Metrics for VandenBroeck and Keller, Equation (24)

analyze205.0ms (12.4%)

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 11 computations (26.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-mult: 17.0ms (22% of total)

ival-tan: 13.0ms (16.8% of total)

ival-div: 12.0ms (15.5% of total)

ival-neg: 12.0ms (15.5% of total)

ival-add: 11.0ms (14.2% of total)

ival-sin: 11.0ms (14.2% of total)

const: 2.0ms (2.6% of total)

sample1.2s (74.4%)

Results

995.0ms

8256×

256

valid

Precisions

Click to see histograms. Total time spent on operations: 766.0ms

ival-sin: 255.0ms (33.3% of total)

ival-tan: 205.0ms (26.8% of total)

ival-div: 140.0ms (18.3% of total)

ival-mult: 64.0ms (8.4% of total)

ival-add: 51.0ms (6.7% of total)

ival-neg: 41.0ms (5.4% of total)

const: 10.0ms (1.3% of total)

Bogosity

preprocess82.0ms (5%)

Algorithm

1×	egg-herbie

Rules

233×	`fma-define`
186×	`fma-neg`
54×	`distribute-lft-neg-in`
41×	`sub-neg`
37×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	342
1	94	252
2	257	252
3	520	252
4	812	252
5	1028	252
6	1154	252
7	1284	252
8	1294	252

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 (neg.f64 B))))) (/.f64 #s(literal 1 binary64) (sin.f64 (neg.f64 B))))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(neg.f64 (+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 (neg.f64 B))))) (/.f64 #s(literal 1 binary64) (sin.f64 (neg.f64 B)))))
(neg.f64 (+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B))))
(+.f64 (neg.f64 (*.f64 B (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))

Outputs
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (tan.f64 B)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (tan.f64 B)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 (neg.f64 B))))) (/.f64 #s(literal 1 binary64) (sin.f64 (neg.f64 B))))
(+.f64 (*.f64 x (neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 B))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 B))))
(+.f64 (/.f64 #s(literal -1 binary64) (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (*.f64 (neg.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 B)))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 x (tan.f64 B)))
(neg.f64 (+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 (neg.f64 B))))) (/.f64 #s(literal 1 binary64) (sin.f64 (neg.f64 B)))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (tan.f64 B)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (/.f64 x (tan.f64 B)))
(neg.f64 (+.f64 (neg.f64 (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B))))
(neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (*.f64 (neg.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 B))))))
(-.f64 (/.f64 #s(literal -1 binary64) (sin.f64 B)) (/.f64 x (tan.f64 B)))
(+.f64 (neg.f64 (*.f64 B (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (*.f64 B (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 B (tan.f64 x)))

Symmetry

(negabs B)

explain106.0ms (6.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`B`
-	-	`x`
-	-	`(sin.f64 B)`
-	-	`(tan.f64 B)`
-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 B))`
-	-	`(/.f64 #s(literal 1 binary64) (sin.f64 B))`
-	-	`(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))`
-	-	`(neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B))))`
-	-	`#s(literal 1 binary64)`
-	-	`(*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))`

Results

71.0ms

512×

256

valid

Compiler

Compiled 100 to 32 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-tan: 14.0ms (31% of total)

ival-sin: 12.0ms (26.5% of total)

ival-div: 8.0ms (17.7% of total)

ival-mult: 5.0ms (11.1% of total)

ival-add: 3.0ms (6.6% of total)

ival-neg: 2.0ms (4.4% of total)

const: 1.0ms (2.2% of total)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`neg-mul-1`
12×	`unsub-neg`
6×	`distribute-lft-neg-in`
6×	`distribute-rgt-neg-in`
6×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	30	42
2	44	42
3	53	42
4	61	42
5	81	42
6	109	42

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))

Outputs
(+.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B)))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(+.f64 (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 B))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 B)) (*.f64 x (/.f64 #s(literal 1 binary64) (tan.f64 B))))
(+.f64 (*.f64 x (/.f64 #s(literal -1 binary64) (tan.f64 B))) (/.f64 #s(literal 1 binary64) (sin.f64 B)))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 13 to 10 computations (23.1% saved)

preprocess24.0ms (1.4%)

Remove: (negabs B)
Compiler: Compiled 106 to 80 computations (24.5% saved)

VandenBroeck and Keller, Equation (24)

analyze205.0ms (12.4%)

sample1.2s (74.4%)

preprocess82.0ms (5%)

explain106.0ms (6.4%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify4.0ms (0.2%)

soundness0.0ms (0%)

preprocess24.0ms (1.4%)

end0.0ms (0%)

Profiling