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)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-div, time spent: 0.0ms, 0.0% of total-time

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation ival-exp, time spent: 0.0ms, 0.0% of total-time

Operation ival-neg, time spent: 0.0ms, 0.0% of total-time

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

sample1.1s (57.9%)

Results

977.0ms	8255×	256	valid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 388.0ms

Operation ival-exp, time spent: 199.0ms, 51.0% of total-time

Operation ival-div, time spent: 81.0ms, 21.0% of total-time

Operation ival-add, time spent: 53.0ms, 14.0% of total-time

Operation ival-neg, time spent: 42.0ms, 11.0% of total-time

Operation const, time spent: 14.0ms, 4.0% of total-time

Bogosity

preprocess260.0ms (14.2%)

Algorithm

1×	egg-herbie

Rules

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

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(exp.f64 (neg.f64 x))`
-	-	`(neg.f64 x)`
-	-	`(exp.f64 x)`
-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
-	-	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
-	-	`2`

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 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

Operation ival-exp, time spent: 58.0ms, 85.0% of total-time

Operation ival-div, time spent: 4.0ms, 6.0% of total-time

Operation ival-add, time spent: 3.0ms, 4.0% of total-time

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize39.0ms (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)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

Operation ival-exp, time spent: 4.0ms, 33.0% of total-time

Operation ival-neg, time spent: 4.0ms, 33.0% of total-time

Operation ival-div, time spent: 2.0ms, 17.0% of total-time

Operation ival-add, time spent: 2.0ms, 17.0% of total-time

Operation const, time spent: 1.0ms, 8.0% of total-time

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))))

rewrite141.0ms (7.7%)

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

simplify85.0ms (4.7%)

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

eval5.0ms (0.3%)

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

prune4.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Accuracy

100.0%

Counts

25 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	52.3%	1
▶	11.1%	1/2
▶	50.4%	0

Compiler

Compiled 15 to 13 computations (13.3% saved)

localize15.0ms (0.8%)

Compiler: Compiled 5 to 5 computations (0% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.0ms
Operation const, time spent: 1.0ms, 158.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	1	1
Total	4	4

Accuracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	52.3%	1
✓	11.1%	1/2
✓	50.4%	0

Compiler

Compiled 27 to 23 computations (14.8% saved)

regimes9.0ms (0.5%)

Counts

4 → 1

Calls

Call 1

Inputs
0
1/2
1
(/.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:

4.0ms	x
3.0ms	(/.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 18 to 13 computations (27.8% saved)

regimes7.0ms (0.4%)

Counts

3 → 2

Calls

Call 1

Inputs
0
1/2
1

Outputs
1
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.4%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1/2

Outputs
1/2
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
58.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% 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
50.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch18.0ms (1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	93.34942227438023	6731.792032642205

Results

15.0ms	111×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 55 to 52 computations (5.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

Operation ival-exp, time spent: 3.0ms, 57.0% of total-time

Operation ival-div, time spent: 1.0ms, 19.0% of total-time

Operation ival-add, time spent: 1.0ms, 19.0% of total-time

Operation ival-neg, time spent: 1.0ms, 19.0% of total-time

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

bsearch15.0ms (0.8%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	93.34942227438023	6731.792032642205

Results

13.0ms	111×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 55 to 52 computations (5.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

Operation ival-exp, time spent: 3.0ms, 60.0% of total-time

Operation ival-div, time spent: 1.0ms, 20.0% of total-time

Operation ival-add, time spent: 1.0ms, 20.0% of total-time

Operation ival-neg, time spent: 1.0ms, 20.0% of total-time

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

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	60
1	30	60
2	32	60
3	33	60

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0

Compiler

Compiled 25 to 21 computations (16% saved)

soundness64.0ms (3.5%)

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%)

preprocess86.0ms (4.7%)

Remove: (abs x)
Compiler: Compiled 116 to 92 computations (20.7% saved)

analyze0.0ms (0%)

sample1.1s (57.9%)

preprocess260.0ms (14.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize39.0ms (2.1%)

series2.0ms (0.1%)

rewrite141.0ms (7.7%)

simplify85.0ms (4.7%)

eval5.0ms (0.3%)

prune4.0ms (0.2%)

localize15.0ms (0.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes9.0ms (0.5%)

regimes7.0ms (0.4%)

regimes7.0ms (0.4%)

regimes3.0ms (0.2%)

bsearch18.0ms (1%)

bsearch15.0ms (0.8%)

simplify4.0ms (0.2%)

soundness64.0ms (3.5%)

end0.0ms (0%)

preprocess86.0ms (4.7%)

Profiling