Metrics for fabs fraction 1

analyze41.0ms (0.8%)

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
50%	49.9%	49.9%	0.1%	0%	0%	0%	3
50%	49.9%	49.9%	0.1%	0%	0%	0%	4
50%	49.9%	49.9%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
75%	74.9%	25%	0.1%	0%	0%	0%	7
75%	74.9%	25%	0.1%	0%	0%	0%	8
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	9
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	10
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	11
93.8%	93.6%	6.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 16 to 11 computations (31.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

Operation ival-mult, time spent: 4.0ms, 20.0% of total-time

Operation ival-div, time spent: 4.0ms, 20.0% of total-time

Operation ival-add, time spent: 4.0ms, 20.0% of total-time

Operation ival-fabs, time spent: 3.0ms, 15.0% of total-time

Operation ival-sub, time spent: 3.0ms, 15.0% of total-time

Operation const, time spent: 1.0ms, 5.0% of total-time

sample1.4s (27.4%)

Results

988.0ms	6536×	valid
262.0ms	1719×	infinite
0.0ms	1×	infinite

Precisions

Click to see histograms. Total time spent on operations: 581.0ms

Operation ival-add, time spent: 167.0ms, 29.0% of total-time

Operation ival-div, time spent: 153.0ms, 26.0% of total-time

Operation ival-sub, time spent: 137.0ms, 24.0% of total-time

Operation ival-mult, time spent: 67.0ms, 12.0% of total-time

Operation ival-fabs, time spent: 36.0ms, 6.0% of total-time

Operation const, time spent: 22.0ms, 4.0% of total-time

Bogosity

preprocess1.3s (25.6%)

Algorithm

1×	egg-herbie

Rules

2010×	`fma-neg`
1076×	`fma-define`
854×	`times-frac`
594×	`sub-neg`
592×	`associate-+l+`

FPErrors

Click to see full error table

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	54	594
1	147	562
2	307	546
3	763	526
4	2438	518
5	4139	491
6	5763	491
7	7943	491

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(abs y)

Compiler

Compiled 109 to 52 computations (52.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 654.0ms

Operation ival-add, time spent: 334.0ms, 51.0% of total-time

Operation ival-div, time spent: 132.0ms, 20.0% of total-time

Operation ival-sub, time spent: 128.0ms, 20.0% of total-time

Operation ival-mult, time spent: 28.0ms, 4.0% of total-time

Operation const, time spent: 21.0ms, 3.0% of total-time

Operation ival-fabs, time spent: 11.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.9%	(fabs.f64 (fma.f64 x (/.f64 z y) (/.f64 (-.f64 -4 x) y)))
▶	93.4%	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	97.0%	(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))

Compiler

Compiled 43 to 29 computations (32.6% saved)

localize1.3s (26.7%)

Compiler: Compiled 121 to 59 computations (51.2% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.2s
Operation ival-add, time spent: 313.0ms, 26.0% of total-time
Operation ival-sub, time spent: 301.0ms, 25.0% of total-time
Operation composed, time spent: 244.0ms, 20.0% of total-time
Operation ival-div, time spent: 165.0ms, 14.0% of total-time
Operation ival-mult, time spent: 120.0ms, 10.0% of total-time
Operation const, time spent: 33.0ms, 3.0% of total-time
Operation ival-fabs, time spent: 21.0ms, 2.0% of total-time

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	0	0
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.9%	(fabs.f64 (fma.f64 x (/.f64 z y) (/.f64 (-.f64 -4 x) y)))
✓	93.4%	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	97.0%	(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))

Compiler

Compiled 80 to 52 computations (35% saved)

regimes29.0ms (0.6%)

Counts

3 → 2

Calls

Call 1

Inputs
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))
(fabs.f64 (fma.f64 x (/.f64 z y) (/.f64 (-.f64 -4 x) y)))

Outputs
(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))
(fabs.f64 (fma.f64 x (/.f64 z y) (/.f64 (-.f64 -4 x) y)))

Calls

5 calls:

9.0ms	x
7.0ms	y
6.0ms	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
4.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
4.0ms	z

Results

Accuracy	Segments	Branch
98.7%	2	`x`
99.9%	2	`y`
97.0%	1	`z`
97.0%	1	`(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))`
97.0%	1	`(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes13.0ms (0.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))

Outputs
(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))

Calls

2 calls:

8.0ms	y
4.0ms	x

Results

Accuracy	Segments	Branch
97.0%	1	`x`
98.8%	3	`y`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes14.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Outputs
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Calls

5 calls:

3.0ms	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
3.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
3.0ms	y
3.0ms	x
3.0ms	z

Results

Accuracy	Segments	Branch
93.4%	1	`y`
93.4%	1	`z`
93.4%	1	`(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))`
93.4%	1	`(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))`
93.4%	1	`x`

Compiler

Compiled 41 to 28 computations (31.7% saved)

bsearch19.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	4.747686038230956e-23	2.4053168797165294e-21

Results

15.0ms	96×	valid
2.0ms	15×	infinite
0.0ms	1×	valid

Compiler

Compiled 231 to 162 computations (29.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

Operation ival-add, time spent: 3.0ms, 38.0% of total-time

Operation ival-div, time spent: 2.0ms, 25.0% of total-time

Operation ival-sub, time spent: 2.0ms, 25.0% of total-time

Operation ival-mult, time spent: 1.0ms, 13.0% of total-time

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

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative`
22×	`sub-neg`
20×	`*-commutative`
16×	`neg-sub0`
16×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	194
1	50	194
2	73	194
3	89	194
4	103	194
5	112	194
6	115	194
7	116	194

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 y 4572544305500111/5316911983139663491615228241121378304) (fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x)))) (fabs.f64 (fma.f64 x (/.f64 z y) (/.f64 (-.f64 -4 x) y))))

(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))

(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Outputs
(if (<=.f64 y 4572544305500111/5316911983139663491615228241121378304) (fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x)))) (fabs.f64 (fma.f64 x (/.f64 z y) (/.f64 (-.f64 -4 x) y))))
(fabs.f64 (*.f64 (/.f64 -1 y) (fma.f64 x z (-.f64 -4 x))))
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 z (/.f64 x y))))

Compiler

Compiled 58 to 39 computations (32.8% saved)

soundness577.0ms (11.7%)

Rules

2010×	`fma-neg`
2010×	`fma-neg`
1076×	`fma-define`
1076×	`fma-define`
854×	`times-frac`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	54	594
1	147	562
2	307	546
3	763	526
4	2438	518
5	4139	491
6	5763	491
7	7943	491
0	54	594
1	147	562
2	307	546
3	763	526
4	2438	518
5	4139	491
6	5763	491
7	7943	491

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 123 to 65 computations (47.2% saved)

end0.0ms (0%)

preprocess295.0ms (6%)

Compiler: Compiled 308 to 200 computations (35.1% saved)

analyze41.0ms (0.8%)

sample1.4s (27.4%)

preprocess1.3s (25.6%)

eval1.0ms (0%)

prune2.0ms (0%)

localize1.3s (26.7%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes29.0ms (0.6%)

regimes13.0ms (0.3%)

regimes14.0ms (0.3%)

bsearch19.0ms (0.4%)

simplify9.0ms (0.2%)

soundness577.0ms (11.7%)

end0.0ms (0%)

preprocess295.0ms (6%)

Profiling