Metrics for tanhf (example 3.4)

analyze214.0ms (7.5%)

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: 96.0ms

ival-sub: 50.0ms (52.1% of total)

ival-cos: 24.0ms (25% of total)

ival-sin: 12.0ms (12.5% of total)

ival-div: 7.0ms (7.3% of total)

const: 2.0ms (2.1% of total)

sample2.2s (78.7%)

Results

502.0ms	4271×	0	valid
370.0ms	2114×	1	valid
1.1s	1863×	2	valid
8.0ms	8×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-cos: 1.1s (64.4% of total)

ival-sin: 225.0ms (13.4% of total)

backward-pass: 141.0ms (8.4% of total)

ival-div: 112.0ms (6.7% of total)

ival-sub: 100.0ms (6% of total)

const: 19.0ms (1.1% of total)

Bogosity

preprocess56.0ms (2%)

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)

explain219.0ms (7.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
64	-	3	(5.2114996604958435e-161)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
61	-	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	0	-	`x`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(cos.f64 x)`

Results

48.0ms	304×	256	valid
116.0ms	134×	2048	valid
15.0ms	46×	1024	valid
4.0ms	24×	512	valid
3.0ms	4×	4096	valid

Compiler

Compiled 46 to 26 computations (43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-sin: 77.0ms (51.4% of total)

ival-cos: 46.0ms (30.7% of total)

ival-div: 12.0ms (8% of total)

ival-sub: 12.0ms (8% of total)

const: 2.0ms (1.3% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 5 to 4 computations (20% saved)

localize28.0ms (1%)

Results

22.0ms

256×

256

valid

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-tan: 6.0ms (57.1% of total)

ival-div: 4.0ms (38% of total)

const: 1.0ms (9.5% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	0	0
Total	1	1

Accuracy

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes3.0ms (0.1%)

Accuracy

Total -27.4b remaining (-∞%)

Threshold costs -27.4b (-∞%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Calls

2 calls:

1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
1.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))

soundness41.0ms (1.5%)

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×	done
1×	saturated

Compiler

Compiled 17 to 13 computations (23.5% saved)

preprocess41.0ms (1.4%)

Remove: (negabs x)
Compiler: Compiled 56 to 44 computations (21.4% saved)

tanhf (example 3.4)

analyze214.0ms (7.5%)

sample2.2s (78.7%)

preprocess56.0ms (2%)

explain219.0ms (7.7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize28.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes3.0ms (0.1%)

simplify2.0ms (0.1%)

soundness41.0ms (1.5%)

preprocess41.0ms (1.4%)

end0.0ms (0%)

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