Details

analyze58.0ms (3.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
28.6%	25%	62.4%	0.1%	12.5%	0%	0%	6
36.4%	25%	43.7%	0.1%	31.2%	0%	0%	7
50%	31.2%	31.2%	0.1%	37.5%	0%	0%	8
62.5%	39%	23.4%	0.1%	37.5%	0%	0%	9
72.4%	42.9%	16.4%	0.1%	40.6%	0%	0%	10
79.6%	47.2%	12.1%	0.1%	40.6%	0%	0%	11
85.5%	49.4%	8.4%	0.1%	42.1%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample926.0ms (55.8%)

Results

883.0ms	8256×	body	256	valid
21.0ms	219×	body	256	infinite

Bogosity

preprocess15.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

52×	`fma-def`
22×	`+-commutative`
12×	`associate-+r+`
12×	`associate-+l+`
8×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	30	42
2	64	42
3	78	42
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))
(+.f64 (+.f64 (.f64 y 2) (.f64 y y)) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 y (+.f64 2 y)))
(fma.f64 y (+.f64 2 y) (*.f64 x x))

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def`
12×	`+-commutative`
6×	`associate-+r+`
6×	`associate-+l+`
4×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	19	21
2	36	21
3	44	21

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))

eval1.0ms (0%)

Compiler: Compiled 30 to 15 computations (50% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Accurracy

100.0%

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))

Compiler

Compiled 11 to 7 computations (36.4% saved)

localize39.0ms (2.4%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 25 to 13 computations (48% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite133.0ms (8%)

Algorithm

1×	batch-egg-rewrite

Rules

1398×	`pow1`
1306×	`add-exp-log`
1304×	`log1p-expm1-u`
1304×	`expm1-log1p-u`
1286×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	134	13
2	1743	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs
(+.f64 (.f64 x x) (.f64 x 2))
(+.f64 (.f64 x 2) (.f64 x x))
(+.f64 (.f64 (.f64 x 2) 1) (.f64 (.f64 x x) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x 2) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 x 2) (.f64 x 2)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x 2) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x 2) (.f64 x x)))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (.f64 x (-.f64 x 2))))
(/.f64 (.f64 x (-.f64 4 (.f64 x x))) (-.f64 2 x))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (+.f64 4 (.f64 x (-.f64 x 2))))
(/.f64 (.f64 (-.f64 4 (.f64 x x)) x) (-.f64 2 x))
(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))))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))

simplify126.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

1148×	`associate-*r/`
766×	`associate-*l/`
698×	`times-frac`
552×	`fma-def`
540×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	556
1	213	516
2	786	508
3	3545	508

Stop Event

1×	node limit

Counts

34 → 32

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 2) (.f64 x x))
(+.f64 (.f64 (.f64 x 2) 1) (.f64 (.f64 x x) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x 2) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 x 2) (.f64 x 2)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x 2) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x 2) (.f64 x x)))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (.f64 x (-.f64 x 2))))
(/.f64 (.f64 x (-.f64 4 (.f64 x x))) (-.f64 2 x))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (+.f64 4 (.f64 x (-.f64 x 2))))
(/.f64 (.f64 (-.f64 4 (.f64 x x)) x) (-.f64 2 x))
(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))))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))

Outputs
(*.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 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 2) (.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 (.f64 x 2) 1) (.f64 (.f64 x x) 1))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (+.f64 (pow.f64 (.f64 x 2) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 x 2) (.f64 x 2)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x 2) (*.f64 x x)))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 x x) 4) (.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 2 x)))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 (.f64 x x) (fma.f64 x (+.f64 x -2) 4)))
(/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x 2) (.f64 x x)))
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (.f64 x (-.f64 x 2))))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (.f64 x (+.f64 x -2))))
(/.f64 (+.f64 (pow.f64 x 4) (*.f64 x 8)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (.f64 x (-.f64 4 (.f64 x x))) (-.f64 2 x))
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (+.f64 4 (.f64 x (-.f64 x 2))))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (.f64 x (+.f64 x -2))))
(/.f64 (+.f64 (pow.f64 x 4) (*.f64 x 8)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (.f64 (-.f64 4 (.f64 x x)) x) (-.f64 2 x))
(*.f64 x (+.f64 2 x))
(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))
(fma.f64 x 2 (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

eval7.0ms (0.4%)

Compiler: Compiled 473 to 248 computations (47.6% saved)

prune40.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Accurracy

100.0%

Counts

33 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
▶	66.1%	(+.f64 (.f64 x x) (.f64 y y))
▶	72.3%	(+.f64 (.f64 2 x) (.f64 y y))

Compiler

Compiled 29 to 18 computations (37.9% saved)

localize7.0ms (0.4%)

Compiler: Compiled 18 to 9 computations (50% saved)

localize6.0ms (0.4%)

Compiler: Compiled 17 to 5 computations (70.6% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
✓	66.1%	(+.f64 (.f64 x x) (.f64 y y))
✓	72.3%	(+.f64 (.f64 2 x) (.f64 y y))

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes61.0ms (3.7%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

46.0ms	y
4.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
4.0ms	(+.f64 (.f64 x 2) (.f64 x x))
4.0ms	x
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))`
100.0%	1	`(+.f64 (.f64 x 2) (.f64 x x))`
100.0%	1	`(*.f64 y y)`

Compiler

Compiled 69 to 37 computations (46.4% saved)

regimes28.0ms (1.7%)

Accuracy

Total -36.8b remaining (-2825.1%)

Threshold costs -36.8b (-2825.1%)

Counts

2 → 3

Calls

Call 1

Inputs
(+.f64 (.f64 2 x) (.f64 y y))
(+.f64 (.f64 x x) (.f64 y y))

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

Calls

3 calls:

14.0ms	y
9.0ms	x
4.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
98.0%	3	`x`
86.6%	5	`y`
84.7%	2	`(*.f64 y y)`

Compiler

Compiled 27 to 15 computations (44.4% saved)

bsearch28.0ms (1.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.3653962749708447e-6	863000.075837827
11.0ms	-68.6742264373805	-1.8564870673166034

Results

24.0ms

272×

body

256

valid

Compiler

Compiled 358 to 233 computations (34.9% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
4×	`*-commutative`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	107
1	32	107

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))

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

(+.f64 (*.f64 2 x) (*.f64 y y))

Outputs
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
(if (<=.f64 x -2) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x 2) (+.f64 (.f64 2 x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
(if (or (<=.f64 x -2) (not (<=.f64 x 2))) (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x 2)))
(+.f64 (.f64 2 x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x 2))

Compiler

Compiled 45 to 28 computations (37.8% saved)

soundness107.0ms (6.4%)

Rules

1148×	`associate-*r/`
766×	`associate-*l/`
698×	`times-frac`
552×	`fma-def`
540×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	19	21
2	36	21
3	44	21
0	73	556
1	213	516
2	786	508
3	3545	508

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 38 to 20 computations (47.4% saved)

end55.0ms (3.3%)

Compiler: Compiled 41 to 22 computations (46.3% saved)

Details

analyze58.0ms (3.5%)

sample926.0ms (55.8%)

preprocess15.0ms (0.9%)

simplify12.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize39.0ms (2.4%)

series1.0ms (0.1%)

rewrite133.0ms (8%)

simplify126.0ms (7.6%)

eval7.0ms (0.4%)

prune40.0ms (2.4%)

localize7.0ms (0.4%)

localize6.0ms (0.4%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes61.0ms (3.7%)

regimes28.0ms (1.7%)

bsearch28.0ms (1.7%)

simplify6.0ms (0.3%)

soundness107.0ms (6.4%)

end55.0ms (3.3%)

Profiling