Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample4.3s (58.4%)

Results

4.3s

8256×

body

256

valid

Bogosity

preprocess10.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

2×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	9	17
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	9	17

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

eval0.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.9b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 7 to 6 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	30.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite323.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3126×	`rational.json-simplify-35`
1872×	`rational.json-simplify-2`
1260×	`rational.json-simplify-1`
1138×	`exponential.json-3`
1138×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	51	30
2	107	30
3	200	30
4	352	30
5	780	30
6	1829	30
7	3060	30
8	3671	30
9	4345	30
10	5144	30
11	5563	30
12	5563	30
13	6034	30
14	6034	30
15	6624	30
16	7495	30
17	7983	30

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 2 (pow.f64 x 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2) (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (sqrt.f64 (.f64 2 (pow.f64 x 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (sqrt.f64 (.f64 2 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (sqrt.f64 (.f64 2 (pow.f64 x 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8)))))))) 1024)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))))))) 2048)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x 2) (pow.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x 2) 1/2) (.f64 (pow.f64 x 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x 2) 3/2) (.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) 16) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (pow.f64 x 2) 16)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))))))) 1024)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16))))))))) 2048)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (pow.f64 x 2)) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2) (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))))))) 1024)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))))))))) 2048)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x 2) (pow.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 2) 1/2) (*.f64 (pow.f64 x 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 2) 3/2) (*.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 16) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 x 2) 16)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16)))))))) 1024)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 16))))))))) 2048)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (pow.f64 x 2)) 1)))))

simplify415.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

4028×	`rational.json-simplify-51`
3042×	`rational.json-simplify-41`
1998×	`rational.json-simplify-35`
1436×	`rational.json-simplify-2`
752×	`rational.json-simplify-43`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1010
1	247	1002
2	639	888
3	1950	888
4	3353	888
5	3741	888
6	3814	888
7	3885	888
8	3945	888
9	4004	888
10	4353	888
11	4412	888
12	4471	888
13	4530	888
14	4589	888
15	4648	888
16	4707	888
17	4766	888
18	4825	888
19	4884	888

Stop Event

1×	node limit

Counts

60 → 54

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 0)
(+.f64 0 (sqrt.f64 (*.f64 2 (pow.f64 x 2))))
(+.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2) (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(-.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 0)
(.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (pow.f64 x 2))))
(.f64 (.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))) 1/2)
(.f64 4 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/4))
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4) 1/4)
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8) 1/8)
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4))
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2) 2)
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/4) 4)
(.f64 1/8 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)
(/.f64 (.f64 2 (sqrt.f64 (.f64 2 (pow.f64 x 2)))) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 4) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))))) 512)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))))))) 1024)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))))))) 2048)
(pow.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) 0)
(+.f64 0 (*.f64 2 (pow.f64 x 2)))
(+.f64 (.f64 (pow.f64 x 2) 1/2) (.f64 (pow.f64 x 2) 3/2))
(+.f64 (.f64 (pow.f64 x 2) 3/2) (.f64 (pow.f64 x 2) 1/2))
(-.f64 (*.f64 2 (pow.f64 x 2)) 0)
(/.f64 (*.f64 2 (pow.f64 x 2)) 1)
(/.f64 (*.f64 (pow.f64 x 2) 4) 2)
(/.f64 (*.f64 (pow.f64 x 2) 8) 4)
(/.f64 (*.f64 (pow.f64 x 2) 16) 8)
(/.f64 (.f64 2 (.f64 (pow.f64 x 2) 16)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))))))) 512)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))))))) 1024)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))))))))) 2048)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1)

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(+.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 0)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(+.f64 0 (sqrt.f64 (*.f64 2 (pow.f64 x 2))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(+.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2) (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(-.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 0)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 1)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 1 (sqrt.f64 (.f64 2 (pow.f64 x 2))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))) 1/2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 4 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/4))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4) 1/4)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8) 1/8)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 2 (pow.f64 x 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 4))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/2) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1/4) 4)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 1/8 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (sqrt.f64 (.f64 2 (pow.f64 x 2)))) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 4) 4)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8) 8)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)) 16)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))) 32)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))) 64)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))) 128)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))))) 256)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))))) 512)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 8)))))))) 1024)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (pow.f64 x 2))) 8))))))))) 2048)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 2))) 1)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) 0)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 0 (*.f64 2 (pow.f64 x 2)))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 (pow.f64 x 2) 1/2) (.f64 (pow.f64 x 2) 3/2))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 (pow.f64 x 2) 3/2) (.f64 (pow.f64 x 2) 1/2))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(-.f64 (*.f64 2 (pow.f64 x 2)) 0)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (*.f64 2 (pow.f64 x 2)) 1)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) 4) 2)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) 8) 4)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) 16) 8)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 (pow.f64 x 2) 16)) 16)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))) 32)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))) 64)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))))) 128)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))))) 256)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))))))) 512)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 16)))))))) 1024)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 16))))))))) 2048)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))

eval14.0ms (0.2%)

Compiler: Compiled 621 to 563 computations (9.3% saved)

prune7.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Error

0.2b

Counts

55 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	30.5b	(*.f64 (sqrt.f64 2) x)
✓	31.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize45.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite225.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1740×	`rational.json-simplify-35`
1606×	`rational.json-1`
1606×	`rational.json-2`
1508×	`rational.json-simplify-53`
1262×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	45	11
2	95	11
3	183	11
4	323	11
5	705	11
6	1680	11
7	2910	11
8	3832	11
9	4975	11
10	6124	11
11	7083	11
12	7083	11
13	7710	11

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

Outputs

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

simplify1.1s (14.4%)

Algorithm

1×	egg-herbie

Rules

3900×	`rational.json-simplify-35`
2832×	`rational.json-simplify-2`
1574×	`rational.json-simplify-53`
960×	`exponential.json-simplify-26`
930×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	165
1	136	165
2	291	165
3	819	165
4	2034	165
5	3334	165
6	4237	165
7	4530	165
8	4672	165
9	4779	165
10	4886	165
11	5468	165
12	5747	165
13	5965	165
14	6156	165
15	6258	165
16	6405	165
17	6484	165
18	6484	165
19	6591	165
20	6698	165
21	6805	165
22	6921	165
23	7028	165
24	7135	165
25	7466	165
26	7573	165
27	7680	165
28	7787	165
29	7894	165

Stop Event

1×	node limit

Counts

15 → 16

Calls

Call 1

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

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 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	@	0	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite132.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1910×	`rational.json-simplify-35`
1610×	`rational.json-1`
1610×	`rational.json-2`
1610×	`rational.json-4`
1610×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	55	15
2	125	15
3	260	15
4	512	15
5	1218	15
6	2586	15
7	4474	15
8	5728	15
9	7320	15

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (neg.f64 x))

Outputs

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

simplify277.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2282×	`rational.json-simplify-2`
1868×	`rational.json-simplify-35`
1724×	`rational.json-simplify-1`
1168×	`rational.json-simplify-41`
1086×	`rational.json-simplify-53`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	577
1	174	577
2	373	577
3	909	577
4	2522	577
5	4652	577
6	5254	577
7	5617	577
8	5876	577
9	6143	577
10	6179	577
11	7445	577
12	7883	577

Stop Event

1×	node limit

Counts

37 → 30

Calls

Call 1

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

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

eval11.0ms (0.1%)

Compiler: Compiled 423 to 364 computations (13.9% saved)

prune6.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	46	3	49

Error

0.2b

Counts

49 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	30.5b	(*.f64 (sqrt.f64 2) x)
✓	31.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

regimes30.0ms (0.4%)

Accuracy

Total -62.2b remaining (-13839.1%)

Threshold costs -62.2b (-13839.1%)

Counts

3 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 (sqrt.f64 2) x)

Calls

4 calls:

8.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
8.0ms	(pow.f64 x 2)
7.0ms	(*.f64 2 (pow.f64 x 2))
6.0ms	x

Results

Error	Segments	Branch
0.4b	2	`x`
14.4b	3	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
14.4b	3	`(*.f64 2 (pow.f64 x 2))`
14.4b	3	`(pow.f64 x 2)`

Compiler

Compiled 35 to 28 computations (20% saved)

bsearch19.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
19.0ms	-1.0079072536098313e-305	3.603476287487585e-298

Results

17.0ms

160×

body

256

valid

Compiler

Compiled 141 to 119 computations (15.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	46

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x -2024022533073/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

(*.f64 (sqrt.f64 2) x)

Outputs

(if (<=.f64 x -2024022533073/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 19 to 15 computations (21.1% saved)

soundness397.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

4028×	`rational.json-simplify-51`
3042×	`rational.json-simplify-41`
1998×	`rational.json-simplify-35`
1436×	`rational.json-simplify-2`
752×	`rational.json-simplify-43`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1010
1	247	1002
2	639	888
3	1950	888
4	3353	888
5	3741	888
6	3814	888
7	3885	888
8	3945	888
9	4004	888
10	4353	888
11	4412	888
12	4471	888
13	4530	888
14	4589	888
15	4648	888
16	4707	888
17	4766	888
18	4825	888
19	4884	888

Stop Event

1×	node limit

Compiler

Compiled 18 to 15 computations (16.7% saved)

end20.0ms (0.3%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

Details

analyze5.0ms (0.1%)

sample4.3s (58.4%)

preprocess10.0ms (0.1%)

simplify46.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite323.0ms (4.4%)

simplify415.0ms (5.6%)

eval14.0ms (0.2%)

prune7.0ms (0.1%)

localize45.0ms (0.6%)

series1.0ms (0%)

rewrite225.0ms (3.1%)

simplify1.1s (14.4%)

localize6.0ms (0.1%)

series0.0ms (0%)

rewrite132.0ms (1.8%)

simplify277.0ms (3.8%)

eval11.0ms (0.1%)

prune6.0ms (0.1%)

regimes30.0ms (0.4%)

bsearch19.0ms (0.3%)

simplify2.0ms (0%)

soundness397.0ms (5.4%)

end20.0ms (0.3%)

Profiling