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)

sample777.0ms (59.1%)

Results

766.0ms

8256×

body

256

valid

Bogosity

preprocess123.0ms (9.4%)

Algorithm

1×	egg-herbie

Rules

1900×	`fma-def`
826×	`fabs-mul`
628×	`swap-sqr`
598×	`*-commutative`
430×	`fabs-div`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	33	124
2	56	124
3	89	124
4	163	124
5	328	124
6	847	124
7	2438	124
8	3664	124
9	4768	124
10	6711	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%)

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)

localize35.0ms (2.6%)

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))))
0.0ms	x	@	0	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite68.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2330	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

simplify64.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1434×	`fma-def`
762×	`distribute-lft-out`
636×	`*-commutative`
572×	`unswap-sqr`
552×	`associate-/l/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	252
1	69	248
2	134	244
3	354	240
4	1238	240
5	3146	240
6	4139	240
7	6424	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 -61/720 (pow.f64 x 6) (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1)))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 4) -61/720 -1/2) (fma.f64 5/24 (pow.f64 x 4) 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 (0.5%)

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))))
▶	56.7%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
▶	57.2%	1
▶	11.9%	1/2
▶	45.5%	0

Compiler

Compiled 23 to 20 computations (13% saved)

localize37.0ms (2.8%)

Compiler: Compiled 24 to 20 computations (16.7% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	4	4
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))))
✓	56.7%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	57.2%	1
✓	11.9%	1/2
✓	45.5%	0

Compiler

Compiled 42 to 36 computations (14.3% saved)

regimes10.0ms (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:

4.0ms	x
4.0ms	(/.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)

regimes9.0ms (0.7%)

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:

8.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.5%)

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)

regimes8.0ms (0.6%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1/2

Outputs
1/2
0

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
54.2%	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
45.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch19.0ms (1.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.87597363440578e-7	329.4180553761104

Results

15.0ms

144×

body

256

valid

Compiler

Compiled 121 to 109 computations (9.9% saved)

bsearch17.0ms (1.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	329.4180553761104	478149.8119138234

Results

16.0ms

128×

body

256

valid

Compiler

Compiled 61 to 58 computations (4.9% saved)

bsearch17.0ms (1.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	329.4180553761104	478149.8119138234

Results

16.0ms

128×

body

256

valid

Compiler

Compiled 61 to 58 computations (4.9% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	95
1	36	95
2	38	95
3	39	95

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 3152519739159347/2251799813685248) (+.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 3152519739159347/2251799813685248) (+.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)

soundness43.0ms (3.3%)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2330	20
0	12	20
1	144	20
2	2330	20

Stop Event

1×	unsound
1×	unsound

end0.0ms (0%)

preprocess56.0ms (4.3%)

Remove: (abs x)
Compiler: Compiled 104 to 84 computations (19.2% saved)

analyze0.0ms (0%)

sample777.0ms (59.1%)

preprocess123.0ms (9.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize35.0ms (2.6%)

series2.0ms (0.1%)

rewrite68.0ms (5.2%)

simplify64.0ms (4.8%)

eval6.0ms (0.4%)

prune6.0ms (0.5%)

localize37.0ms (2.8%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes10.0ms (0.8%)

regimes9.0ms (0.7%)

regimes7.0ms (0.5%)

regimes8.0ms (0.6%)

regimes3.0ms (0.2%)

bsearch19.0ms (1.4%)

bsearch17.0ms (1.3%)

bsearch17.0ms (1.3%)

simplify4.0ms (0.3%)

soundness43.0ms (3.3%)

end0.0ms (0%)

preprocess56.0ms (4.3%)

Profiling