Metrics for Hyperbolic secant

analyze0.0ms (0%)

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
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample797.0ms (54.5%)

Results

786.0ms

8256×

body

256

valid

Bogosity

preprocess156.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

1900×	`fma-def`
826×	`fabs-mul`
624×	`swap-sqr`
592×	`*-commutative`
446×	`fabs-div`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	33	124
2	59	124
3	92	124
4	166	124
5	331	124
6	850	124
7	2446	124
8	3669	124
9	4774	124
10	6716	124

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Symmetry

(abs x)

Compiler

Compiled 34 to 16 computations (52.9% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize30.0ms (2.1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 25 to 9 computations (64% saved)

series2.0ms (0.1%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	inf	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	0	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite136.0ms (9.3%)

Algorithm

1×	batch-egg-rewrite

Rules

94×	`associate-r`
62×	`add-exp-log`
62×	`add-log-exp`
62×	`log1p-expm1-u`
62×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2329	20

Stop Event

1×

unsound

Counts

1 → 10

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
-4
-2
-1
0
1/2
1
3/2
2
3
4

simplify82.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1434×	`fma-def`
778×	`distribute-lft-out`
652×	`*-commutative`
572×	`unswap-sqr`
560×	`associate-/l/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	252
1	72	248
2	137	244
3	358	240
4	1245	240
5	3156	240
6	4166	240
7	6469	240

Stop Event

1×	node limit

Counts

18 → 24

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
-4
-2
-1
0
1/2
1
3/2
2
3
4

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (*.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (fma.f64 5/24 (pow.f64 x 4) 1)))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 5/24 -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) 1)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
-4
-2
-1
0
1/2
1
3/2
2
3
4

eval6.0ms (0.4%)

Compiler: Compiled 195 to 161 computations (17.4% saved)

prune6.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Accuracy

100.0%

Counts

25 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0

Compiler

Compiled 46 to 40 computations (13% saved)

localize36.0ms (2.5%)

Compiler: Compiled 21 to 17 computations (19% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0

Compiler

Compiled 46 to 40 computations (13% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	0	0
Done	2	2
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0

Compiler

Compiled 46 to 40 computations (13% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	0	0
Done	2	2
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	53.1%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
	53.5%	1
	11.4%	1/2
	48.5%	0

Compiler

Compiled 42 to 36 computations (14.3% saved)

regimes11.0ms (0.8%)

Counts

5 → 1

Calls

Call 1

Inputs
0
1/2
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Calls

3 calls:

6.0ms	x
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
100.0%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 37 to 29 computations (21.6% saved)

regimes8.0ms (0.5%)

Counts

4 → 2

Calls

Call 1

Inputs
0
1/2
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))

Outputs
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes7.0ms (0.5%)

Counts

3 → 2

Calls

Call 1

Inputs
0
1/2
1

Outputs
1
0

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.9%	2	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes11.0ms (0.8%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1/2

Outputs
1/2
0

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
56.8%	2	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
48.5%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch14.0ms (1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.15519736566550835	11.911189989890259

Results

13.0ms

112×

body

256

valid

Compiler

Compiled 97 to 87 computations (10.3% saved)

bsearch14.0ms (0.9%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	11.911189989890259	924.0736630780995

Results

12.0ms

112×

body

256

valid

Compiler

Compiled 55 to 52 computations (5.5% saved)

bsearch16.0ms (1.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	11.911189989890259	924.0736630780995

Results

15.0ms

112×

body

256

valid

Compiler

Compiled 55 to 52 computations (5.5% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`*-commutative`
3×	`1-exp`
2×	`sub-neg`
2×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	95
1	39	95
2	41	95
3	42	95

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 6530219459687219/4503599627370496) (+.f64 1 (*.f64 -1/2 (pow.f64 x 2))) 0)
(if (<=.f64 x 360) 1 0)
(if (<=.f64 x 360) 1/2 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 6530219459687219/4503599627370496) (+.f64 1 (*.f64 -1/2 (pow.f64 x 2))) 0)
(if (<=.f64 x 360) 1 0)
(if (<=.f64 x 360) 1/2 0)
0

Compiler

Compiled 38 to 32 computations (15.8% saved)

soundness66.0ms (4.5%)

Rules

94×	`associate-r`
94×	`associate-r`
62×	`add-exp-log`
62×	`add-log-exp`
62×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2329	20
0	12	20
1	144	20
2	2329	20

Stop Event

1×	unsound
1×	unsound

end0.0ms (0%)

preprocess46.0ms (3.1%)

Remove: (abs x)
Compiler: Compiled 140 to 112 computations (20% saved)

analyze0.0ms (0%)

sample797.0ms (54.5%)

preprocess156.0ms (10.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize30.0ms (2.1%)

series2.0ms (0.1%)

rewrite136.0ms (9.3%)

simplify82.0ms (5.6%)

eval6.0ms (0.4%)

prune6.0ms (0.4%)

localize36.0ms (2.5%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes11.0ms (0.8%)

regimes8.0ms (0.5%)

regimes7.0ms (0.5%)

regimes11.0ms (0.8%)

regimes3.0ms (0.2%)

bsearch14.0ms (1%)

bsearch14.0ms (0.9%)

bsearch16.0ms (1.1%)

simplify5.0ms (0.3%)

soundness66.0ms (4.5%)

end0.0ms (0%)

preprocess46.0ms (3.1%)

Profiling