Hyperbolic secant

Details

Time bar (total: 1.4s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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)

sample708.0ms (50.5%)

Results
695.0ms8256×body256valid
Bogosity

preprocess93.0ms (6.7%)

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)

IterNodesCost
01025
11725
22325
33025
45025
59025
618725
743125
8116125
9295125
10413925
11531125
12699425
011
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)

simplify90.0ms (6.4%)

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)

IterNodesCost
01025
11725
22325
33025
45025
59025
618725
743125
8116125
9295125
10413925
11531125
12699425
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 (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Accurracy
100.0%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶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)

localize32.0ms (2.3%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓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 → 12
Calls

3 calls:

TimeVariablePointExpression
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))))

rewrite32.0ms (2.3%)

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)

IterNodesCost
01017
121617
2334017
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

simplify76.0ms (5.4%)

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)

IterNodesCost
046318
180314
2144310
3365306
41267306
53171306
64352306
77244306
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 (0.4%)

Compiler

Compiled 210 to 157 computations (25.2% saved)

prune5.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New30333
Fresh000
Picked101
Done000
Total31334
Accurracy
100.0%
Counts
34 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
▶58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
Compiler

Compiled 24 to 20 computations (16.7% saved)

localize30.0ms (2.1%)

Compiler

Compiled 20 to 11 computations (45% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New000
Fresh022
Picked011
Done000
Total033
Accurracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
✓58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
Compiler

Compiled 24 to 20 computations (16.7% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New000
Fresh022
Picked000
Done011
Total033
Accurracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
✓58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
Compiler

Compiled 24 to 20 computations (16.7% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New000
Fresh022
Picked000
Done011
Total033
Accurracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓58.3%
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
58.6%
1
44.4%
0
Compiler

Compiled 30 to 24 computations (20% saved)

regimes9.0ms (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:

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
AccuracySegmentsBranch
100.0%1x
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)

regimes11.0ms (0.8%)

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:

10.0ms
x
Results
AccuracySegmentsBranch
100.0%3x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes9.0ms (0.6%)

Counts
2 → 3
Calls
Call 1
Inputs
0
1
Outputs
0
1
0
Calls

1 calls:

8.0ms
x
Results
AccuracySegmentsBranch
99.9%3x
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:

2.0ms
x
Results
AccuracySegmentsBranch
44.4%1x
Compiler

Compiled 4 to 3 computations (25% saved)

bsearch39.0ms (2.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
20.0ms
2.154928189181266e-19
52253311069679.18
19.0ms
-507413915.4918772
-1.0567315237920714e-5
Results
35.0ms336×body256valid
Compiler

Compiled 265 to 220 computations (17% saved)

bsearch39.0ms (2.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
19.0ms
2.154928189181266e-19
52253311069679.18
20.0ms
-507413915.4918772
-1.0567315237920714e-5
Results
36.0ms336×body256valid
Compiler

Compiled 139 to 136 computations (2.2% saved)

simplify6.0ms (0.4%)

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)

IterNodesCost
03186
14686
24886
34986
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 -350) 0 (if (<=.f64 x 360) 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 -350) 0 (if (<=.f64 x 360) 1 0))
0
Compiler

Compiled 41 to 33 computations (19.5% saved)

soundness141.0ms (10.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
121617
2334017
046318
180314
2144310
3365306
41267306
53171306
64352306
77244306
Stop Event
1×node limit
1×unsound
Compiler

Compiled 15 to 12 computations (20% saved)

end63.0ms (4.5%)

Compiler

Compiled 94 to 74 computations (21.3% saved)

Profiling

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