Details

analyze3.0ms (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 10 to 5 computations (50% saved)

sample985.0ms (37%)

Results

839.0ms	8256×	body	256	valid
0.0ms	3×	body	256	infinite

Bogosity

preprocess5.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

2×	`rational_best-simplify-80`
2×	`rational_best-simplify-2`
2×	`rational_best-simplify-47`
2×	`rational_best-simplify-74`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	10	17
2	12	17
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 10 to 5 computations (50% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`rational_best-simplify-80`
2×	`rational_best-simplify-2`
2×	`rational_best-simplify-47`
2×	`rational_best-simplify-74`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	10	17
2	12	17

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 15 to 7 computations (53.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.3b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 7 to 4 computations (42.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	27.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 16 to 4 computations (75% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite72.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1658×	`rational_best-5`
1656×	`rational_best-4`
1656×	`rational_best-2`
1656×	`rational_best-3`
1656×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	59	17
2	207	17
3	831	17
4	3493	17

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

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

Outputs

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

simplify177.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1886×	`rational_best-simplify-78`
1104×	`rational_best-simplify-132`
914×	`rational_best-simplify-2`
792×	`rational_best-simplify-54`
504×	`rational_best-simplify-80`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	842
1	89	834
2	190	834
3	659	834
4	2258	834
5	5553	834

Stop Event

1×	node limit

Counts

32 → 40

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 x (+.f64 x x))) 0)
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x))))))
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))))
(.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x))))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))))) (sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))) (.f64 x (.f64 x (*.f64 x 4)))))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (*.f64 x 4))))))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 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 -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 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x))))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 (.f64 x 4) (.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))
(.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 (.f64 x 4) (.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))
(.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))))) (sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))) (.f64 x (.f64 x (*.f64 x 4)))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))))) (sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x 4))) (.f64 x (.f64 x (.f64 x (*.f64 x 4))))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))))) (sqrt.f64 (.f64 x (.f64 x (.f64 (.f64 x (.f64 x (.f64 x 4))) (.f64 x (.f64 x (*.f64 x 4))))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))))) (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x 4))) (.f64 (.f64 x (.f64 x 4)) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 (.f64 x 4) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 (.f64 x 4) (.f64 x x)) (.f64 (.f64 x (.f64 x 4)) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4)))))) (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x 4))) (.f64 (.f64 x (.f64 x (.f64 x 4))) (*.f64 x x)))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x)))) (sqrt.f64 (.f64 (.f64 x (.f64 4 (.f64 x x))) (.f64 x (.f64 (.f64 4 (.f64 x x)) (*.f64 x x))))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))))
(.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))) (/.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (.f64 (.f64 x 4) (.f64 x x)))) (/.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))) (/.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 x (.f64 x (*.f64 x 4))))))
(.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x 4))))) (/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (.f64 (.f64 x 4) (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))) (/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))

eval8.0ms (0.3%)

Compiler: Compiled 887 to 307 computations (65.4% saved)

prune6.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Error

0.2b

Counts

41 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	47.3b	(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))
▶	30.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	32.0b	(*.f64 (sqrt.f64 2) x)
✓	28.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 38 to 25 computations (34.2% 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)

series0.0ms (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)

rewrite67.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1432×	`rational_best-2`
1432×	`rational_best-3`
1432×	`rational_best-1`
1430×	`rational_best-4`
1430×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	58	11
2	184	11
3	754	11
4	2981	11

Stop Event

1×	node limit

Counts

1 → 9

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

simplify131.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1570×	`rational_best-simplify-132`
1338×	`rational_best-simplify-80`
1212×	`rational_best-simplify-78`
998×	`rational_best-simplify-82`
718×	`rational_best-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	99
1	36	99
2	75	99
3	205	99
4	967	99
5	2641	99
6	5361	99

Stop Event

1×	node limit

Counts

9 → 10

Calls

Call 1

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

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

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))

rewrite69.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1656×	`rational_best-2`
1656×	`rational_best-1`
1650×	`rational_best-3`
1648×	`rational_best-4`
1648×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	70	15
2	226	15
3	876	15
4	3511	15

Stop Event

1×	node limit

Counts

1 → 9

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

simplify128.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1454×	`rational_best-simplify-132`
1292×	`rational_best-simplify-80`
1160×	`rational_best-simplify-78`
1124×	`rational_best-simplify-2`
1016×	`rational_best-simplify-82`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	315
1	45	315
2	89	315
3	229	315
4	1179	315
5	2748	315
6	5464	315

Stop Event

1×	node limit

Counts

21 → 11

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

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))
✓	16.9b	(sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x)))
	27.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	27.4b	(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))

Compiler

Compiled 72 to 25 computations (65.3% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))
0.0ms	x	@	inf	(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))
0.0ms	x	@	0	(sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x)))
0.0ms	x	@	0	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.0ms	x	@	inf	(sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x)))

rewrite68.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1834×	`rational_best-simplify-54`
818×	`rational_best-5`
816×	`rational_best-4`
816×	`rational_best-2`
816×	`rational_best-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	109
1	127	109
2	411	109
3	1786	69

Stop Event

1×	node limit

Counts

3 → 67

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x)))
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))) (*.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 4 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 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simplify191.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

1024×	`rational_best-simplify-2`
824×	`rational_best-simplify-49`
786×	`rational_best-simplify-50`
692×	`rational_best-simplify-132`
634×	`rational_best-simplify-44`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	3375
1	251	3375
2	477	3367
3	1388	3367
4	2865	3367
5	5872	3367

Stop Event

1×	node limit

Counts

103 → 122

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 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 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) 0)
(+.f64 0 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))
(-.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) 0)
(.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))) 1)
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (neg.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (*.f64 x x) 16) x))))))
(.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) 16) x))))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x))))))
(.f64 (fabs.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) 16) x)))))) (.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) 16) x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) 16) x)))))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (*.f64 x x) 16) x))))))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) 16) x))))))
(/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) 1)
(/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(/.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))) 2) 2)
(pow.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) 1)
(fabs.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))
(fabs.f64 (neg.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))))
(fabs.f64 (/.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))))
(fabs.f64 (-.f64 0 (neg.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(fabs.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (neg.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (neg.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(fabs.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(fabs.f64 (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(fabs.f64 (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))) (neg.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(fabs.f64 (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))) (fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(fabs.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))))
(fabs.f64 (.f64 (fabs.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))))
(fabs.f64 (.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (fabs.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))))
(+.f64 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(-.f64 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))) 0)
(.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) 1)
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (/.f64 1 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))))
(.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x))))))
(pow.f64 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))) 1)

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 (/.f64 x (sqrt.f64 2)) -2)
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 (/.f64 x (sqrt.f64 2)) -2)
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 (/.f64 x (sqrt.f64 2)) -2)
(*.f64 -2 (/.f64 x (sqrt.f64 2)))
(*.f64 (/.f64 x (sqrt.f64 2)) -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 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 1 (*.f64 (sqrt.f64 2) x))
(/.f64 1 (*.f64 x (sqrt.f64 2)))
(/.f64 -1 (*.f64 (sqrt.f64 2) x))
(/.f64 -1 (*.f64 x (sqrt.f64 2)))
(/.f64 -1 (*.f64 (sqrt.f64 2) x))
(/.f64 -1 (*.f64 x (sqrt.f64 2)))
(/.f64 -1 (*.f64 (sqrt.f64 2) x))
(/.f64 -1 (*.f64 x (sqrt.f64 2)))
(/.f64 -1 (*.f64 (sqrt.f64 2) x))
(/.f64 -1 (*.f64 x (sqrt.f64 2)))
(+.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 0)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x x))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 1)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) 0)
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))
(sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))
(+.f64 0 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))
(sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))
(-.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) 0)
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))
(sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))
(.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))))
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))
(sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 x (+.f64 x x)) (.f64 4 (.f64 (.f64 x x) (.f64 x x))))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))) 1)
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))
(sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (*.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x 4)))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))))
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))
(sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))
(sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (+.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 x (+.f64 x x)) (.f64 4 (.f64 (.f64 x x) (.f64 x x))))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (/.f64 (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4)))) (sqrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x)))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x))))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4)))) (/.f64 1 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))))
(.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 (.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 (+.f64 x x) (.f64 (*.f64 x (+.f64 x x)) x)))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (*.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 4 (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (sqrt.f64 (.f64 x (+.f64 x x))) (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x 4)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (neg.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(sqrt.f64 (.f64 (.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 (+.f64 x x) (.f64 (*.f64 x (+.f64 x x)) x)))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (*.f64 x x) 16) x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) 16) (*.f64 x x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) 16)) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))) (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) 16)))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) 16) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))) (sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 16))) (.f64 x (*.f64 x x))))))
(.f64 (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) 16) x))))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (*.f64 x x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) 16) (*.f64 x x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) 16)) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 x x) (.f64 4 (.f64 x x))))) (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) 16)))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 4 (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) 16) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 4))))) (sqrt.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x 16))) (.f64 x (*.f64 x x))))))
(.f64 (fabs.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
(sqrt.f64 (.f64 (.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 (+.f64 x x) (.f64 (*.f64 x (+.f64 x x)) x)))
(.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 1 (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))) (sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x)))))
(sqrt.f64 (.f64 4 (.f64 (.f64 x x) (.f64 x x))))
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(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))
(pow.f64 (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x)))) 1)
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 x x))))

eval47.0ms (1.8%)

Compiler: Compiled 5642 to 2024 computations (64.1% saved)

prune26.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	182	5	187

Error

0.0b

Counts

187 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.9b	(*.f64 (/.f64 x (sqrt.f64 2)) -2)
✓	30.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	32.0b	(*.f64 (sqrt.f64 2) x)
▶	32.1b	(*.f64 2 (/.f64 x (sqrt.f64 2)))
✓	28.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 32 to 25 computations (21.9% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 15 to 12 computations (20% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite67.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1384×	`rational_best-2`
1384×	`rational_best-3`
1384×	`rational_best-1`
1382×	`rational_best-4`
1380×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	57	11
2	183	11
3	745	11
4	2889	11

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

simplify144.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1316×	`rational_best-simplify-80`
1176×	`rational_best-simplify-78`
818×	`rational_best-simplify-54`
810×	`rational_best-simplify-2`
656×	`rational_best-simplify-82`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	341
1	112	341
2	277	341
3	883	341
4	2315	341
5	4788	341

Stop Event

1×	node limit

Counts

31 → 32

Calls

Call 1

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

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

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.5b	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval29.0ms (1.1%)

Compiler: Compiled 1687 to 1383 computations (18% saved)

prune9.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	64	5	69

Error

0.0b

Counts

69 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.9b	(*.f64 (/.f64 x (sqrt.f64 2)) -2)
✓	30.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	32.0b	(*.f64 (sqrt.f64 2) x)
✓	32.1b	(*.f64 2 (/.f64 x (sqrt.f64 2)))
✓	28.3b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 32 to 25 computations (21.9% saved)

regimes43.0ms (1.6%)

Accuracy

Total -63.1b remaining (-15982.6%)

Threshold costs -63.1b (-15982.6%)

Counts

7 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 2 (/.f64 x (sqrt.f64 2)))
(*.f64 (/.f64 x (sqrt.f64 2)) -2)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (.f64 (.f64 4 (.f64 x x)) (.f64 x x))))

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

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
11.0ms	(+.f64 (.f64 x x) (.f64 x x))
10.0ms	x
9.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.4b	2	`x`
11.4b	3	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
11.4b	3	`(+.f64 (.f64 x x) (.f64 x x))`
11.4b	3	`(*.f64 x x)`

Compiler

Compiled 78 to 41 computations (47.4% saved)

bsearch16.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-1.635127462965333e-306	8.806479124310309e-301

Results

14.0ms

160×

body

256

valid

Compiler

Compiled 143 to 117 computations (18.2% 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 -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Outputs

(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (*.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)

soundness279.0ms (10.5%)

Algorithm

3×	egg-herbie

Rules

1886×	`rational_best-simplify-78`
1104×	`rational_best-simplify-132`
914×	`rational_best-simplify-2`
792×	`rational_best-simplify-54`
504×	`rational_best-simplify-80`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	10	17
2	12	17
0	53	842
1	89	834
2	190	834
3	659	834
4	2258	834
5	5553	834
0	7	17
1	10	17
2	12	17

Stop Event

1×	saturated
1×	node limit
1×	saturated

Compiler

Compiled 54 to 34 computations (37% saved)

end19.0ms (0.7%)

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

Details

analyze3.0ms (0.1%)

sample985.0ms (37%)

preprocess5.0ms (0.2%)

simplify14.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite72.0ms (2.7%)

simplify177.0ms (6.6%)

eval8.0ms (0.3%)

prune6.0ms (0.2%)

localize4.0ms (0.2%)

series0.0ms (0%)

rewrite67.0ms (2.5%)

simplify131.0ms (4.9%)

localize6.0ms (0.2%)

series0.0ms (0%)

rewrite69.0ms (2.6%)

simplify128.0ms (4.8%)

localize19.0ms (0.7%)

series3.0ms (0.1%)

rewrite68.0ms (2.6%)

simplify191.0ms (7.2%)

eval47.0ms (1.8%)

prune26.0ms (1%)

localize7.0ms (0.3%)

series1.0ms (0%)

rewrite67.0ms (2.5%)

simplify144.0ms (5.4%)

localize7.0ms (0.3%)

eval29.0ms (1.1%)

prune9.0ms (0.4%)

regimes43.0ms (1.6%)

bsearch16.0ms (0.6%)

simplify2.0ms (0.1%)

soundness279.0ms (10.5%)

end19.0ms (0.7%)

Profiling