Details

analyze6.0ms (0.2%)

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 10 to 8 computations (20% saved)

sample883.0ms (35.4%)

Results

872.0ms

8256×

body

256

valid

Bogosity

preprocess71.0ms (2.8%)

Algorithm

2×	egg-herbie

Rules

1268×	`rational_best-simplify-96`
892×	`rational_best-simplify-88`
744×	`rational_best-simplify-61`
730×	`rational_best-simplify-3`
686×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	10	23
2	38	23
3	171	23
4	837	17
5	3496	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 10 to 8 computations (20% saved)

simplify67.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1268×	`rational_best-simplify-96`
892×	`rational_best-simplify-88`
744×	`rational_best-simplify-61`
730×	`rational_best-simplify-3`
686×	`rational_best-simplify-65`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	10	23
2	38	23
3	171	23
4	837	17
5	3496	17

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 21 to 17 computations (19% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

31.0b

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.0b	(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

Compiler

Compiled 7 to 6 computations (14.3% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 x 2) 2)
✓	29.9b	(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite75.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`rational_best-simplify-3`
2×	`egg-rr`
2×	`exponential-simplify-21`
2×	`exponential-simplify-24`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	12	30
2	15	30

Stop Event

1×

saturated

Counts

2 → 2

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 x) 2))))))
()

simplify50.0ms (2%)

Algorithm

1×	egg-herbie

Rules

624×	`rational_best-simplify-113`
446×	`rational_best-simplify-124`
438×	`rational_best-simplify-96`
432×	`rational_best-simplify-127`
430×	`rational_best-simplify-126`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	354
1	21	338
2	27	338
3	35	338
4	71	338
5	279	338
6	1831	338

Stop Event

1×	node limit

Counts

26 → 11

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

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 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 -1 x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 2)
(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 x) 2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (*.f64 (pow.f64 x 2) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 x) 2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

eval2.0ms (0.1%)

Compiler: Compiled 65 to 53 computations (18.5% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	8	3	11
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	4	12

Error

0.2b

Counts

12 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.6b	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
▶	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize4.0ms (0.2%)

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	@	-inf	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) x)

rewrite15.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2×	`rational_best-simplify-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11

Stop Event

1×

saturated

Counts

1 → 0

Calls

Call 1

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

Outputs
()

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

localize6.0ms (0.2%)

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))

rewrite92.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1254×	`rational_best-simplify-3`
700×	`rational_best-simplify-1`
416×	`rational_best-simplify-96`
406×	`rational_best-simplify-124`
404×	`rational_best-simplify-117`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	18	15
2	60	15
3	286	15
4	1874	15
5	7380	15

Stop Event

1×	node limit

Counts

1 → 26

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

simplify68.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1268×	`rational_best-simplify-61`
1102×	`rational_best-simplify-3`
794×	`rational_best-simplify-62`
688×	`rational_best-simplify-53`
624×	`rational_best-simplify-56`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	672
1	589	664
2	3955	656

Stop Event

1×	node limit

Counts

38 → 33

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 (*.f64 (sqrt.f64 2) (neg.f64 x)) 0)
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(/.f64 (*.f64 (sqrt.f64 2) x) -1)
(/.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 (sqrt.f64 2) x) 1))
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (-.f64 -1 (.f64 (sqrt.f64 2) x)))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) -4)
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) -8)
(/.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (+.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (+.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))))
(/.f64 (-.f64 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (-.f64 16 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (*.f64 (sqrt.f64 2) (+.f64 x x))))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (-.f64 (.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))))) (-.f64 (.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)))))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))) (-.f64 (.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))))
(pow.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(if (!=.f64 0 0) 1 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 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 (*.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 (*.f64 (sqrt.f64 2) (neg.f64 x)) 1)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 2) x) -1)
(*.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 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (+.f64 (.f64 (sqrt.f64 2) x) 1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (.f64 (.f64 (sqrt.f64 2) x) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (-.f64 -1 (.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) -4)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (*.f64 (sqrt.f64 2) (+.f64 x x)) -2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) -8)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (+.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (+.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x))))) (-.f64 16 (.f64 -4 (+.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (*.f64 (sqrt.f64 2) (+.f64 x x))))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (-.f64 (.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1))) (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (+.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (+.f64 (.f64 (sqrt.f64 2) x) 1)))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))))) (-.f64 (.f64 (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2) (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) (.f64 (sqrt.f64 2) (+.f64 x x)))) (-.f64 4 (.f64 (.f64 (sqrt.f64 2) (+.f64 x x)) -2)))))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))) (-.f64 (.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x)))))) (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 2) x) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 -1 (.f64 (sqrt.f64 2) x)))) (.f64 (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))) (.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (-.f64 (+.f64 (.f64 (sqrt.f64 2) x) 1) (.f64 (.f64 (sqrt.f64 2) x) (-.f64 -1 (.f64 (sqrt.f64 2) x))))))))
(*.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))
(if (!=.f64 0 0) 1 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (neg.f64 (.f64 2 (pow.f64 x 2))) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (.f64 (sqrt.f64 2) (neg.f64 x))) (.f64 (sqrt.f64 2) (neg.f64 x)))
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 2) (*.f64 (sqrt.f64 2) (neg.f64 x))) 0)
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (neg.f64 (.f64 2 (pow.f64 x 2))) (*.f64 (sqrt.f64 2) x)) 0)
(if (!=.f64 (.f64 (sqrt.f64 2) (neg.f64 x)) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (*.f64 (sqrt.f64 2) x)) 0)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
✓	0.3b	(pow.f64 (sqrt.f64 x) 2)

Compiler

Compiled 18 to 12 computations (33.3% saved)

series3.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 x) 2)
0.0ms	x	@	0	(pow.f64 (sqrt.f64 x) 2)
0.0ms	x	@	inf	(pow.f64 (sqrt.f64 x) 2)
0.0ms	x	@	inf	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))

rewrite15.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`exponential-simplify-20`
4×	`rational_best-simplify-3`
2×	`exponential-simplify-25`
1×	`egg-rr`
1×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	12	28
2	16	28
3	16	28

Stop Event

1×

saturated

Counts

2 → 2

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x 2))))))
((#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (pow.f64 x 2)))))))

simplify59.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

606×	`rational_best-simplify-111`
562×	`rational_best-simplify-124`
526×	`rational_best-simplify-96`
506×	`rational_best-simplify-117`
506×	`rational_best-simplify-110`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	208
1	32	184
2	49	176
3	72	176
4	146	176
5	447	176
6	2479	176

Stop Event

1×	node limit

Counts

14 → 9

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) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(sqrt.f64 (pow.f64 x 2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

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) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 (sqrt.f64 2) (.f64 -1 (*.f64 x 1)))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 (sqrt.f64 2) (.f64 -1 (*.f64 x 1)))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 (sqrt.f64 2) (.f64 -1 (*.f64 x 1)))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(.f64 (sqrt.f64 2) (.f64 -1 (*.f64 x 1)))
(.f64 (sqrt.f64 2) (.f64 x -1))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (pow.f64 x 2))
(pow.f64 (sqrt.f64 x) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

eval23.0ms (0.9%)

Compiler: Compiled 1415 to 1099 computations (22.3% saved)

prune6.0ms (0.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	41	5	46

Error

0.2b

Counts

46 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	48.0b	(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))
✓	32.6b	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

Compiler

Compiled 49 to 41 computations (16.3% saved)

localize82.0ms (3.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 x 2) -2)
✓	0.4b	(*.f64 (sqrt.f64 2) x)
	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	30.1b	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))

Compiler

Compiled 64 to 49 computations (23.4% saved)

series2.0ms (0.1%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
0.0ms	x	@	inf	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
0.0ms	x	@	-inf	(/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x))
0.0ms	x	@	inf	(*.f64 (pow.f64 x 2) -2)
0.0ms	x	@	0	(*.f64 (pow.f64 x 2) -2)

rewrite84.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1372×	`rational_best-simplify-61`
1130×	`rational_best-simplify-52`
806×	`rational_best-simplify-53`
748×	`rational_best-simplify-56`
564×	`rational_best-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	22	53
2	103	53
3	640	53
4	4407	53

Stop Event

1×	node limit

Counts

3 → 16

Calls

Call 1

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

Outputs

()

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

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

simplify68.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

910×	`rational_best-simplify-3`
838×	`rational_best-simplify-61`
832×	`rational_best-simplify-65`
470×	`rational_best-simplify-53`
458×	`rational_best-simplify-52`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	600
1	161	552
2	905	552
3	4896	552

Stop Event

1×	node limit

Counts

40 → 20

Calls

Call 1

Inputs
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(*.f64 -2 (pow.f64 x 2))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(-.f64 (*.f64 x (sqrt.f64 2)) 0)
(-.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(/.f64 (*.f64 x (sqrt.f64 2)) 1)
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) -1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(+.f64 (*.f64 (pow.f64 x 2) -2) 0)
(+.f64 0 (*.f64 (pow.f64 x 2) -2))
(-.f64 (*.f64 (pow.f64 x 2) -2) 0)
(-.f64 0 (*.f64 2 (pow.f64 x 2)))
(/.f64 (*.f64 (pow.f64 x 2) -2) 1)
(/.f64 (*.f64 2 (pow.f64 x 2)) -1)
(pow.f64 (*.f64 (pow.f64 x 2) -2) 1)
(neg.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(-.f64 (*.f64 x (sqrt.f64 2)) 0)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(-.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(/.f64 (*.f64 x (sqrt.f64 2)) 1)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)) -1)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(+.f64 (*.f64 (pow.f64 x 2) -2) 0)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(+.f64 0 (*.f64 (pow.f64 x 2) -2))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(-.f64 (*.f64 (pow.f64 x 2) -2) 0)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(-.f64 0 (*.f64 2 (pow.f64 x 2)))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(/.f64 (*.f64 (pow.f64 x 2) -2) 1)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(/.f64 (*.f64 2 (pow.f64 x 2)) -1)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 2) -2) 1)
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))
(neg.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 -2 (pow.f64 x 2))
(.f64 -2 (.f64 x x))

eval54.0ms (2.2%)

Compiler: Compiled 2601 to 2045 computations (21.4% saved)

prune9.0ms (0.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	62	5	67

Error

0.1b

Counts

67 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.2b	(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
✓	32.6b	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

Compiler

Compiled 45 to 38 computations (15.6% saved)

localize21.0ms (0.8%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 52 to 40 computations (23.1% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite61.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1224×	`rational_best-simplify-61`
1190×	`rational_best-simplify-65`
1054×	`rational_best-simplify-3`
736×	`rational_best-simplify-62`
632×	`rational_best-simplify-53`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	16	11
2	90	11
3	549	11
4	3646	11

Stop Event

1×	node limit

Counts

1 → 0

Calls

Call 1

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

Outputs
()

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval66.0ms (2.6%)

Compiler: Compiled 1964 to 1553 computations (20.9% saved)

prune7.0ms (0.3%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	42	5	47

Error

0.1b

Counts

47 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.2b	(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
✓	32.6b	(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
✓	31.2b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.8b	(*.f64 (sqrt.f64 2) x)
✓	31.0b	(sqrt.f64 (*.f64 (pow.f64 x 2) 2))

Compiler

Compiled 45 to 38 computations (15.6% saved)

regimes149.0ms (6%)

Accuracy

Total -62.8b remaining (-13983.9%)

Threshold costs -62.8b (-13983.9%)

Counts

7 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (*.f64 (pow.f64 x 2) 2))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (.f64 -2 (/.f64 x (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (neg.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 x) 2) (sqrt.f64 2))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(if (!=.f64 (.f64 (sqrt.f64 2) x) 0) (/.f64 (.f64 (pow.f64 x 2) -2) (.f64 (sqrt.f64 2) x)) (.f64 (sqrt.f64 2) (neg.f64 x)))

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

Calls

4 calls:

70.0ms	x
58.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
10.0ms	(pow.f64 x 2)
9.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))

Results

Error	Segments	Branch
0.4b	2	`x`
14.3b	3	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
14.3b	3	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
14.3b	3	`(pow.f64 x 2)`

Compiler

Compiled 94 to 73 computations (22.3% saved)

bsearch19.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
19.0ms	-1.3475538675960855e-297	2.570630597080787e-302

Results

17.0ms

160×

body

256

valid

Compiler

Compiled 143 to 120 computations (16.1% saved)

simplify2.0ms (0.1%)

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 -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Outputs

(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (*.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)

soundness304.0ms (12.2%)

Algorithm

3×	egg-herbie

Rules

1268×	`rational_best-simplify-96`
1268×	`rational_best-simplify-96`
892×	`rational_best-simplify-88`
892×	`rational_best-simplify-88`
744×	`rational_best-simplify-61`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	10	23
2	38	23
3	171	23
4	837	17
5	3496	17
0	15	354
1	21	338
2	27	338
3	35	338
4	71	338
5	279	338
6	1831	338
0	8	23
1	10	23
2	38	23
3	171	23
4	837	17
5	3496	17

Stop Event

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

Compiler

Compiled 246 to 206 computations (16.3% saved)

end69.0ms (2.8%)

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

Details

analyze6.0ms (0.2%)

sample883.0ms (35.4%)

preprocess71.0ms (2.8%)

simplify67.0ms (2.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.3%)

series2.0ms (0.1%)

rewrite75.0ms (3%)

simplify50.0ms (2%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series1.0ms (0%)

rewrite15.0ms (0.6%)

simplify13.0ms (0.5%)

localize6.0ms (0.2%)

series0.0ms (0%)

rewrite92.0ms (3.7%)

simplify68.0ms (2.7%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite15.0ms (0.6%)

simplify59.0ms (2.4%)

eval23.0ms (0.9%)

prune6.0ms (0.2%)

localize82.0ms (3.3%)

series2.0ms (0.1%)

rewrite84.0ms (3.4%)

simplify68.0ms (2.7%)

eval54.0ms (2.2%)

prune9.0ms (0.3%)

localize21.0ms (0.8%)

series1.0ms (0%)

rewrite61.0ms (2.4%)

simplify13.0ms (0.5%)

eval66.0ms (2.6%)

prune7.0ms (0.3%)

regimes149.0ms (6%)

bsearch19.0ms (0.8%)

simplify2.0ms (0.1%)

soundness304.0ms (12.2%)

end69.0ms (2.8%)

Profiling