Details

analyze51.0ms (4.7%)

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
65.6%	65.6%	34.3%	0.1%	0%	0%	0%	8
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	9
82%	82%	18%	0.1%	0%	0%	0%	10
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	11
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample693.0ms (63.4%)

Results

681.0ms

8256×

body

256

valid

Bogosity

preprocess123.0ms (11.2%)

Algorithm

2×	egg-herbie

Rules

1254×	`rational.json-simplify-51`
1240×	`rational.json-simplify-35`
1192×	`rational.json-simplify-2`
864×	`rational.json-simplify-57`
698×	`rational.json-simplify-39`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	18	30
2	39	30
3	265	30
4	1578	30
5	4247	30
6	7801	30
0	2	2
1	2	2

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))

Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt.f64 (fabs.f64 (-.f64 x y)))

Symmetry

(sort x y)

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify55.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1996×	`rational.json-simplify-35`
1548×	`rational.json-simplify-51`
1404×	`rational.json-simplify-43`
1062×	`rational.json-simplify-39`
904×	`rational.json-simplify-59`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	13	15
2	25	15
3	103	15
4	1037	15
5	3864	15

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

eval0.0ms (0%)

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

prune1.0ms (0.1%)

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	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 16 to 5 computations (68.8% saved)

series2.0ms (0.2%)

Counts

1 → 8

Calls

6 calls:

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

rewrite53.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1490×	`rational.json-simplify-35`
1202×	`exponential.json-3`
1202×	`rational.json-1`
1202×	`rational.json-2`
1202×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	55	15
2	145	15
3	496	15
4	3753	15

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (fabs.f64 (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (fabs.f64 (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4)) (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)))))

Outputs

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

simplify68.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1312×	`rational.json-simplify-2`
1098×	`rational.json-simplify-53`
1034×	`rational.json-simplify-51`
800×	`rational.json-simplify-44`
770×	`rational.json-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	409
1	91	393
2	217	377
3	734	377
4	4496	377

Stop Event

1×	node limit

Counts

23 → 22

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(+.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 0)
(+.f64 0 (sqrt.f64 (fabs.f64 (-.f64 x y))))
(-.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 0)
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)
(*.f64 1 (sqrt.f64 (fabs.f64 (-.f64 x y))))
(*.f64 2 (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2))
(.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 1/2)
(.f64 1/2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2))
(*.f64 (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 2)
(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4)) (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4))) 16)
(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)

Outputs
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (neg.f64 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (neg.f64 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (neg.f64 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (*.f64 -1 x)))))
(sqrt.f64 (fabs.f64 (neg.f64 (+.f64 y (neg.f64 x)))))
(sqrt.f64 (fabs.f64 (+.f64 y (neg.f64 x))))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 x (*.f64 y -1))))
(sqrt.f64 (fabs.f64 (+.f64 x (neg.f64 y))))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 x (*.f64 y -1))))
(sqrt.f64 (fabs.f64 (+.f64 x (neg.f64 y))))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 x (*.f64 y -1))))
(sqrt.f64 (fabs.f64 (+.f64 x (neg.f64 y))))
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 -1 y) x)))
(sqrt.f64 (fabs.f64 (+.f64 x (*.f64 y -1))))
(sqrt.f64 (fabs.f64 (+.f64 x (neg.f64 y))))
(+.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 0)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(+.f64 0 (sqrt.f64 (fabs.f64 (-.f64 x y))))
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(-.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 0)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(*.f64 1 (sqrt.f64 (fabs.f64 (-.f64 x y))))
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(*.f64 2 (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2))
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(.f64 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 1/2)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(.f64 1/2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2))
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(*.f64 (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 2)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 2) 2)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4) 4)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4)) 8)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4)) (.f64 2 (.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 4))) 16)
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) 1)
(sqrt.f64 (fabs.f64 (-.f64 x y)))

eval7.0ms (0.6%)

Compiler: Compiled 183 to 87 computations (52.5% saved)

prune6.0ms (0.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	1	23

Error

0.0b

Counts

23 → 1

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness0.0ms (0%)

end25.0ms (2.3%)

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

Details

analyze51.0ms (4.7%)

sample693.0ms (63.4%)

preprocess123.0ms (11.2%)

simplify55.0ms (5%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize6.0ms (0.5%)

series2.0ms (0.2%)

rewrite53.0ms (4.9%)

simplify68.0ms (6.2%)

eval7.0ms (0.6%)

prune6.0ms (0.5%)

simplify3.0ms (0.3%)

soundness0.0ms (0%)

end25.0ms (2.3%)

Profiling