Metrics for Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample929.0ms (57.4%)

Results

775.0ms	7220×	body	256	valid
116.0ms	1036×	body	256	infinite

Bogosity

preprocess190.0ms (11.8%)

Algorithm

1×	egg-herbie

Rules

2918×	`fma-def`
326×	`fma-neg`
244×	`cancel-sign-sub-inv`
178×	`distribute-lft-neg-in`
160×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	212
1	70	200
2	124	168
3	263	168
4	587	168
5	1253	168
6	2306	168
7	3165	168
8	3229	168
9	3237	168
10	3237	168

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 (neg.f64 x) y) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 x (neg.f64 y)) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 (neg.f64 z) 8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))

Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(fma.f64 (/.f64 y 2) x (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (.f64 1/2 y) (.f64 z -1/8))
(fma.f64 x (.f64 y 1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(fma.f64 (/.f64 y 2) x (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (.f64 1/2 y) (.f64 z -1/8))
(fma.f64 x (.f64 y 1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 (neg.f64 x) y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 (neg.f64 y))) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 -2 y)) (/.f64 z 8))
(fma.f64 (/.f64 x -2) y (*.f64 -1/8 z))
(fma.f64 y (.f64 -1/2 x) (.f64 z -1/8))
(fma.f64 x (.f64 y -1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 x (neg.f64 y)) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 (neg.f64 y))) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 -2 y)) (/.f64 z 8))
(fma.f64 (/.f64 x -2) y (*.f64 -1/8 z))
(fma.f64 y (.f64 -1/2 x) (.f64 z -1/8))
(fma.f64 x (.f64 y -1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 (neg.f64 z) 8))
(-.f64 (/.f64 x (/.f64 2 y)) (neg.f64 (/.f64 z 8)))
(+.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(fma.f64 (/.f64 x 2) y (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 1/8 z))
(fma.f64 x (.f64 1/2 y) (.f64 z 1/8))
(fma.f64 x (.f64 y 1/2) (.f64 z 1/8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(fma.f64 (/.f64 y 2) x (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (.f64 1/2 y) (.f64 z -1/8))
(fma.f64 x (.f64 y 1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 z (/.f64 2 y)) (/.f64 x 8))
(-.f64 (*.f64 (/.f64 z 2) y) (/.f64 x 8))
(fma.f64 (/.f64 z 2) y (/.f64 x -8))
(fma.f64 y (/.f64 z 2) (*.f64 -1/8 x))
(fma.f64 y (.f64 1/2 z) (.f64 x -1/8))
(fma.f64 y (.f64 z 1/2) (.f64 x -1/8))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))
(-.f64 (/.f64 x (/.f64 2 z)) (/.f64 y 8))
(fma.f64 (/.f64 x 2) z (/.f64 y -8))
(fma.f64 z (/.f64 x 2) (*.f64 -1/8 y))
(fma.f64 x (.f64 1/2 z) (.f64 y -1/8))
(fma.f64 x (.f64 z 1/2) (.f64 y -1/8))

Symmetry

(sort x y)

Compiler

Compiled 12 to 9 computations (25% saved)

eval1.0ms (0.1%)

Compiler: Compiled 53 to 35 computations (34% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 24 to 18 computations (25% saved)

localize96.0ms (5.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 (*.f64 x y) 2)

Compiler

Compiled 29 to 16 computations (44.8% saved)

series11.0ms (0.7%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	0	(/.f64 (*.f64 x y) 2)
2.0ms	x	@	inf	(/.f64 (*.f64 x y) 2)
2.0ms	x	@	0	(/.f64 (*.f64 x y) 2)
2.0ms	y	@	inf	(/.f64 (*.f64 x y) 2)
2.0ms	x	@	-inf	(/.f64 (*.f64 x y) 2)

rewrite89.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1434×	`pow1`
1330×	`add-exp-log`
1330×	`log1p-expm1-u`
1330×	`expm1-log1p-u`
1302×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	149	13
2	1811	13

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (.f64 x (.f64 y 1/2))) 1)
(*.f64 x (/.f64 1 (/.f64 2 y)))
(.f64 x (.f64 y 1/2))
(.f64 y (.f64 x 1/2))
(.f64 (.f64 x y) 1/2)
(.f64 (.f64 x (*.f64 y 1/2)) 1)
(.f64 1 (.f64 x (*.f64 y 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 1/2))
(.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) (pow.f64 (cbrt.f64 (.f64 x (*.f64 y 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 2) (cbrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 1/2))
(.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) (sqrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (.f64 x (neg.f64 y)) -1/2)
(.f64 1/2 (.f64 x y))
(*.f64 (/.f64 x 2) y)
(pow.f64 (.f64 x (.f64 y 1/2)) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) 2)
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(neg.f64 (/.f64 (*.f64 x y) -2))
(sqrt.f64 (.f64 (pow.f64 (.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 y 1/2))))
(exp.f64 (log.f64 (.f64 x (.f64 y 1/2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 y 1/2))))

simplify141.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

920×	`fma-def`
872×	`associate-*r/`
786×	`associate-/l*`
722×	`associate-+r+`
662×	`log-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	669
1	157	669
2	583	669
3	2098	669

Stop Event

1×	node limit

Counts

51 → 28

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 1 (.f64 x (.f64 y 1/2))) 1)
(*.f64 x (/.f64 1 (/.f64 2 y)))
(.f64 x (.f64 y 1/2))
(.f64 y (.f64 x 1/2))
(.f64 (.f64 x y) 1/2)
(.f64 (.f64 x (*.f64 y 1/2)) 1)
(.f64 1 (.f64 x (*.f64 y 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 1/2))
(.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) (pow.f64 (cbrt.f64 (.f64 x (*.f64 y 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 2) (cbrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 1/2))
(.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) (sqrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (.f64 x (neg.f64 y)) -1/2)
(.f64 1/2 (.f64 x y))
(*.f64 (/.f64 x 2) y)
(pow.f64 (.f64 x (.f64 y 1/2)) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) 2)
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(neg.f64 (/.f64 (*.f64 x y) -2))
(sqrt.f64 (.f64 (pow.f64 (.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 y 1/2))))
(exp.f64 (log.f64 (.f64 x (.f64 y 1/2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 y 1/2))))

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 1 (.f64 x (.f64 y 1/2))) 1)
(.f64 1/2 (.f64 y x))
(*.f64 x (/.f64 1 (/.f64 2 y)))
(.f64 1/2 (.f64 y x))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 x y) 1/2)
(.f64 1/2 (.f64 y x))
(.f64 (.f64 x (*.f64 y 1/2)) 1)
(.f64 1/2 (.f64 y x))
(.f64 1 (.f64 x (*.f64 y 1/2)))
(.f64 1/2 (.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) (pow.f64 (cbrt.f64 (.f64 x (*.f64 y 1/2))) 2))
(.f64 1/2 (.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 2) (cbrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) (sqrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 x (neg.f64 y)) -1/2)
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 x y))
(.f64 1/2 (.f64 y x))
(*.f64 (/.f64 x 2) y)
(.f64 1/2 (.f64 y x))
(pow.f64 (.f64 x (.f64 y 1/2)) 1)
(.f64 1/2 (.f64 y x))
(pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 3)
(.f64 1/2 (.f64 y x))
(pow.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3) 1/3)
(.f64 1/2 (.f64 y x))
(pow.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) 2)
(.f64 1/2 (.f64 y x))
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(.f64 1/2 (.f64 y x))
(neg.f64 (/.f64 (*.f64 x y) -2))
(.f64 1/2 (.f64 y x))
(sqrt.f64 (.f64 (pow.f64 (.f64 x y) 2) 1/4))
(.f64 1/2 (.f64 y x))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3))
(.f64 1/2 (.f64 y x))
(expm1.f64 (log1p.f64 (.f64 x (.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(exp.f64 (log.f64 (.f64 x (.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(log1p.f64 (expm1.f64 (.f64 x (.f64 y 1/2))))
(.f64 1/2 (.f64 y x))

eval27.0ms (1.7%)

Compiler: Compiled 336 to 232 computations (31% saved)

prune19.0ms (1.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	1	29

Accuracy

100.0%

Counts

29 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 24 to 18 computations (25% saved)

simplify13.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

6×	`sub-neg`
6×	`+-commutative`
6×	`*-commutative`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	15	25
2	22	25
3	26	25
4	29	25
5	30	25

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 12 to 9 computations (25% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess98.0ms (6%)

Remove: (sort x y)
Compiler: Compiled 72 to 54 computations (25% saved)

analyze0.0ms (0%)

sample929.0ms (57.4%)

preprocess190.0ms (11.8%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

localize96.0ms (5.9%)

series11.0ms (0.7%)

rewrite89.0ms (5.5%)

simplify141.0ms (8.7%)

eval27.0ms (1.7%)

prune19.0ms (1.2%)

simplify13.0ms (0.8%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess98.0ms (6%)

Profiling