Details

analyze124.0ms (4.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
64.5%	62.4%	34.3%	0.1%	3.1%	0%	0%	8
75.4%	71.8%	23.4%	0.1%	4.7%	0%	0%	9
80.7%	74.9%	18%	0.1%	7%	0%	0%	10
86.8%	79.6%	12.1%	0.1%	8.2%	0%	0%	11
89.8%	81.2%	9.2%	0.1%	9.6%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.5s (82%)

Results

2.3s	8256×	body	256	valid
34.0ms	281×	body	256	infinite

Bogosity

preprocess27.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

2×	`swap-x-y`
2×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	9	26
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

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

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

Symmetry

(sort x y)

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

2×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 6 computations (53.8% saved)

series6.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/.f64 (*.f64 x y) 2)
1.0ms	y	@	0	(/.f64 (*.f64 x y) 2)
1.0ms	x	@	inf	(/.f64 (*.f64 x y) 2)
1.0ms	y	@	inf	(/.f64 (*.f64 x y) 2)
0.0ms	y	@	-inf	(/.f64 (*.f64 x y) 2)

rewrite103.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1354×	`rational.json-5`
1352×	`exponential.json-3`
1352×	`rational.json-1`
1352×	`rational.json-2`
1352×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	58	13
2	185	13
3	661	13
4	2588	13

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

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

Outputs

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

simplify219.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

990×	`rational.json-simplify-47`
918×	`rational.json-simplify-1`
854×	`rational.json-simplify-111`
850×	`exponential.json-simplify-26`
674×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	533
1	85	533
2	175	533
3	791	533
4	3880	533
5	7197	533

Stop Event

1×	node limit

Counts

41 → 19

Calls

Call 1

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

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

eval5.0ms (0.2%)

Compiler: Compiled 358 to 189 computations (47.2% saved)

prune4.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	1	20

Error

0.0b

Counts

20 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness0.0ms (0%)

end24.0ms (0.8%)

Remove: (sort x y)
Compiler: Compiled 21 to 15 computations (28.6% saved)

Details

analyze124.0ms (4.1%)

sample2.5s (82%)

preprocess27.0ms (0.9%)

simplify25.0ms (0.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.3%)

series6.0ms (0.2%)

rewrite103.0ms (3.4%)

simplify219.0ms (7.2%)

eval5.0ms (0.2%)

prune4.0ms (0.1%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end24.0ms (0.8%)

Profiling