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)

sample1.0s (59.6%)

Results

1.0s

8256×

body

256

valid

Bogosity

preprocess102.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

1688×	`fma-def`
864×	`swap-sqr`
832×	`fabs-mul`
708×	`sqr-pow`
586×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	25	75
2	45	75
3	76	75
4	147	75
5	310	75
6	826	75
7	2404	75
8	3614	75
9	4681	75
10	6353	75

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)))))

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))))

Symmetry

(abs x)

Compiler

Compiled 9 to 7 computations (22.2% 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)

localize34.0ms (1.9%)

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))))

rewrite43.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

222×	`add-sqr-sqrt`
210×	`add-exp-log`
210×	`pow1`
210×	`*-un-lft-identity`
208×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	216	17
2	3340	17

Stop Event

1×

unsound

Counts

1 → 18

Calls

Call 1

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

Outputs
-8
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4
8
9
16
27
64
512
x

simplify90.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	218
1	74	214
2	139	210
3	359	206
4	1247	206
5	3148	206
6	4186	206
7	6488	206

Stop Event

1×	node limit

Counts

26 → 35

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))))
-8
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4
8
9
16
27
64
512

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 5/24 (pow.f64 x 4) (fma.f64 -1/2 (*.f64 x x) 1))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) 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 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(fma.f64 x (fma.f64 -1/2 x (*.f64 5/24 (pow.f64 x 3))) (fma.f64 -61/720 (pow.f64 x 6) 1))
(fma.f64 -61/720 (pow.f64 x 6) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) 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))))
-8
-4
-2
-1
-1/2
0
1/2
1
3/2
2
3
4
8
9
16
27
64
512

eval11.0ms (0.6%)

Compiler: Compiled 232 to 165 computations (28.9% saved)

prune11.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	4	36

Accuracy

100.0%

Counts

36 → 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))))
▶	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0

Compiler

Compiled 42 to 34 computations (19% saved)

localize32.0ms (1.9%)

Compiler: Compiled 20 to 11 computations (45% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
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))))
✓	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0

Compiler

Compiled 42 to 34 computations (19% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	2	2
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))))
✓	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0

Compiler

Compiled 42 to 34 computations (19% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	2	2
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))))
✓	57.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	57.3%	1
	45.1%	0

Compiler

Compiled 39 to 31 computations (20.5% saved)

regimes13.0ms (0.7%)

Counts

4 → 1

Calls

Call 1

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

5.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	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 36 to 27 computations (25% saved)

regimes14.0ms (0.8%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.4%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1

Outputs
1
0

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
99.3%	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
45.1%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch20.0ms (1.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	0.40978433406168563	7237.66309684634

Results

18.0ms

128×

body

256

valid

Compiler

Compiled 109 to 90 computations (17.4% saved)

bsearch22.0ms (1.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	0.40978433406168563	7237.66309684634

Results

20.0ms

128×

body

256

valid

Compiler

Compiled 61 to 58 computations (4.9% saved)

simplify10.0ms (0.6%)

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	25	66
1	32	66
2	34	66
3	35	66

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 (.f64 x x))) 0)
(if (<=.f64 x 350) 1 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 6530219459687219/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) 0)
(if (<=.f64 x 350) 1 0)
0

Compiler

Compiled 31 to 25 computations (19.4% saved)

soundness161.0ms (9.3%)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	216	17
2	3340	17
0	42	218
1	74	214
2	139	210
3	359	206
4	1247	206
5	3148	206
6	4186	206
7	6488	206

Stop Event

1×	node limit
1×	unsound

Compiler

Compiled 15 to 12 computations (20% saved)

end0.0ms (0%)

preprocess117.0ms (6.8%)

Remove: (abs x)
Compiler: Compiled 92 to 72 computations (21.7% saved)

analyze0.0ms (0%)

sample1.0s (59.6%)

preprocess102.0ms (5.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize34.0ms (1.9%)

series2.0ms (0.1%)

rewrite43.0ms (2.5%)

simplify90.0ms (5.2%)

eval11.0ms (0.6%)

prune11.0ms (0.6%)

localize32.0ms (1.9%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes13.0ms (0.7%)

regimes14.0ms (0.8%)

regimes7.0ms (0.4%)

regimes3.0ms (0.2%)

bsearch20.0ms (1.2%)

bsearch22.0ms (1.3%)

simplify10.0ms (0.6%)

soundness161.0ms (9.3%)

end0.0ms (0%)

preprocess117.0ms (6.8%)

Profiling