Metrics for tanhf (example 3.4)

analyze151.0ms (4.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-sub: 29.0ms (42.2% of total)

ival-cos: 17.0ms (24.8% of total)

ival-sin: 14.0ms (20.4% of total)

ival-div: 6.0ms (8.7% of total)

const: 2.0ms (2.9% of total)

sample3.2s (87.6%)

Results

1.9s	2054×	2048	valid
640.0ms	4554×	256	valid
303.0ms	1037×	1024	valid
76.0ms	108×	4096	valid
70.0ms	502×	512	valid
2.0ms	1×	8192	valid

Precisions

Click to see histograms. Total time spent on operations: 2.6s

ival-sin: 1.4s (52.7% of total)

ival-cos: 882.0ms (33.8% of total)

ival-div: 205.0ms (7.9% of total)

ival-sub: 127.0ms (4.9% of total)

const: 20.0ms (0.8% of total)

Bogosity

preprocess56.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-define`
83×	`fma-neg`
47×	`times-frac`
47×	`div-sub`
37×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	46	60
2	85	56
3	191	56
4	470	56
5	815	56
6	981	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64)))
(neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))))
(tan.f64 (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Symmetry

(negabs x)

explain217.0ms (5.9%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
66	0	-	3	(9.175975063976972e-156)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
61	1	(1.8750097293936267e+235)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`

Results

117.0ms	136×	2048	valid
45.0ms	304×	256	valid
14.0ms	46×	1024	valid
8.0ms	4×	4096	valid
3.0ms	22×	512	valid

Compiler

Compiled 46 to 20 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 154.0ms

ival-sin: 78.0ms (50.7% of total)

ival-cos: 52.0ms (33.8% of total)

ival-div: 14.0ms (9.1% of total)

ival-sub: 8.0ms (5.2% of total)

const: 1.0ms (0.6% of total)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
2×	`sub-neg`
2×	`+-commutative`
1×	`*-commutative`
1×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	18	27
2	22	27
3	24	27
4	25	27

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 8 to 6 computations (25% saved)

preprocess31.0ms (0.8%)

Remove: (negabs x)
Compiler: Compiled 74 to 56 computations (24.3% saved)

tanhf (example 3.4)

analyze151.0ms (4.1%)

sample3.2s (87.6%)

preprocess56.0ms (1.5%)

explain217.0ms (5.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

preprocess31.0ms (0.8%)

end0.0ms (0%)

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