Details

analyze751.0ms (21.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.7%	0.3%	0%	0%	0%	0
0%	0%	99.7%	0.3%	0%	0%	0%	1
0%	0%	99.7%	0.3%	0%	0%	0%	2
0%	0%	99.7%	0.3%	0%	0%	0%	3
0%	0%	99.7%	0.3%	0%	0%	0%	4
0%	0%	99.7%	0.3%	0%	0%	0%	5
0%	0%	99.7%	0.3%	0%	0%	0%	6
0%	0%	99.7%	0.3%	0%	0%	0%	7
0%	0%	99.7%	0.3%	0%	0%	0%	8
0%	0%	99.7%	0.3%	0%	0%	0%	9
0%	0%	99.7%	0.3%	0%	0%	0%	10
0%	0%	99.7%	0.3%	0%	0%	0%	11
0%	0%	99.7%	0.3%	0%	0%	0%	12

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.4s (69.2%)

Results

1.6s	8256×	body	256	valid
557.0ms	3222×	body	256	invalid
227.0ms	1379×	body	256	infinite

Bogosity

preprocess81.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

1472×	`distribute-lft-neg-in`
1414×	`distribute-rgt-neg-in`
1310×	`times-frac`
1064×	`distribute-neg-frac`
670×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	848
1	394	848
2	1393	848
3	3383	848
4	6705	848
0	6	6
1	6	6

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4
5

Outputs
0
1
2
1
3
4
5

Call 2

Inputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 w0 D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M w0) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 w0 l)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h w0)))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 w0)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 h D) (.f64 2 d)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 l D) (.f64 2 d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 d D) (.f64 2 M)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M h) (.f64 2 d)) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M l) (.f64 2 d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M d) (.f64 2 D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 l)) 2) (/.f64 h d)))))

Outputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 D (/.f64 M d)) 2) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 M (.f64 (/.f64 2 D) d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 w0 D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 w0 (/.f64 (*.f64 2 d) D)) 2)))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 D 2) (/.f64 w0 d)) 2)))))
(.f64 M (sqrt.f64 (neg.f64 (fma.f64 (/.f64 h l) (pow.f64 (.f64 D (/.f64 (/.f64 w0 2) d)) 2) -1))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M w0) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 w0 M) (.f64 2 d)) 2)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 M d) (/.f64 w0 2)) 2)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 w0 (/.f64 M (.f64 2 d))) 2)))))
(.f64 D (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 M d) (/.f64 w0 2)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 D (/.f64 M d)) 2) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (*.f64 (/.f64 2 D) d)) 2) (/.f64 w0 l)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 D (/.f64 M d)) 2) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (fma.f64 (pow.f64 (/.f64 M (.f64 (/.f64 2 D) d)) 2) (neg.f64 (/.f64 h w0)) 1)))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 w0)) 2) (/.f64 h l)))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 w0 2)) 2)))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M w0)) 2)))))
(.f64 d (sqrt.f64 (fma.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 w0 2))) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 D (/.f64 M d)) 2) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 M (.f64 (/.f64 2 D) d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 h D) (.f64 2 d)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 h (/.f64 (*.f64 2 d) D)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 h d) (/.f64 D 2)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 h (.f64 2 d))) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 l D) (.f64 2 d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 l (/.f64 (*.f64 2 d) D)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 l d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 l 2) d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 D (/.f64 2 (/.f64 l d))) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 d D) (.f64 2 M)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 d 2) (/.f64 D M)) 2)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 D 2) (/.f64 d M)) 2)))))
(.f64 w0 (sqrt.f64 (fma.f64 (/.f64 h l) (neg.f64 (pow.f64 (.f64 D (/.f64 (/.f64 d 2) M)) 2)) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M h) (.f64 2 d)) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M d) (/.f64 h 2)) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 h (/.f64 M (.f64 2 d))) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M l) (.f64 2 d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 l d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M d) (/.f64 l 2)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M d) (.f64 2 D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 M (/.f64 (*.f64 D 2) d)) 2)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 d 2) (/.f64 M D)) 2)))))
(.f64 w0 (sqrt.f64 (fma.f64 (/.f64 h l) (neg.f64 (pow.f64 (.f64 d (/.f64 M (*.f64 D 2))) 2)) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 D (/.f64 M d)) 2) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 M (.f64 (/.f64 2 D) d)) 2) (/.f64 (neg.f64 l) h) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (/.f64 M (/.f64 h D)) 2) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 D (/.f64 h (/.f64 M 2))) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 l)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 l) D)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M l) (/.f64 D 2)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M l) 2)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 l))) 2) (/.f64 h d)))))

Symmetry

(sort M D)

Compiler

Compiled 30 to 24 computations (20% saved)

simplify59.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1504×	`distribute-neg-frac`
1208×	`distribute-lft-neg-in`
1190×	`distribute-rgt-neg-in`
1090×	`distribute-lft-in`
1020×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	44	53
2	130	53
3	776	53
4	3139	53
5	5457	53

Stop Event

1×	node limit

Counts

1 → 5

Calls

Call 1

Inputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Outputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 D (/.f64 M 2)) d) 2) (/.f64 (neg.f64 h) l) 1)))

eval2.0ms (0%)

Compiler: Compiled 96 to 63 computations (34.4% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Error

76.1%

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	74.2%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
▶	75.3%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h l)))))

Compiler

Compiled 48 to 36 computations (25% saved)

localize35.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	95.9%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h l)))))
✓	93.4%	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))))
✓	91.7%	(.f64 D (/.f64 M (.f64 2 d)))
✓	82.5%	(.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))

Compiler

Compiled 103 to 61 computations (40.8% saved)

series46.0ms (1.3%)

Counts

4 → 204

Calls

57 calls:

Time	Variable		Point	Expression
3.0ms	M	@	-inf	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))))
3.0ms	D	@	0	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))))
3.0ms	l	@	0	(.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))
2.0ms	D	@	0	(.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))
2.0ms	M	@	0	(.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))

rewrite97.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

580×	`distribute-rgt-in`
508×	`distribute-lft-in`
430×	`add-sqr-sqrt`
420×	`*-un-lft-identity`
418×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	156
1	423	156
2	5593	156

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))
(.f64 D (/.f64 M (.f64 2 d)))
(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (*.f64 2 d))) 2) (/.f64 h l))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 d))) 2) (/.f64 h l)))))

Outputs
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Details

analyze751.0ms (21.6%)

sample2.4s (69.2%)

preprocess81.0ms (2.3%)

simplify59.0ms (1.7%)

eval2.0ms (0%)

prune2.0ms (0.1%)

localize35.0ms (1%)

series46.0ms (1.3%)

rewrite97.0ms (2.8%)

end0.0ms (0%)

Profiling