Metrics for tanhf (example 3.4)

analyze194.0ms (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: 91.0ms

Operation ival-<=, time spent: 21.0ms, 23.0% of total-time

Operation ival-sub, time spent: 14.0ms, 15.0% of total-time

Operation ival-cos, time spent: 13.0ms, 14.0% of total-time

Operation ival-neg, time spent: 12.0ms, 13.0% of total-time

Operation ival-sin, time spent: 11.0ms, 12.0% of total-time

Operation ...c/syntax/syntax.rkt:188:8, time spent: 10.0ms, 11.0% of total-time

Operation ival-div, time spent: 7.0ms, 8.0% 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

sample4.5s (87.5%)

Results

923.0ms	4554×	256	valid
2.6s	2048×	2048	valid
494.0ms	1046×	1024	valid
170.0ms	547×	512	valid
51.0ms	60×	4096	valid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

Operation ival-sin, time spent: 1.4s, 42.0% of total-time

Operation ival-cos, time spent: 848.0ms, 25.0% of total-time

Operation ival-<=, time spent: 407.0ms, 12.0% of total-time

Operation ival-sub, time spent: 214.0ms, 6.0% of total-time

Operation ival-neg, time spent: 186.0ms, 6.0% of total-time

Operation ival-div, time spent: 178.0ms, 5.0% of total-time

Operation ...c/syntax/syntax.rkt:188:8, time spent: 69.0ms, 2.0% of total-time

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

Operation const, time spent: 11.0ms, 0.0% of total-time

Bogosity

preprocess326.0ms (6.4%)

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
76	2	(6.688617444560222e+206)	2	(1.5905937889773137e+66)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
66	0	-	8	(2.6993642042172246e-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: 189.0ms

Operation ival-sin, time spent: 112.0ms, 59.0% of total-time

Operation ival-cos, time spent: 51.0ms, 27.0% of total-time

Operation ival-sub, time spent: 15.0ms, 8.0% of total-time

Operation ival-div, time spent: 9.0ms, 5.0% 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)

localize31.0ms (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: 6.0ms, 55.0% of total-time
Operation ival-div, time spent: 4.0ms, 37.0% 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)

regimes5.0ms (0.1%)

Accuracy

Total -30.2b remaining (-∞%)

Threshold costs -30.2b (-∞%)

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:

3.0ms	x
2.0ms	(/.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)

soundness42.0ms (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%)

preprocess35.0ms (0.7%)

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

analyze194.0ms (3.8%)

sample4.5s (87.5%)

preprocess326.0ms (6.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize31.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes5.0ms (0.1%)

simplify2.0ms (0%)

soundness42.0ms (0.8%)

end0.0ms (0%)

preprocess35.0ms (0.7%)

Profiling