Metrics for Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

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 9 computations (30.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.6s (61.1%)

Results

922.0ms	5486×	valid
628.0ms	2769×	infinite
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 832.0ms

Operation ival-sub, time spent: 569.0ms, 68.0% of total-time

Operation ival-mult, time spent: 243.0ms, 29.0% of total-time

Operation const, time spent: 20.0ms, 2.0% of total-time

Bogosity

preprocess528.0ms (20%)

Algorithm

1×	egg-herbie

Rules

1190×	`fma-def`
192×	`distribute-lft-neg-in`
188×	`associate-r`
188×	`cancel-sign-sub-inv`
124×	`distribute-rgt-neg-in`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`z`
-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))`
-	-	`(.f64 (.f64 y 4) z)`
-	-	`4`
-	-	`y`
-	-	`(*.f64 y 4)`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	435
1	116	375
2	284	375
3	713	375
4	1184	375
5	1623	375
6	1717	375
7	1725	375
8	1725	375

Stop Event

1×

saturated

Calls

Call 1

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

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

Symmetry

(abs x)

(sort y z)

Compiler

Compiled 68 to 38 computations (44.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 199.0ms

Operation ival-mult, time spent: 134.0ms, 67.0% of total-time

Operation ival-sub, time spent: 52.0ms, 26.0% of total-time

Operation const, time spent: 13.0ms, 7.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 20 to 12 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (.f64 y (.f64 z -4)))
▶	99.6%	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Compiler

Compiled 23 to 15 computations (34.8% saved)

localize312.0ms (11.8%)

Compiler: Compiled 48 to 25 computations (47.9% saved)
Precisions: Click to see histograms. Total time spent on operations: 190.0ms
Operation ival-mult, time spent: 127.0ms, 67.0% of total-time
Operation ival-fma, time spent: 28.0ms, 15.0% of total-time
Operation ival-sub, time spent: 25.0ms, 13.0% of total-time
Operation const, time spent: 10.0ms, 5.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune3.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (.f64 y (.f64 z -4)))
✓	99.6%	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Compiler

Compiled 43 to 27 computations (37.2% saved)

regimes19.0ms (0.7%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

7 calls:

3.0ms	x
3.0ms	(*.f64 y 4)
3.0ms	z
3.0ms	y
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Results

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

Compiler

Compiled 44 to 32 computations (27.3% saved)

regimes17.0ms (0.6%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

3.0ms	z
3.0ms	y
3.0ms	(*.f64 y 4)
2.0ms	x
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`z`
99.6%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))`
99.6%	1	`(*.f64 x x)`
99.6%	1	`(.f64 (.f64 y 4) z)`
99.6%	1	`(*.f64 y 4)`

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	70
1	29	70
2	47	70
3	57	70
4	65	70
5	68	70

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 23 to 15 computations (34.8% saved)

soundness110.0ms (4.2%)

Rules

1190×	`fma-def`
192×	`distribute-lft-neg-in`
188×	`associate-r`
188×	`cancel-sign-sub-inv`
124×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	435
1	116	375
2	284	375
3	713	375
4	1184	375
5	1623	375
6	1717	375
7	1725	375
8	1725	375

Stop Event

1×

saturated

Compiler

Compiled 65 to 37 computations (43.1% saved)

end0.0ms (0%)

preprocess33.0ms (1.3%)

Remove

(sort y z)

(abs x)

Compiler

Compiled 196 to 124 computations (36.7% saved)

analyze0.0ms (0%)

sample1.6s (61.1%)

preprocess528.0ms (20%)

eval1.0ms (0%)

prune1.0ms (0%)

localize312.0ms (11.8%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes19.0ms (0.7%)

regimes17.0ms (0.6%)

simplify4.0ms (0.1%)

soundness110.0ms (4.2%)

end0.0ms (0%)

preprocess33.0ms (1.3%)

Profiling