Metrics for tanhf (example 3.4)

analyze330.0ms (6.6%)

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: 59.0ms

Operation ival-cos, time spent: 19.0ms, 32.0% of total-time

Operation ival-sin, time spent: 16.0ms, 27.0% of total-time

Operation ival-sub, time spent: 13.0ms, 22.0% of total-time

Operation ival-div, time spent: 7.0ms, 12.0% of total-time

Operation const, time spent: 3.0ms, 5.0% of total-time

sample4.2s (83.1%)

Results

903.0ms	4582×	256	valid
2.2s	2133×	2048	valid
712.0ms	977×	1024	valid
181.0ms	512×	512	valid
40.0ms	51×	4096	valid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 3.1s

Operation ival-sin, time spent: 1.5s, 48.0% of total-time

Operation ival-cos, time spent: 1.3s, 42.0% of total-time

Operation ival-div, time spent: 162.0ms, 5.0% of total-time

Operation ival-sub, time spent: 128.0ms, 4.0% of total-time

Operation const, time spent: 25.0ms, 1.0% of total-time

Bogosity

preprocess404.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

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

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
83	3	(7.822288302969291e-162)	1	(2.597821881156887e+52)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
54	0	-	2	(8.165129636194487e-156)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)`

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)

Compiler

Compiled 46 to 26 computations (43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

Operation ival-sin, time spent: 90.0ms, 56.0% of total-time

Operation ival-cos, time spent: 47.0ms, 29.0% of total-time

Operation ival-sub, time spent: 12.0ms, 7.0% of total-time

Operation ival-div, time spent: 9.0ms, 6.0% of total-time

Operation const, time spent: 3.0ms, 2.0% of total-time

eval1.0ms (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)

localize32.0ms (0.6%)

Compiler: Compiled 11 to 8 computations (27.3% saved)
Precisions: Click to see histograms. Total time spent on operations: 11.0ms
Operation ival-tan, time spent: 7.0ms, 61.0% of total-time
Operation ival-div, time spent: 4.0ms, 35.0% of total-time
Operation const, time spent: 1.0ms, 9.0% of total-time

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 -30.7b remaining (-∞%)

Threshold costs -30.7b (-∞%)

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

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 5 to 4 computations (20% saved)

soundness43.0ms (0.9%)

Rules

199×	`fma-define`
83×	`fmm-def`
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

Compiler

Compiled 12 to 9 computations (25% saved)

end0.0ms (0%)

preprocess31.0ms (0.6%)

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

analyze330.0ms (6.6%)

sample4.2s (83.1%)

preprocess404.0ms (8.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize32.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes3.0ms (0.1%)

simplify2.0ms (0%)

soundness43.0ms (0.9%)

end0.0ms (0%)

preprocess31.0ms (0.6%)

Profiling