Details

analyze56.0ms (1.9%)

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)

sample796.0ms (26.9%)

Results

768.0ms	8256×	body	256	valid
18.0ms	205×	body	256	infinite

Bogosity

preprocess112.0ms (3.8%)

Algorithm

2×	egg-herbie

Rules

1092×	`rational.json-simplify-2`
932×	`rational.json-simplify-44`
812×	`rational.json-simplify-39`
810×	`rational.json-simplify-47`
712×	`rational.json-simplify-51`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	26	50
2	46	50
3	90	50
4	388	50
5	3976	50
6	6366	50
7	7571	50
0	2	2

Stop Event

1×	saturated
1×	node limit

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify112.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1086×	`rational.json-simplify-2`
926×	`rational.json-simplify-44`
894×	`rational.json-simplify-37`
820×	`rational.json-simplify-39`
816×	`rational.json-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	18	25
2	32	25
3	73	25
4	373	25
5	3928	25
6	6253	25
7	7399	25

Stop Event

1×	node limit

Counts

1 → 2

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 x 2)) (.f64 y y))

eval1.0ms (0%)

Compiler: Compiled 22 to 12 computations (45.5% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
✓	0.0b	(*.f64 x (+.f64 x 2))

Compiler

Compiled 25 to 13 computations (48% saved)

series2.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

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

rewrite67.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1998×	`rational.json-simplify-35`
1396×	`rational.json-1`
1396×	`rational.json-2`
1396×	`rational.json-4`
1396×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	61	38
2	132	38
3	312	38
4	1175	38
5	4534	38

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 x (+.f64 x 2)) 2) (/.f64 (.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 x (+.f64 x 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 x 2) (.f64 x 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x 2)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 x (+.f64 x 2)) 2) (/.f64 (*.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x 2) (*.f64 x 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4)))) (*.f64 2 (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x 2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (/.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4))) (*.f64 2 (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))))

simplify135.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1150×	`rational.json-simplify-2`
708×	`rational.json-simplify-43`
706×	`rational.json-simplify-59`
672×	`rational.json-simplify-19`
658×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	1226
1	153	1226
2	316	1226
3	825	1226
4	2571	1226
5	4815	1226
6	6400	1226
7	7710	1226

Stop Event

1×	node limit

Counts

62 → 45

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))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(*.f64 (+.f64 2 x) x)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (*.f64 x (+.f64 x 2)) 0)
(+.f64 0 (*.f64 x (+.f64 x 2)))
(+.f64 (/.f64 (.f64 x (+.f64 x 2)) 2) (/.f64 (.f64 x (+.f64 x 2)) 2))
(-.f64 (*.f64 x (+.f64 x 2)) 0)
(/.f64 (*.f64 x (+.f64 x 2)) 1)
(/.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 2)
(/.f64 (.f64 (+.f64 x 2) (.f64 x 4)) 4)
(/.f64 (.f64 2 (.f64 (+.f64 x 2) (*.f64 x 4))) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) 16)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))))) 32)
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(-.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 0)
(.f64 2 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2))
(.f64 2 (.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2) 1))
(.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 1)
(.f64 1 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
(.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 1/2)
(.f64 1/2 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))
(.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 2)
(/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)
(/.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))) 2)
(/.f64 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 4))) 16)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)))) 32)
(pow.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)

Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (pow.f64 y 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 y 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(*.f64 (+.f64 2 x) x)
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 x (+.f64 x 2)) 0)
(*.f64 x (+.f64 2 x))
(+.f64 0 (*.f64 x (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(+.f64 (/.f64 (.f64 x (+.f64 x 2)) 2) (/.f64 (.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(-.f64 (*.f64 x (+.f64 x 2)) 0)
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 2)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 (+.f64 x 2) (.f64 x 4)) 4)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 (+.f64 x 2) (*.f64 x 4))) 8)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) 16)
(*.f64 x (+.f64 2 x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) (.f64 2 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))))) 32)
(*.f64 x (+.f64 2 x))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 0)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 2 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 2 (.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2) 1))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 1)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 1 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 1/2)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 1/2 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 2)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))) 2)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 4) 4)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) 8)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 4))) 16)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) (.f64 2 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)))) 32)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(pow.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 32 to 14 computations (56.3% saved)

series4.0ms (0.2%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
0.0ms	y	@	0	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
0.0ms	x	@	0	(+.f64 (.f64 x 2) (.f64 x x))
0.0ms	x	@	inf	(+.f64 (.f64 x 2) (.f64 x x))
0.0ms	y	@	inf	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

rewrite84.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2294×	`rational.json-1`
2294×	`rational.json-2`
1280×	`rational.json-simplify-35`
906×	`exponential.json-3`
906×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	70	38
2	164	38
3	439	38
4	2053	38
5	7142	38

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (+.f64 x (/.f64 (.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x x) (/.f64 (+.f64 x 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x x) (+.f64 1 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (+.f64 x (+.f64 x 4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x (+.f64 x 4)) (/.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 x (+.f64 x (+.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x 2) (+.f64 x (+.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 x (+.f64 x 2)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 x 2) 2) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 x (+.f64 x 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 x 2) (.f64 x 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))) (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (+.f64 x 2)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (+.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (*.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 x (/.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) (/.f64 (+.f64 x 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) (+.f64 1 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 x 4)) (/.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x (+.f64 x (+.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 2) (+.f64 x (+.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (+.f64 x 2)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x 2) 2) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x 2) (*.f64 x 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4))) (*.f64 2 (*.f64 (+.f64 x 2) (*.f64 x 4)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x 2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4)) (*.f64 2 (*.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) 1)))))

simplify105.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1520×	`rational.json-simplify-46`
1344×	`rational.json-simplify-54`
1214×	`rational.json-simplify-2`
900×	`rational.json-simplify-35`
782×	`rational.json-simplify-43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	1390
1	158	1390
2	337	1390
3	857	1390
4	2880	1390
5	7652	1390

Stop Event

1×	node limit

Counts

70 → 52

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))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(-.f64 (*.f64 x (+.f64 x 2)) 0)
(*.f64 x (+.f64 x 2))
(.f64 2 (/.f64 (.f64 x (+.f64 x 2)) 2))
(.f64 2 (+.f64 x (/.f64 (.f64 x x) 2)))
(*.f64 (+.f64 x x) (/.f64 (+.f64 x 2) 2))
(*.f64 (+.f64 x x) (+.f64 1 (/.f64 x 2)))
(.f64 (.f64 x (+.f64 x 2)) 1)
(.f64 1 (.f64 x (+.f64 x 2)))
(*.f64 (+.f64 x 2) x)
(.f64 (.f64 x (+.f64 x (+.f64 x 4))) 1/2)
(*.f64 (+.f64 x (+.f64 x 4)) (/.f64 x 2))
(.f64 1/2 (.f64 x (+.f64 x (+.f64 x 4))))
(*.f64 (/.f64 x 2) (+.f64 x (+.f64 x 4)))
(.f64 (/.f64 (.f64 x (+.f64 x 2)) 2) 2)
(*.f64 (/.f64 (+.f64 x 2) 2) (+.f64 x x))
(/.f64 (*.f64 x (+.f64 x 2)) 1)
(/.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 2)
(/.f64 (.f64 (+.f64 x 2) (.f64 x 4)) 4)
(/.f64 (.f64 2 (.f64 (+.f64 x 2) (*.f64 x 4))) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))) (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) 16)
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(-.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 0)
(.f64 2 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2))
(.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 1)
(.f64 1 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
(.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 1/2)
(.f64 1/2 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))
(.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 2)
(/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)
(/.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))) 2)
(/.f64 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) 16)
(pow.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)

Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (pow.f64 y 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 y 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 x 2) (pow.f64 y 2)))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 y 2) (+.f64 x x)))
(+.f64 (pow.f64 x 2) (+.f64 x (+.f64 x (pow.f64 y 2))))
(-.f64 (*.f64 x (+.f64 x 2)) 0)
(*.f64 x (+.f64 2 x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(.f64 2 (/.f64 (.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(.f64 2 (+.f64 x (/.f64 (.f64 x x) 2)))
(.f64 2 (+.f64 x (.f64 x (/.f64 x 2))))
(.f64 (+.f64 x x) (+.f64 1 (.f64 x 1/2)))
(*.f64 (+.f64 x x) (/.f64 (+.f64 x 2) 2))
(*.f64 x (+.f64 2 x))
(*.f64 (+.f64 x x) (+.f64 1 (/.f64 x 2)))
(.f64 2 (+.f64 x (/.f64 (.f64 x x) 2)))
(.f64 2 (+.f64 x (.f64 x (/.f64 x 2))))
(.f64 (+.f64 x x) (+.f64 1 (.f64 x 1/2)))
(.f64 (.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(.f64 1 (.f64 x (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(*.f64 (+.f64 x 2) x)
(*.f64 x (+.f64 2 x))
(.f64 (.f64 x (+.f64 x (+.f64 x 4))) 1/2)
(*.f64 x (+.f64 2 x))
(*.f64 (+.f64 x (+.f64 x 4)) (/.f64 x 2))
(*.f64 x (+.f64 2 x))
(.f64 1/2 (.f64 x (+.f64 x (+.f64 x 4))))
(*.f64 x (+.f64 2 x))
(*.f64 (/.f64 x 2) (+.f64 x (+.f64 x 4)))
(*.f64 x (+.f64 2 x))
(.f64 (/.f64 (.f64 x (+.f64 x 2)) 2) 2)
(*.f64 x (+.f64 2 x))
(*.f64 (/.f64 (+.f64 x 2) 2) (+.f64 x x))
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 x (+.f64 x 4))) 2)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 (+.f64 x 2) (.f64 x 4)) 4)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 (+.f64 x 2) (*.f64 x 4))) 8)
(*.f64 x (+.f64 2 x))
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4))) (.f64 2 (.f64 (+.f64 x 2) (.f64 x 4)))) 16)
(*.f64 x (+.f64 2 x))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 0)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 2 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 1)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 1 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 1/2)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 1/2 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(.f64 (/.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 2) 2)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 2 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))) 2)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)) 4) 4)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) 8)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4)) (.f64 2 (.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 4))) 16)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(pow.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) 1)
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))

eval20.0ms (0.7%)

Compiler: Compiled 1147 to 667 computations (41.8% saved)

prune9.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Error

0.0b

Counts

99 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	22.7b	(+.f64 (pow.f64 x 2) (*.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	17.6b	(+.f64 (+.f64 x x) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
▶	22.0b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 49 to 31 computations (36.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 12 to 8 computations (33.3% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite223.0ms (7.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2622×	`rational.json-simplify-2`
2140×	`rational.json-simplify-35`
1218×	`rational.json-simplify-1`
1150×	`exponential.json-3`
1150×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	40	13
2	88	13
3	175	13
4	324	13
5	723	13
6	1830	13
7	3282	13
8	4329	13
9	5694	13
10	6379	13
11	6379	13
12	7326	13
13	7589	13

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 2 x) (*.f64 x 1/2)) (*.f64 (+.f64 2 x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (+.f64 2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 2 x) (+.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 (+.f64 2 x) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 (+.f64 2 x) 8)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8)))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8))))))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 (+.f64 2 x) 8)))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 2 x)) 1)))))

simplify500.0ms (16.9%)

Algorithm

1×	egg-herbie

Rules

2902×	`rational.json-simplify-2`
2830×	`rational.json-simplify-35`
1910×	`rational.json-simplify-53`
1028×	`rational.json-simplify-1`
984×	`exponential.json-simplify-26`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	387
1	128	387
2	237	387
3	536	387
4	1925	387
5	3888	387
6	4526	387
7	4690	387
8	4808	387
9	4924	387
10	5038	387
11	6090	387
12	6762	387
13	6766	387
14	6766	387
15	6926	387
16	7040	387
17	7154	387
18	7767	387

Stop Event

1×	node limit

Counts

27 → 22

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 (+.f64 2 x)) 0)
(+.f64 0 (*.f64 x (+.f64 2 x)))
(+.f64 (.f64 (+.f64 2 x) (.f64 x 1/2)) (.f64 (+.f64 2 x) (.f64 x 1/2)))
(-.f64 (*.f64 x (+.f64 2 x)) 0)
(/.f64 (*.f64 x (+.f64 2 x)) 1)
(/.f64 (*.f64 (+.f64 2 x) (+.f64 x x)) 2)
(/.f64 (.f64 x (.f64 (+.f64 2 x) 4)) 4)
(/.f64 (.f64 x (.f64 (+.f64 2 x) 8)) 8)
(/.f64 (.f64 2 (.f64 x (*.f64 (+.f64 2 x) 8))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8)))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 2 x) 8))))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8)))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 2 x) 8))))))) 256)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8))))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8)))))))) 512)
(pow.f64 (*.f64 x (+.f64 2 x)) 1)

Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (pow.f64 x 2) (+.f64 x x))
(+.f64 x (+.f64 x (pow.f64 x 2)))
(+.f64 (*.f64 x (+.f64 2 x)) 0)
(*.f64 x (+.f64 2 x))
(+.f64 0 (*.f64 x (+.f64 2 x)))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 (+.f64 2 x) (.f64 x 1/2)) (.f64 (+.f64 2 x) (.f64 x 1/2)))
(*.f64 x (+.f64 2 x))
(-.f64 (*.f64 x (+.f64 2 x)) 0)
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 2 x)) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 (+.f64 2 x) (+.f64 x x)) 2)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 x (.f64 (+.f64 2 x) 4)) 4)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 x (.f64 (+.f64 2 x) 8)) 8)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 x (*.f64 (+.f64 2 x) 8))) 16)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8)))) 32)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 2 x) 8))))) 64)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8)))))) 128)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 2 x) 8))))))) 256)
(*.f64 x (+.f64 2 x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8))))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 2 x) 8)))))))) 512)
(*.f64 x (+.f64 2 x))
(pow.f64 (*.f64 x (+.f64 2 x)) 1)
(*.f64 x (+.f64 2 x))

localize6.0ms (0.2%)

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

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x 2) (*.f64 y y))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite60.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

1388×	`rational.json-simplify-2`
1334×	`rational.json-1`
1334×	`rational.json-2`
1334×	`rational.json-4`
1334×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	53	19
2	121	19
3	284	19
4	1102	19
5	4364	19

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (pow.f64 x 2) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 4)) (*.f64 2 (*.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)))))

simplify108.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1152×	`rational.json-simplify-59`
1016×	`rational.json-simplify-1`
1010×	`rational.json-simplify-2`
752×	`rational.json-simplify-41`
750×	`rational.json-simplify-19`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	631
1	68	631
2	138	631
3	384	631
4	1139	631
5	4123	631
6	6562	631

Stop Event

1×	node limit

Counts

37 → 17

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(-.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 0)
(.f64 2 (/.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 2))
(.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 1)
(.f64 1 (+.f64 (pow.f64 x 2) (.f64 y y)))
(.f64 (.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))) 1/2)
(.f64 1/2 (.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))))
(.f64 (/.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 2) 2)
(/.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)
(/.f64 (.f64 2 (+.f64 (pow.f64 x 2) (.f64 y y))) 2)
(/.f64 (.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 4)) (.f64 2 (.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 4))) 16)
(pow.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)

Outputs
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(-.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 0)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(.f64 2 (/.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 2))
(+.f64 (pow.f64 x 2) (*.f64 y y))
(.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 1)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(.f64 1 (+.f64 (pow.f64 x 2) (.f64 y y)))
(+.f64 (pow.f64 x 2) (*.f64 y y))
(.f64 (.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))) 1/2)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(.f64 1/2 (.f64 2 (+.f64 (pow.f64 x 2) (*.f64 y y))))
(+.f64 (pow.f64 x 2) (*.f64 y y))
(.f64 (/.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 2) 2)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(/.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(/.f64 (.f64 2 (+.f64 (pow.f64 x 2) (.f64 y y))) 2)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(/.f64 (.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 4) 4)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(/.f64 (.f64 2 (.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 4)) 8)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 4)) (.f64 2 (.f64 (+.f64 (pow.f64 x 2) (.f64 y y)) 4))) 16)
(+.f64 (pow.f64 x 2) (*.f64 y y))
(pow.f64 (+.f64 (pow.f64 x 2) (*.f64 y y)) 1)
(+.f64 (pow.f64 x 2) (*.f64 y y))

eval8.0ms (0.3%)

Compiler: Compiled 395 to 281 computations (28.9% saved)

prune7.0ms (0.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	44.6b	(pow.f64 x 2)
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	17.6b	(+.f64 (+.f64 x x) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
▶	39.7b	(+.f64 x x)
✓	22.0b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 50 to 32 computations (36% saved)

localize2.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize3.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

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

Error

0.0b

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	44.6b	(pow.f64 x 2)
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	17.6b	(+.f64 (+.f64 x x) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
✓	39.7b	(+.f64 x x)
✓	22.0b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 50 to 32 computations (36% saved)

regimes26.0ms (0.9%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	(+.f64 (.f64 x 2) (.f64 x x))
5.0ms	y
5.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
5.0ms	x
3.0ms	(*.f64 y y)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))`
0.0b	1	`(+.f64 (.f64 x 2) (.f64 x x))`
0.0b	1	`(*.f64 y y)`

Compiler

Compiled 80 to 43 computations (46.3% saved)

regimes28.0ms (0.9%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	y
10.0ms	x
7.0ms	(*.f64 y y)

Results

Error	Segments	Branch
3.1b	3	`x`
7.8b	3	`y`
8.8b	2	`(*.f64 y y)`

Compiler

Compiled 28 to 15 computations (46.4% saved)

bsearch22.0ms (0.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
10.0ms	4.814165114097997e-12	2.770456037909198e-11
12.0ms	-116787.08674395943	-923.6451861878346

Results

20.0ms

208×

body

256

valid

Compiler

Compiled 252 to 168 computations (33.3% saved)

regimes8.0ms (0.3%)

Accuracy

Total -17.7b remaining (-80.2%)

Threshold costs -17.7b (-80.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	y
3.0ms	x

Results

Error	Segments	Branch
22.0b	1	`x`
22.0b	1	`y`

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	108

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
(if (<=.f64 x -950) (.f64 (+.f64 2 x) x) (if (<=.f64 x 2011652563838743/77371252455336267181195264) (+.f64 (+.f64 x x) (.f64 y y)) (*.f64 (+.f64 2 x) x)))
(*.f64 (+.f64 2 x) x)
(+.f64 x x)

Outputs
(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
(if (<=.f64 x -950) (.f64 (+.f64 2 x) x) (if (<=.f64 x 2011652563838743/77371252455336267181195264) (+.f64 (+.f64 x x) (.f64 y y)) (*.f64 (+.f64 2 x) x)))
(*.f64 (+.f64 2 x) x)
(+.f64 x x)

Compiler

Compiled 50 to 32 computations (36% saved)

soundness258.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

1086×	`rational.json-simplify-2`
926×	`rational.json-simplify-44`
894×	`rational.json-simplify-37`
820×	`rational.json-simplify-39`
816×	`rational.json-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	18	25
2	32	25
3	73	25
4	373	25
5	3928	25
6	6253	25
7	7399	25

Stop Event

1×	node limit

Compiler

Compiled 22 to 12 computations (45.5% saved)

end151.0ms (5.1%)

Compiler: Compiled 44 to 24 computations (45.5% saved)

Details

analyze56.0ms (1.9%)

sample796.0ms (26.9%)

preprocess112.0ms (3.8%)

simplify112.0ms (3.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.3%)

series2.0ms (0.1%)

rewrite67.0ms (2.3%)

simplify135.0ms (4.6%)

localize10.0ms (0.4%)

series4.0ms (0.2%)

rewrite84.0ms (2.8%)

simplify105.0ms (3.6%)

eval20.0ms (0.7%)

prune9.0ms (0.3%)

localize5.0ms (0.2%)

series0.0ms (0%)

rewrite223.0ms (7.6%)

simplify500.0ms (16.9%)

localize6.0ms (0.2%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite60.0ms (2%)

simplify108.0ms (3.7%)

eval8.0ms (0.3%)

prune7.0ms (0.2%)

localize2.0ms (0.1%)

localize3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes26.0ms (0.9%)

regimes28.0ms (0.9%)

bsearch22.0ms (0.8%)

regimes8.0ms (0.3%)

simplify3.0ms (0.1%)

soundness258.0ms (8.7%)

end151.0ms (5.1%)

Profiling