Details

analyze1.2s (28%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	199.9%	-99.9%	0%	0%	0%	1
0%	0%	399.8%	-299.8%	0%	0%	0%	2
0%	0%	799.6%	-699.6%	0%	0%	0%	3
0%	0%	1599.2%	-1499.2%	0%	0%	0%	4
0%	0%	3198.4%	-3098.4%	0%	0%	0%	5
0%	0%	6396.9%	-6296.9%	0%	0%	0%	6
0%	0%	12793.8%	-12693.8%	0%	0%	0%	7
0%	0%	25587.5%	-25487.5%	0%	0%	0%	8
0%	0%	51175%	-51075%	0%	0%	0%	9
0%	0%	102350%	-102250%	0%	0%	0%	10
0%	0%	204700%	-204600%	0%	0%	0%	11
0%	0%	409400%	-409300%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample2.1s (49.7%)

Results

945.0ms	5144×	body	256	valid
824.0ms	2062×	body	1024	valid
298.0ms	1050×	body	512	valid

Bogosity

preprocess98.0ms (2.4%)

Algorithm

2×	egg-herbie

Rules

1992×	`fma-def`
868×	`unswap-sqr`
716×	`fabs-mul`
616×	`exp-prod`
544×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	17	25
2	23	25
3	30	25
4	50	25
5	90	25
6	187	25
7	431	25
8	1161	25
9	2951	25
10	4139	25
11	5311	25
12	6994	25
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 10 to 8 computations (20% saved)

simplify91.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1992×	`fma-def`
868×	`unswap-sqr`
716×	`fabs-mul`
616×	`exp-prod`
544×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	17	25
2	23	25
3	30	25
4	50	25
5	90	25
6	187	25
7	431	25
8	1161	25
9	2951	25
10	4139	25
11	5311	25
12	6994	25

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Accurracy

100.0%

Counts

2 → 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)

localize122.0ms (2.9%)

Local Accuracy

Found 1 expressions with local accuracy:

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%)

Counts

1 → 12

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))))

rewrite36.0ms (0.9%)

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

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1444×	`fma-def`
798×	`distribute-lft-out`
694×	`distribute-lft-in`
652×	`*-commutative`
572×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	318
1	80	314
2	144	310
3	365	306
4	1267	306
5	3171	306
6	4352	306
7	7244	306

Stop Event

1×	node limit

Counts

30 → 33

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

eval6.0ms (0.1%)

Compiler: Compiled 210 to 157 computations (25.2% saved)

prune8.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Accurracy

100.0%

Counts

34 → 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%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	52.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	0

Compiler

Compiled 42 to 34 computations (19% saved)

localize94.0ms (2.3%)

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

eval0.0ms (0%)

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

prune3.0ms (0.1%)

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

Accurracy

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%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	52.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	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 (0.1%)

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

Accurracy

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%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	0
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	52.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	0

Compiler

Compiled 42 to 34 computations (19% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune5.0ms (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

Accurracy

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%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	52.6%	1
	49.7%	0

Compiler

Compiled 39 to 31 computations (20.5% saved)

regimes9.0ms (0.2%)

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:

4.0ms	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 36 to 27 computations (25% saved)

regimes13.0ms (0.3%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

Results

Accuracy	Segments	Branch
99.5%	3	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes12.0ms (0.3%)

Counts

2 → 3

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
99.2%	3	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.1%)

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
49.7%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch65.0ms (1.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
34.0ms	1.1641572980082722e-8	687.9969706055459
30.0ms	-1797.6815517814734	-0.01954306293468043

Results

60.0ms

304×

body

256

valid

Compiler

Compiled 241 to 200 computations (17% saved)

bsearch60.0ms (1.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
33.0ms	1.1641572980082722e-8	687.9969706055459
27.0ms	-1797.6815517814734	-0.01954306293468043

Results

56.0ms

304×

body

256

valid

Compiler

Compiled 127 to 124 computations (2.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`if-if-or-not`
4×	`*-commutative`
2×	`sub-neg`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	86
1	46	86
2	48	86
3	49	86

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x -799388933858263/562949953421312) 0 (if (<=.f64 x 3152519739159347/2251799813685248) (+.f64 1 (.f64 -1/2 (.f64 x x))) 0))
(if (<=.f64 x -355) 0 (if (<=.f64 x 350) 1 0))
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x -799388933858263/562949953421312) 0 (if (<=.f64 x 3152519739159347/2251799813685248) (+.f64 1 (.f64 -1/2 (.f64 x x))) 0))
(if (<=.f64 x -355) 0 (if (<=.f64 x 350) 1 0))
0

Compiler

Compiled 41 to 33 computations (19.5% saved)

soundness146.0ms (3.5%)

Rules

1444×	`fma-def`
798×	`distribute-lft-out`
694×	`distribute-lft-in`
652×	`*-commutative`
572×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	216	17
2	3340	17
0	46	318
1	80	314
2	144	310
3	365	306
4	1267	306
5	3171	306
6	4352	306
7	7244	306

Stop Event

1×	node limit
1×	unsound

Compiler

Compiled 15 to 12 computations (20% saved)

end68.0ms (1.6%)

Compiler: Compiled 94 to 74 computations (21.3% saved)

Hyperbolic secant

Details

analyze1.2s (28%)

sample2.1s (49.7%)

preprocess98.0ms (2.4%)

simplify91.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize122.0ms (2.9%)

series2.0ms (0%)

rewrite36.0ms (0.9%)

simplify78.0ms (1.9%)

eval6.0ms (0.1%)

prune8.0ms (0.2%)

localize94.0ms (2.3%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune5.0ms (0.1%)

regimes9.0ms (0.2%)

regimes13.0ms (0.3%)

regimes12.0ms (0.3%)

regimes3.0ms (0.1%)

bsearch65.0ms (1.5%)

bsearch60.0ms (1.4%)

simplify6.0ms (0.1%)

soundness146.0ms (3.5%)

end68.0ms (1.6%)

Profiling