Details

analyze58.0ms (2.5%)

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)

sample901.0ms (38.5%)

Results

868.0ms	8256×	body	256	valid
23.0ms	243×	body	256	infinite

Bogosity

preprocess237.0ms (10.1%)

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)

simplify111.0ms (4.7%)

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

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

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)

localize14.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 13 computations (48% saved)

series1.0ms (0%)

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))

rewrite216.0ms (9.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2648×	`rational.json-simplify-2`
2140×	`rational.json-simplify-35`
1212×	`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	721	13
6	1837	13
7	3280	13
8	4325	13
9	5690	13
10	6375	13
11	6375	13
12	7339	13
13	7602	13

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

simplify570.0ms (24.4%)

Algorithm

1×	egg-herbie

Rules

2996×	`rational.json-simplify-2`
2734×	`rational.json-simplify-35`
1838×	`rational.json-simplify-53`
1112×	`exponential.json-simplify-26`
1098×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	387
1	131	387
2	243	387
3	525	387
4	1830	387
5	3750	387
6	4413	387
7	4572	387
8	4686	387
9	4798	387
10	4908	387
11	5928	387
12	6559	387
13	6742	387
14	6742	387
15	6742	387
16	6852	387
17	6962	387
18	7072	387
19	7657	387
20	7908	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 x 2)) 0)
(+.f64 0 (*.f64 x (+.f64 x 2)))
(+.f64 (.f64 (+.f64 x 2) (.f64 x 1/2)) (.f64 (+.f64 x 2) (.f64 x 1/2)))
(-.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 x (.f64 (+.f64 x 2) 4)) 4)
(/.f64 (.f64 x (.f64 (+.f64 x 2) 8)) 8)
(/.f64 (.f64 2 (.f64 x (*.f64 (+.f64 x 2) 8))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8)))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 x 2) 8))))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8)))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 x 2) 8))))))) 256)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8))))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8)))))))) 512)
(pow.f64 (*.f64 x (+.f64 x 2)) 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 x 2)) 0)
(*.f64 x (+.f64 2 x))
(+.f64 0 (*.f64 x (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 (+.f64 x 2) (.f64 x 1/2)) (.f64 (+.f64 x 2) (.f64 x 1/2)))
(*.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 x (.f64 (+.f64 x 2) 4)) 4)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 x (.f64 (+.f64 x 2) 8)) 8)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 x (*.f64 (+.f64 x 2) 8))) 16)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8)))) 32)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 x 2) 8))))) 64)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8)))))) 128)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (*.f64 (+.f64 x 2) 8))))))) 256)
(*.f64 x (+.f64 2 x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8))))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 (+.f64 x 2) 8)))))))) 512)
(*.f64 x (+.f64 2 x))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 32 to 14 computations (56.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite71.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1426×	`rational.json-1`
1426×	`rational.json-2`
1426×	`rational.json-4`
1426×	`rational.json-3`
1420×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	50	13
2	122	13
3	284	13
4	1115	13
5	4533	13

Stop Event

1×	node limit

Counts

1 → 29

Calls

Call 1

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

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

simplify70.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1202×	`rational.json-simplify-2`
1086×	`rational.json-simplify-41`
980×	`rational.json-simplify-46`
972×	`rational.json-simplify-44`
954×	`rational.json-simplify-59`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	569
1	184	569
2	407	569
3	1172	569
4	5510	569

Stop Event

1×	node limit

Counts

41 → 36

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

eval12.0ms (0.5%)

Compiler: Compiled 764 to 436 computations (42.9% saved)

prune7.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	57	3	60

Error

Counts

60 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	16.1b	(+.f64 (+.f64 x x) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

Compiler

Compiled 33 to 20 computations (39.4% saved)

localize7.0ms (0.3%)

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

eval0.0ms (0%)

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

prune2.0ms (0.1%)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	16.1b	(+.f64 (+.f64 x x) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

Compiler

Compiled 33 to 20 computations (39.4% saved)

regimes19.0ms (0.8%)

Counts

3 → 1

Calls

Call 1

Inputs
(+.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))

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

Calls

5 calls:

4.0ms	(+.f64 (.f64 x 2) (.f64 x x))
4.0ms	x
4.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
3.0ms	y
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 62 to 35 computations (43.5% saved)

regimes10.0ms (0.4%)

Accuracy

Total -16.0b remaining (-82106.6%)

Threshold costs -16.0b (-82106.6%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
3.0ms	y
2.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 29 to 16 computations (44.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	75

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

Compiler

Compiled 33 to 20 computations (39.4% saved)

soundness0.0ms (0%)

end21.0ms (0.9%)

Compiler: Compiled 29 to 14 computations (51.7% saved)

Details

analyze58.0ms (2.5%)

sample901.0ms (38.5%)

preprocess237.0ms (10.1%)

simplify111.0ms (4.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize14.0ms (0.6%)

series1.0ms (0%)

rewrite216.0ms (9.2%)

simplify570.0ms (24.4%)

localize10.0ms (0.4%)

series1.0ms (0%)

rewrite71.0ms (3%)

simplify70.0ms (3%)

eval12.0ms (0.5%)

prune7.0ms (0.3%)

localize7.0ms (0.3%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes19.0ms (0.8%)

regimes10.0ms (0.4%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end21.0ms (0.9%)

Profiling