	valid

Bogosity

preprocess75.0ms (4.1%)

Algorithm

2×	egg-herbie

Rules

1906×	`fma-def`
1604×	`fma-neg`
1178×	`distribute-lft-in`
1078×	`associate--r-`
1078×	`distribute-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	25	19
2	58	13
3	138	13
4	583	13
5	2037	13
6	5456	13
7	7831	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

Outputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(fma.f64 (+.f64 x 1) (+.f64 x 1) -1)
(*.f64 (+.f64 x 2) (+.f64 x 0))
(*.f64 x (+.f64 x 2))
(*.f64 x (-.f64 x -2))

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify69.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1906×	`fma-def`
1604×	`fma-neg`
1178×	`distribute-lft-in`
1078×	`associate--r-`
1078×	`distribute-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	25	19
2	58	13
3	138	13
4	583	13
5	2037	13
6	5456	13
7	7831	13

Stop Event

1×	node limit

Counts

1 → 5

Calls

Call 1

Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

Outputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(fma.f64 (+.f64 x 1) (+.f64 x 1) -1)
(*.f64 (+.f64 x 2) (+.f64 x 0))
(*.f64 x (+.f64 x 2))
(*.f64 x (-.f64 x -2))

eval1.0ms (0.1%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	4	1	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	1	6

Accurracy

100.0%

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 x (-.f64 x -2))
▶	100.0%	(*.f64 x (-.f64 x -2))

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize19.0ms (1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(*.f64 x (-.f64 x -2))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(*.f64 x (-.f64 x -2))
0.0ms	x	@	inf	(*.f64 x (-.f64 x -2))
0.0ms	x	@	0	(*.f64 x (-.f64 x -2))

rewrite51.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1366×	`pow1`
1274×	`add-exp-log`
1274×	`log1p-expm1-u`
1274×	`expm1-log1p-u`
1252×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	133	13
2	1674	13

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(*.f64 x (-.f64 x -2))

Outputs
(+.f64 (.f64 x x) (.f64 x 2))
(+.f64 (.f64 x x) (.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))

simplify62.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1670×	`fma-def`
1268×	`log-prod`
724×	`*-commutative`
646×	`distribute-lft-out`
640×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	451
1	134	443
2	398	435
3	2440	431
4	5933	431

Stop Event

1×	node limit

Counts

29 → 29

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 x 2))
(+.f64 (.f64 x x) (.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))

Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 x x) (.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 x x) (.f64 2 x))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 x (/.f64 (fma.f64 x x (+.f64 4 (*.f64 x -2))) (+.f64 (pow.f64 x 3) 8)))
(/.f64 x (/.f64 (fma.f64 x x (fma.f64 x -2 4)) (+.f64 (pow.f64 x 3) 8)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x x (fma.f64 x -2 4)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(*.f64 (/.f64 x (+.f64 x -2)) (fma.f64 x x -4))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 x (/.f64 (fma.f64 x x (+.f64 4 (*.f64 x -2))) (+.f64 (pow.f64 x 3) 8)))
(/.f64 x (/.f64 (fma.f64 x x (fma.f64 x -2 4)) (+.f64 (pow.f64 x 3) 8)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x x (fma.f64 x -2 4)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(*.f64 (/.f64 x (+.f64 x -2)) (fma.f64 x x -4))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(*.f64 x (+.f64 2 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(*.f64 x (+.f64 2 x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(*.f64 x (+.f64 2 x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(*.f64 x (+.f64 2 x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))

eval5.0ms (0.3%)

Compiler: Compiled 254 to 169 computations (33.5% saved)

prune5.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	4	30

Accurracy

100.0%

Counts

30 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 x x) (.f64 x 2))
▶	55.8%	(+.f64 x x)
✓	100.0%	(*.f64 x (-.f64 x -2))
▶	47.1%	(*.f64 x x)
▶	100.0%	(+.f64 (.f64 x x) (.f64 x 2))
▶	55.8%	(+.f64 x x)
✓	100.0%	(*.f64 x (-.f64 x -2))
▶	47.1%	(*.f64 x x)

Compiler

Compiled 44 to 26 computations (40.9% saved)

localize28.0ms (1.5%)

Compiler: Compiled 25 to 10 computations (60% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	1	1
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 x 2))
✓	55.8%	(+.f64 x x)
✓	100.0%	(*.f64 x (-.f64 x -2))
✓	47.1%	(*.f64 x x)

Compiler

Compiled 50 to 29 computations (42% saved)

regimes13.0ms (0.7%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)
(*.f64 x (-.f64 x -2))
(+.f64 (.f64 x x) (.f64 x 2))
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

Outputs
(+.f64 (.f64 x x) (.f64 x 2))

Calls

4 calls:

4.0ms	x
3.0ms	(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
3.0ms	(+.f64 x 1)
2.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

Results

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

Compiler

Compiled 52 to 34 computations (34.6% saved)

regimes4.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)
(*.f64 x (-.f64 x -2))

Outputs
(*.f64 x (-.f64 x -2))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 14 to 7 computations (50% saved)

regimes8.0ms (0.4%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
97.7%	3	`x`

Compiler

Compiled 9 to 4 computations (55.6% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
47.1%	1	`x`

Compiler

Compiled 6 to 3 computations (50% saved)

bsearch24.0ms (1.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	8.327109139728908e-6	12.034149998445095
11.0ms	-297.9978040663507	-0.08956599848904573

Results

22.0ms

272×

body

256

valid

Compiler

Compiled 184 to 113 computations (38.6% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
6×	`*-commutative`
4×	`sub-neg`
2×	`neg-mul-1`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	78
1	29	78
2	34	78
3	36	78
4	37	78

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 x 2))
(*.f64 x (-.f64 x -2))
(if (<=.f64 x -2) (.f64 x x) (if (<=.f64 x 2) (+.f64 x x) (.f64 x x)))
(*.f64 x x)

Outputs
(+.f64 (.f64 x x) (.f64 x 2))
(*.f64 x (-.f64 x -2))
(if (<=.f64 x -2) (.f64 x x) (if (<=.f64 x 2) (+.f64 x x) (.f64 x x)))
(*.f64 x x)

Compiler

Compiled 36 to 20 computations (44.4% saved)

soundness413.0ms (22.4%)

Rules

1906×	`fma-def`
1670×	`fma-def`
1670×	`fma-def`
1604×	`fma-neg`
1366×	`pow1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	25	19
2	58	13
3	138	13
4	583	13
5	2037	13
6	5456	13
7	7831	13
0	6	13
1	133	13
2	1674	13
0	58	451
1	134	443
2	398	435
3	2440	431
4	5933	431
0	58	451
1	134	443
2	398	435
3	2440	431
4	5933	431

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 177 to 128 computations (27.7% saved)

end224.0ms (12.1%)

Compiler: Compiled 86 to 46 computations (46.5% saved)

analyze0.0ms (0%)

sample833.0ms (45.1%)

preprocess75.0ms (4.1%)

simplify69.0ms (3.8%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

localize19.0ms (1%)

series1.0ms (0.1%)

rewrite51.0ms (2.8%)

simplify62.0ms (3.3%)

eval5.0ms (0.3%)

prune5.0ms (0.3%)

localize28.0ms (1.5%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes13.0ms (0.7%)

regimes4.0ms (0.2%)

regimes8.0ms (0.4%)

regimes3.0ms (0.2%)

bsearch24.0ms (1.3%)

simplify5.0ms (0.3%)

soundness413.0ms (22.4%)

end224.0ms (12.1%)

Profiling