Metrics for VandenBroeck and Keller, Equation (24)

analyze201.0ms (3.7%)

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
0%	0%	99.9%	0.1%	0%	0%	0%	3
25%	25%	74.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	7
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	8
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	9
46.9%	46.8%	53.1%	0.1%	0%	0%	0%	10
46.9%	46.8%	53.1%	0.1%	0%	0%	0%	11
48.4%	48.4%	51.5%	0.1%	0%	0%	0%	12

Compiler

Compiled 15 to 12 computations (20% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

Operation ival-mult, time spent: 18.0ms, 22.0% of total-time

Operation ival-sin, time spent: 15.0ms, 18.0% of total-time

Operation ival-tan, time spent: 13.0ms, 16.0% of total-time

Operation ival-add, time spent: 11.0ms, 13.0% of total-time

Operation ival-div, time spent: 11.0ms, 13.0% of total-time

Operation ival-neg, time spent: 11.0ms, 13.0% of total-time

Operation const, time spent: 3.0ms, 4.0% of total-time

sample2.1s (39.2%)

Results

1.7s	7220×	0	valid
148.0ms	1031×	0	infinite
7.0ms	3×	2	valid
0.0ms	1×	0	valid
1.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 917.0ms

Operation ival-tan, time spent: 295.0ms, 32.0% of total-time

Operation ival-sin, time spent: 200.0ms, 22.0% of total-time

Operation ival-div, time spent: 151.0ms, 16.0% of total-time

Operation ival-add, time spent: 135.0ms, 15.0% of total-time

Operation ival-mult, time spent: 72.0ms, 8.0% of total-time

Operation ival-neg, time spent: 40.0ms, 4.0% of total-time

Operation const, time spent: 25.0ms, 3.0% of total-time

Bogosity

preprocess1.9s (34.3%)

Algorithm

1×	egg-herbie

Rules

1366×	`fma-def`
242×	`associate-/r*`
232×	`associate-*r/`
226×	`associate-r`
200×	`times-frac`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`B`
-	-	`x`
-	-	`(sin.f64 B)`
-	-	`(tan.f64 B)`
-	-	`(*.f64 x (/.f64 1 (tan.f64 B)))`
-	-	`(/.f64 1 (sin.f64 B))`
-	-	`(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))`
-	-	`(/.f64 1 (tan.f64 B))`
-	-	`(neg.f64 (*.f64 x (/.f64 1 (tan.f64 B))))`
-	-	`1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	342
1	94	260
2	244	252
3	581	252
4	915	252
5	1595	252
6	2145	252
7	2833	252
8	2977	252
9	3019	252
10	3030	252
11	3035	252

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 (neg.f64 B))))) (/.f64 1 (sin.f64 (neg.f64 B))))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
(neg.f64 (+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 (neg.f64 B))))) (/.f64 1 (sin.f64 (neg.f64 B)))))
(neg.f64 (+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B))))
(+.f64 (neg.f64 (*.f64 B (/.f64 1 (tan.f64 x)))) (/.f64 1 (sin.f64 x)))

Outputs
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (neg.f64 x) 1) (tan.f64 B)))
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (neg.f64 x) 1) (tan.f64 B)))
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 (neg.f64 B))))) (/.f64 1 (sin.f64 (neg.f64 B))))
(+.f64 (*.f64 x (neg.f64 (/.f64 1 (neg.f64 (tan.f64 B))))) (/.f64 1 (neg.f64 (sin.f64 B))))
(-.f64 (/.f64 1 (neg.f64 (sin.f64 B))) (/.f64 x (neg.f64 (tan.f64 B))))
(-.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))
(+.f64 (/.f64 x (tan.f64 B)) (/.f64 -1 (sin.f64 B)))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (neg.f64 (/.f64 1 (tan.f64 B)))))
(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
(neg.f64 (+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 (neg.f64 B))))) (/.f64 1 (sin.f64 (neg.f64 B)))))
(+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (neg.f64 x) 1) (tan.f64 B)))
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
(neg.f64 (+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B))))
(neg.f64 (+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (neg.f64 (/.f64 1 (tan.f64 B))))))
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 B (/.f64 1 (tan.f64 x)))) (/.f64 1 (sin.f64 x)))
(+.f64 (*.f64 B (neg.f64 (/.f64 1 (tan.f64 x)))) (/.f64 1 (sin.f64 x)))
(-.f64 (/.f64 1 (sin.f64 x)) (/.f64 B (tan.f64 x)))

Symmetry

(negabs B)

Compiler

Compiled 100 to 59 computations (41% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.3s

Operation ival-tan, time spent: 682.0ms, 52.0% of total-time

Operation ival-sin, time spent: 283.0ms, 22.0% of total-time

Operation ival-div, time spent: 158.0ms, 12.0% of total-time

Operation ival-mult, time spent: 75.0ms, 6.0% of total-time

Operation ival-add, time spent: 53.0ms, 4.0% of total-time

Operation ival-neg, time spent: 32.0ms, 2.0% of total-time

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

eval1.0ms (0%)

Compiler: Compiled 23 to 15 computations (34.8% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
▶	99.7%	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 25 to 19 computations (24% saved)

localize1.0s (18.5%)

Compiler: Compiled 67 to 31 computations (53.7% saved)
Precisions: Click to see histograms. Total time spent on operations: 716.0ms
Operation ival-tan, time spent: 341.0ms, 48.0% of total-time
Operation ival-sin, time spent: 136.0ms, 19.0% of total-time
Operation ival-div, time spent: 112.0ms, 16.0% of total-time
Operation ival-mult, time spent: 45.0ms, 6.0% of total-time
Operation ival-add, time spent: 27.0ms, 4.0% of total-time
Operation ival-sub, time spent: 26.0ms, 4.0% of total-time
Operation ival-neg, time spent: 15.0ms, 2.0% of total-time
Operation const, time spent: 14.0ms, 2.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0%)

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

99.8%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
✓	99.7%	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 48 to 34 computations (29.2% saved)

regimes11.0ms (0.2%)

Accuracy

Total -0.1b remaining (-67.7%)

Threshold costs -0.1b (-67.7%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Outputs
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Calls

3 calls:

5.0ms	B
3.0ms	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
3.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`B`
99.8%	1	`x`
99.8%	1	`(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))`

Compiler

Compiled 20 to 15 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	21	36
2	27	36
3	31	36
4	34	36
5	35	36

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Outputs
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 11 to 8 computations (27.3% saved)

soundness189.0ms (3.5%)

Rules

1366×	`fma-def`
242×	`associate-/r*`
232×	`associate-*r/`
226×	`associate-r`
200×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	342
1	94	260
2	244	252
3	581	252
4	915	252
5	1595	252
6	2145	252
7	2833	252
8	2977	252
9	3019	252
10	3030	252
11	3035	252

Stop Event

1×

saturated

Compiler

Compiled 91 to 52 computations (42.9% saved)

end0.0ms (0%)

preprocess27.0ms (0.5%)

Remove: (negabs B)
Compiler: Compiled 94 to 70 computations (25.5% saved)

analyze201.0ms (3.7%)

sample2.1s (39.2%)

preprocess1.9s (34.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize1.0s (18.5%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes11.0ms (0.2%)

simplify3.0ms (0.1%)

soundness189.0ms (3.5%)

end0.0ms (0%)

preprocess27.0ms (0.5%)

Profiling