Metrics for Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

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 11 to 8 computations (27.3% saved)

sample854.0ms (57.5%)

Results

764.0ms	7242×	body	256	valid
80.0ms	1014×	body	256	infinite

Bogosity

preprocess64.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1164×	`fma-def`
232×	`associate-r`
200×	`cancel-sign-sub-inv`
186×	`distribute-lft-neg-in`
156×	`fma-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	145
1	89	135
2	207	109
3	568	109
4	1124	109
5	1626	109
6	1699	109
7	1711	109
8	1713	109
9	1713	109

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x (.f64 (.f64 y 4) z))
(-.f64 (neg.f64 x) (.f64 (.f64 y 4) z))
(-.f64 x (.f64 (.f64 (neg.f64 y) 4) z))
(-.f64 x (.f64 (.f64 y 4) (neg.f64 z)))
(-.f64 y (.f64 (.f64 x 4) z))
(-.f64 z (.f64 (.f64 y 4) x))
(-.f64 x (.f64 (.f64 z 4) y))

Outputs
(-.f64 x (.f64 (.f64 y 4) z))
(-.f64 x (.f64 y (.f64 4 z)))
(-.f64 x (.f64 4 (.f64 z y)))
(fma.f64 z (*.f64 y -4) x)
(fma.f64 y (*.f64 z -4) x)
(-.f64 (neg.f64 x) (.f64 (.f64 y 4) z))
(-.f64 (neg.f64 x) (.f64 y (.f64 4 z)))
(fma.f64 -1 x (.f64 z (.f64 y -4)))
(-.f64 (.f64 z (.f64 y -4)) x)
(fma.f64 z (*.f64 y -4) (neg.f64 x))
(-.f64 x (.f64 (.f64 (neg.f64 y) 4) z))
(-.f64 x (.f64 z (neg.f64 (.f64 y 4))))
(+.f64 x (.f64 4 (.f64 z y)))
(fma.f64 (*.f64 y 4) z x)
(fma.f64 y (*.f64 4 z) x)
(-.f64 x (.f64 (.f64 y 4) (neg.f64 z)))
(-.f64 x (.f64 z (neg.f64 (.f64 y 4))))
(+.f64 x (.f64 4 (.f64 z y)))
(fma.f64 (*.f64 y 4) z x)
(fma.f64 y (*.f64 4 z) x)
(-.f64 y (.f64 (.f64 x 4) z))
(-.f64 y (.f64 x (.f64 4 z)))
(-.f64 y (.f64 z (.f64 x 4)))
(fma.f64 z (*.f64 x -4) y)
(-.f64 z (.f64 (.f64 y 4) x))
(-.f64 z (.f64 x (.f64 y 4)))
(+.f64 z (.f64 x (.f64 y -4)))
(fma.f64 x (*.f64 y -4) z)
(-.f64 x (.f64 (.f64 z 4) y))
(-.f64 x (.f64 y (.f64 4 z)))
(-.f64 x (.f64 4 (.f64 z y)))
(fma.f64 z (*.f64 y -4) x)
(fma.f64 y (*.f64 z -4) x)

Symmetry

(sort y z)

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify25.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def`
90×	`cancel-sign-sub-inv`
86×	`distribute-lft-neg-in`
54×	`sub-neg`
46×	`fma-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

Stop Event

1×

saturated

Counts

1 → 5

Calls

Call 1

Inputs
(-.f64 x (.f64 (.f64 y 4) z))

Outputs
(-.f64 x (.f64 (.f64 y 4) z))
(-.f64 x (.f64 4 (.f64 y z)))
(fma.f64 y (*.f64 z -4) x)
(fma.f64 -4 (*.f64 y z) x)
(fma.f64 z (*.f64 y -4) x)

eval1.0ms (0.1%)

Compiler: Compiled 35 to 19 computations (45.7% saved)

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	4	1	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	1	6

Accurracy

100.0%

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (.f64 4 (.f64 y z)))
▶	100.0%	(-.f64 x (.f64 4 (.f64 y z)))

Compiler

Compiled 20 to 14 computations (30% saved)

localize163.0ms (11%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(.f64 4 (.f64 y z))

Compiler

Compiled 23 to 11 computations (52.2% saved)

series3.0ms (0.2%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(.f64 4 (.f64 y z))
1.0ms	y	@	0	(.f64 4 (.f64 y z))
1.0ms	y	@	inf	(.f64 4 (.f64 y z))
0.0ms	z	@	inf	(.f64 4 (.f64 y z))
0.0ms	z	@	-inf	(.f64 4 (.f64 y z))

rewrite131.0ms (8.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1298×	`pow1`
1194×	`add-exp-log`
1194×	`log1p-expm1-u`
1194×	`expm1-log1p-u`
1168×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	142	13
2	1633	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 4 (.f64 y z))

Outputs
(-.f64 (+.f64 1 (.f64 4 (.f64 y z))) 1)
(pow.f64 (.f64 4 (.f64 y z)) 1)
(pow.f64 (cbrt.f64 (.f64 4 (.f64 y z))) 3)
(pow.f64 (pow.f64 (.f64 4 (.f64 y z)) 3) 1/3)
(pow.f64 (.f64 (sqrt.f64 (.f64 y z)) 2) 2)
(sqrt.f64 (.f64 (pow.f64 (.f64 y z) 2) 16))
(log.f64 (pow.f64 (exp.f64 (*.f64 4 y)) z))
(cbrt.f64 (pow.f64 (.f64 4 (.f64 y z)) 3))
(expm1.f64 (log1p.f64 (.f64 4 (.f64 y z))))
(exp.f64 (log.f64 (.f64 4 (.f64 y z))))
(log1p.f64 (expm1.f64 (.f64 4 (.f64 y z))))

simplify58.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2480×	`log-prod`
1246×	`distribute-rgt-in`
1232×	`distribute-lft-in`
974×	`associate-r`
842×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	275
1	92	209
2	339	143
3	2455	143
4	7773	143

Stop Event

1×	node limit

Counts

11 → 14

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (.f64 4 (.f64 y z))) 1)
(pow.f64 (.f64 4 (.f64 y z)) 1)
(pow.f64 (cbrt.f64 (.f64 4 (.f64 y z))) 3)
(pow.f64 (pow.f64 (.f64 4 (.f64 y z)) 3) 1/3)
(pow.f64 (.f64 (sqrt.f64 (.f64 y z)) 2) 2)
(sqrt.f64 (.f64 (pow.f64 (.f64 y z) 2) 16))
(log.f64 (pow.f64 (exp.f64 (*.f64 4 y)) z))
(cbrt.f64 (pow.f64 (.f64 4 (.f64 y z)) 3))
(expm1.f64 (log1p.f64 (.f64 4 (.f64 y z))))
(exp.f64 (log.f64 (.f64 4 (.f64 y z))))
(log1p.f64 (expm1.f64 (.f64 4 (.f64 y z))))

Outputs
(-.f64 (+.f64 1 (.f64 4 (.f64 y z))) 1)
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(pow.f64 (.f64 4 (.f64 y z)) 1)
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(pow.f64 (cbrt.f64 (.f64 4 (.f64 y z))) 3)
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(pow.f64 (pow.f64 (.f64 4 (.f64 y z)) 3) 1/3)
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(pow.f64 (.f64 (sqrt.f64 (.f64 y z)) 2) 2)
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(sqrt.f64 (.f64 (pow.f64 (.f64 y z) 2) 16))
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(log.f64 (pow.f64 (exp.f64 (*.f64 4 y)) z))
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(cbrt.f64 (pow.f64 (.f64 4 (.f64 y z)) 3))
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(expm1.f64 (log1p.f64 (.f64 4 (.f64 y z))))
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(exp.f64 (log.f64 (.f64 4 (.f64 y z))))
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))
(log1p.f64 (expm1.f64 (.f64 4 (.f64 y z))))
(+.f64 1 (-.f64 (.f64 4 (.f64 y z)) 1))
(+.f64 (.f64 4 (.f64 y z)) 0)
(.f64 4 (.f64 y z))

eval3.0ms (0.2%)

Compiler: Compiled 137 to 83 computations (39.4% saved)

prune3.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	1	15

Accurracy

100.0%

Counts

15 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 x (.f64 4 (.f64 y z)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

regimes60.0ms (4.1%)

Accuracy

Total -0.2b remaining (-∞%)

Threshold costs -0.2b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 x (.f64 4 (.f64 y z)))
(-.f64 x (.f64 (.f64 y 4) z))

Outputs
(-.f64 x (.f64 4 (.f64 y z)))

Calls

6 calls:

47.0ms	z
3.0ms	(*.f64 y 4)
3.0ms	y
3.0ms	(-.f64 x (.f64 (.f64 y 4) z))
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(-.f64 x (.f64 (.f64 y 4) z))`
100.0%	1	`(.f64 (.f64 y 4) z)`
100.0%	1	`(*.f64 y 4)`

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative`
12×	`sub-neg`
12×	`+-commutative`
10×	`neg-mul-1`
10×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	29	19
3	41	19
4	49	19
5	54	19
6	56	19

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 x (.f64 4 (.f64 y z)))

Outputs
(-.f64 x (.f64 4 (.f64 y z)))

Compiler

Compiled 10 to 7 computations (30% saved)

soundness45.0ms (3%)

Rules

738×	`fma-def`
90×	`cancel-sign-sub-inv`
86×	`distribute-lft-neg-in`
54×	`sub-neg`
46×	`fma-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

Stop Event

1×

saturated

Compiler

Compiled 24 to 15 computations (37.5% saved)

end0.0ms (0%)

preprocess69.0ms (4.7%)

Remove: (sort y z)
Compiler: Compiled 60 to 42 computations (30% saved)

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

analyze0.0ms (0%)

sample854.0ms (57.5%)

preprocess64.0ms (4.3%)

simplify25.0ms (1.7%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

localize163.0ms (11%)

series3.0ms (0.2%)

rewrite131.0ms (8.9%)

simplify58.0ms (3.9%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

regimes60.0ms (4.1%)

simplify5.0ms (0.3%)

soundness45.0ms (3%)

end0.0ms (0%)

preprocess69.0ms (4.7%)

Profiling

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15

Iter	Nodes	Cost
0	9	19
1	19	19
2	49	15
3	107	15
4	159	15
5	220	15
6	314	15
7	387	15
8	513	15
9	725	15
10	811	15
11	823	15