Metrics for tanhf (example 3.4)

analyze208.0ms (3.8%)

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 16 to 11 computations (31.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

Operation ival-<=, time spent: 26.0ms, 26.0% of total-time

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

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

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

Operation ...c/syntax/syntax.rkt:185:8, time spent: 11.0ms, 11.0% of total-time

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

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

Operation ival-and, time spent: 3.0ms, 3.0% of total-time

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

sample4.8s (86.9%)

Results

1.0s	4572×	256	valid
2.8s	2101×	2048	valid
512.0ms	1018×	1024	valid
143.0ms	497×	512	valid
57.0ms	66×	4096	valid
0.0ms	1×	1024	valid
2.0ms	1×	8192	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

Operation ival-sin, time spent: 1.8s, 51.0% of total-time

Operation ival-cos, time spent: 950.0ms, 27.0% of total-time

Operation ival-sub, time spent: 222.0ms, 6.0% of total-time

Operation ival-div, time spent: 166.0ms, 5.0% of total-time

Operation ival-<=, time spent: 159.0ms, 5.0% of total-time

Operation ival-neg, time spent: 95.0ms, 3.0% of total-time

Operation ...c/syntax/syntax.rkt:185:8, time spent: 94.0ms, 3.0% of total-time

Operation ival-and, time spent: 26.0ms, 1.0% of total-time

Operation const, time spent: 12.0ms, 0.0% of total-time

Bogosity

preprocess312.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

398×	`fma-define`
166×	`fma-neg`
94×	`times-frac`
94×	`div-sub`
74×	`distribute-rgt-in`

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
75	1	(3.6019773481185794e+197)	0	-	`(-.f64 1 (cos.f64 x))`
50	0	-	3	(2.1636985101644254e-161)	`(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`1`

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 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))

Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
(/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(tan.f64 (/.f64 (neg.f64 x) 2))
(neg.f64 (tan.f64 (/.f64 x 2)))
(tan.f64 (*.f64 x -1/2))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))

Symmetry

(negabs x)

Compiler

Compiled 46 to 26 computations (43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

Operation ival-sin, time spent: 65.0ms, 48.0% of total-time

Operation ival-cos, time spent: 46.0ms, 34.0% of total-time

Operation ival-sub, time spent: 13.0ms, 10.0% of total-time

Operation ival-div, time spent: 9.0ms, 7.0% of total-time

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

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 2))

Compiler

Compiled 5 to 4 computations (20% saved)

localize30.0ms (0.5%)

Compiler: Compiled 11 to 8 computations (27.3% saved)
Precisions: Click to see histograms. Total time spent on operations: 12.0ms
Operation ival-tan, time spent: 7.0ms, 60.0% 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 2))

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes80.0ms (1.4%)

Accuracy

Total -27.6b remaining (-∞%)

Threshold costs -27.6b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(tan.f64 (/.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Outputs
(tan.f64 (/.f64 x 2))

Calls

2 calls:

77.0ms	x
2.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 1 (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 2))

Outputs
(tan.f64 (/.f64 x 2))

Compiler

Compiled 5 to 4 computations (20% saved)

soundness43.0ms (0.8%)

Rules

398×	`fma-define`
166×	`fma-neg`
94×	`times-frac`
94×	`div-sub`
74×	`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%)

preprocess49.0ms (0.9%)

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

analyze208.0ms (3.8%)

sample4.8s (86.9%)

preprocess312.0ms (5.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize30.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes80.0ms (1.4%)

simplify2.0ms (0%)

soundness43.0ms (0.8%)

end0.0ms (0%)

preprocess49.0ms (0.9%)

Profiling