Metrics for tanhf (example 3.4)

analyze185.0ms (5.1%)

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)

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	741	4	0.0ms
const	500-600	4	0.0ms
const	400-500	4	0.0ms
const	200-300	5	0.0ms
const	100-200	2051	2.0ms
const	128	2070	2.0ms
ival-cos	741	4	0.0ms
ival-cos	500-600	4	0.0ms
ival-cos	400-500	4	0.0ms
ival-cos	200-300	5	0.0ms
ival-cos	100-200	2051	14.0ms
ival-cos	128	1	0.0ms
ival-div	128	2069	8.0ms
ival-sin	128	2069	10.0ms
ival-sub	128	2069	15.0ms

sample3.0s (84%)

Results

1.1s	4621×	body	256	valid
1.1s	2109×	body	1024	valid
511.0ms	482×	body	2048	valid
256.0ms	1043×	body	512	valid
2.0ms	1×	body	4096	valid

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	6163	1	0.0ms
const	4096	1	0.0ms
const	3900-4000	425	0.0ms
const	3800-3900	58	0.0ms
const	2048	483	1.0ms
const	1800-1900	2590	2.0ms
const	1000-1100	1	0.0ms
const	1024	2593	3.0ms
const	800-900	3548	3.0ms
const	700-800	82	0.0ms
const	500-600	1	0.0ms
const	512	3639	4.0ms
const	256	16512	18.0ms
ival-cos	6163	1	0.0ms
ival-cos	3900-4000	425	116.0ms
ival-cos	3800-3900	58	17.0ms
ival-cos	1800-1900	2590	432.0ms
ival-cos	1000-1100	1	0.0ms
ival-cos	1024	1	0.0ms
ival-cos	800-900	3548	61.0ms
ival-cos	700-800	82	1.0ms
ival-cos	500-600	1	0.0ms
ival-cos	512	4	0.0ms
ival-cos	256	8256	292.0ms
ival-div	4096	1	0.0ms
ival-div	2048	483	7.0ms
ival-div	1024	2592	24.0ms
ival-div	512	3635	37.0ms
ival-div	256	8256	83.0ms
ival-sin	4096	1	0.0ms
ival-sin	2048	483	201.0ms
ival-sin	1024	2592	85.0ms
ival-sin	512	3635	35.0ms
ival-sin	256	8256	235.0ms
ival-sub	4096	1	0.0ms
ival-sub	2048	483	4.0ms
ival-sub	1024	2592	21.0ms
ival-sub	512	3635	32.0ms
ival-sub	256	8256	65.0ms

Bogosity

preprocess211.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-def`
410×	`div-sub`
200×	`associate-/r*`
176×	`associate-/l*`
118×	`sub-neg`

Problems

103×	No Errors
90×	`(-.f64 1 (cos.f64 x))`
63×	`(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	41	60
2	66	56
3	140	56
4	323	56
5	730	56
6	1382	56
7	1766	56
8	1847	56
9	1924	56
10	1975	56
11	1987	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))
(tan.f64 (*.f64 -1/2 x))
(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 27 to 16 computations (40.7% saved)

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	3920	26	0.0ms
const	3800-3900	2	0.0ms
const	2048	28	0.0ms
const	1800-1900	164	0.0ms
const	1024	164	0.0ms
const	800-900	236	0.0ms
const	512	236	0.0ms
const	256	1024	1.0ms
ival-cos	3920	13	3.0ms
ival-cos	3800-3900	1	1.0ms
ival-cos	1800-1900	82	11.0ms
ival-cos	800-900	118	2.0ms
ival-cos	256	256	28.0ms
ival-div	2048	14	0.0ms
ival-div	1024	82	1.0ms
ival-div	512	118	1.0ms
ival-div	256	256	2.0ms
ival-sin	2048	14	7.0ms
ival-sin	1024	82	4.0ms
ival-sin	512	118	1.0ms
ival-sin	256	256	7.0ms
ival-sub	2048	28	0.0ms
ival-sub	1024	164	1.0ms
ival-sub	512	236	1.0ms
ival-sub	256	512	5.0ms

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 2))
▶	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 10 to 8 computations (20% saved)

localize34.0ms (0.9%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	256	1024	1.0ms
ival-div	256	512	5.0ms
ival-tan	256	256	6.0ms

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)

regimes6.0ms (0.2%)

Accuracy

Total -30.8b remaining (-∞%)

Threshold costs -30.8b (-∞%)

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:

3.0ms	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 22 to 16 computations (27.3% saved)

simplify4.0ms (0.1%)

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)

soundness102.0ms (2.8%)

Rules

750×	`fma-def`
410×	`div-sub`
200×	`associate-/r*`
176×	`associate-/l*`
118×	`sub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	41	60
2	66	56
3	140	56
4	323	56
5	730	56
6	1382	56
7	1766	56
8	1847	56
9	1924	56
10	1975	56
11	1987	56

Stop Event

1×

saturated

Compiler

Compiled 12 to 9 computations (25% saved)

end0.0ms (0%)

preprocess34.0ms (0.9%)

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

analyze185.0ms (5.1%)

sample3.0s (84%)

preprocess211.0ms (5.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize34.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes6.0ms (0.2%)

simplify4.0ms (0.1%)

soundness102.0ms (2.8%)

end0.0ms (0%)

preprocess34.0ms (0.9%)

Profiling