Hyperbolic secant

Time bar (total: 2.9s)

analyze0.0ms (0%)

Algorithm
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)

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

sample1.4s (49.4%)

Results
1.4s8255×256valid
0.0ms256valid
Precisions
Click to see histograms. Total time spent on operations: 653.0ms
Operation ival-exp, time spent: 345.0ms, 53.0% of total-time
Operation ival-add, time spent: 130.0ms, 20.0% of total-time
Operation ival-div, time spent: 84.0ms, 13.0% of total-time
Operation ival-neg, time spent: 80.0ms, 12.0% of total-time
Operation const, time spent: 14.0ms, 2.0% of total-time
Bogosity

preprocess141.0ms (4.8%)

Algorithm
egg-herbie
Rules
40×fma-define
40×fmm-def
24×sub-neg
14×distribute-lft-neg-in
14×cancel-sign-sub-inv
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-x
00-0-(exp.f64 (neg.f64 x))
00-0-(neg.f64 x)
00-0-(exp.f64 x)
00-0-(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
00-0-#s(literal 2 binary64)
00-0-(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017124
135124
267124
3113124
4170124
5231124
6286124
7302124
8309124
9320124
10332124
11334124
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
Outputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 #s(literal -2 binary64) (+.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: 22.0ms
Operation ival-exp, time spent: 9.0ms, 42.0% of total-time
Operation ival-div, time spent: 5.0ms, 23.0% of total-time
Operation ival-add, time spent: 3.0ms, 14.0% of total-time
Operation ival-neg, time spent: 2.0ms, 9.0% of total-time
Operation const, time spent: 1.0ms, 5.0% 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
StatusAccuracyProgram
100.0%
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

localize37.0ms (1.3%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
100.0%
(/.f64 #s(literal 2 binary64) (+.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: 10.0ms
Operation ival-exp, time spent: 5.0ms, 50.0% of total-time
Operation ival-div, time spent: 2.0ms, 20.0% of total-time
Operation ival-add, time spent: 2.0ms, 20.0% of total-time
Operation const, time spent: 1.0ms, 10.0% of total-time
Operation ival-neg, time spent: 1.0ms, 10.0% of total-time

series3.0ms (0.1%)

Counts
1 → 8
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))>
Outputs
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
#<alt (/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))>
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/ 2 (+ (exp x) (exp (neg x))))
1.0ms
x
@inf
(/ 2 (+ (exp x) (exp (neg x))))
1.0ms
x
@0
(/ 2 (+ (exp x) (exp (neg x))))

rewrite396.0ms (13.5%)

Algorithm
batch-egg-rewrite
Rules
62×add-exp-log
62×add-log-exp
62×log1p-expm1-u
62×expm1-log1p-u
60×add-cube-cbrt
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
114420
2234320
Stop Event
unsound
Counts
1 → 10
Calls
Call 1
Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
#s(literal -4 binary64)
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 3/2 binary64)
#s(literal 2 binary64)
#s(literal 3 binary64)
#s(literal 4 binary64)

simplify469.0ms (16%)

Algorithm
egg-herbie
Rules
2386×fma-define
583×fmm-def
386×distribute-lft-in
264×associate-+l-
250×distribute-rgt-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037256
168240
2136240
3294240
4582240
5929240
61108240
71587240
82418240
93805240
104690240
115136240
125208240
135216240
145216240
155348240
165404240
175404240
187287240
197287240
207287240
217287240
227287240
237289240
Stop Event
saturated
Counts
18 → 23
Calls
Call 1
Inputs
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
#s(literal -4 binary64)
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 3/2 binary64)
#s(literal 2 binary64)
#s(literal 3 binary64)
#s(literal 4 binary64)
Outputs
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 5/24 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -61/720 binary64))) #s(literal -1/2 binary64))))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal -61/720 binary64) #s(literal 5/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 5/24 binary64) (fma.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal -61/720 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal 5/24 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (*.f64 #s(literal -1 binary64) x))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
#s(literal -4 binary64)
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 0 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 3/2 binary64)
#s(literal 2 binary64)
#s(literal 3 binary64)
#s(literal 4 binary64)

eval65.0ms (2.2%)

Compiler

Compiled 173 to 143 computations (17.3% saved)

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New20323
Fresh000
Picked101
Done000
Total21324
Accuracy
100.0%
Counts
24 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
48.3%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
48.8%
#s(literal 1 binary64)
54.2%
#s(literal 0 binary64)
Compiler

Compiled 12 to 11 computations (8.3% saved)

localize182.0ms (6.2%)

Compiler

Compiled 23 to 19 computations (17.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 145.0ms
Operation ival-pow, time spent: 139.0ms, 96.0% of total-time
Operation ival-mult, time spent: 3.0ms, 2.0% of total-time
Operation const, time spent: 2.0ms, 1.0% of total-time
Operation ival-add, time spent: 2.0ms, 1.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked033
Done000
Total033
Accuracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
48.3%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
48.8%
#s(literal 1 binary64)
54.2%
#s(literal 0 binary64)
Compiler

Compiled 30 to 26 computations (13.3% saved)

regimes4.0ms (0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Calls

3 calls:

2.0ms
x
1.0ms
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 #s(literal 2 binary64) (+.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 (0.3%)

Counts
3 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
Outputs
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(literal 0 binary64)
Calls

1 calls:

9.0ms
x
Results
AccuracySegmentsBranch
100.0%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

Counts
2 → 2
Calls
Call 1
Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
Outputs
#s(literal 1 binary64)
#s(literal 0 binary64)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
99.9%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
Outputs
#s(literal 0 binary64)
Calls

1 calls:

1.0ms
x
Results
AccuracySegmentsBranch
54.2%1x
Compiler

Compiled 2 to 1 computations (50% saved)

bsearch24.0ms (0.8%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
24.0ms
4.780471924983433e-7
69869040.65072925
Results
21.0ms159×256valid
0.0ms256valid
Compiler

Compiled 133 to 120 computations (9.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
Operation ival-exp, time spent: 4.0ms, 52.0% of total-time
Operation ival-div, time spent: 1.0ms, 13.0% of total-time
Operation ival-add, time spent: 1.0ms, 13.0% of total-time
Operation ival-neg, time spent: 1.0ms, 13.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch62.0ms (2.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
62.0ms
4.780471924983433e-7
69869040.65072925
Results
59.0ms159×256valid
0.0ms256valid
Compiler

Compiled 73 to 70 computations (4.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
Operation ival-div, time spent: 41.0ms, 87.0% of total-time
Operation ival-exp, time spent: 4.0ms, 8.0% of total-time
Operation ival-add, time spent: 1.0ms, 2.0% of total-time
Operation ival-neg, time spent: 1.0ms, 2.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

simplify5.0ms (0.2%)

Algorithm
egg-herbie
Rules
1-exp
+-commutative
*-commutative
sub-neg
neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02781
13781
23981
34081
Stop Event
done
saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64))
(if (<=.f64 x #s(literal 350 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
Outputs
(/.f64 #s(literal 2 binary64) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64))
(if (<=.f64 x #s(literal 350 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
Compiler

Compiled 31 to 26 computations (16.1% saved)

soundness32.0ms (1.1%)

Rules
62×add-exp-log
62×add-log-exp
62×log1p-expm1-u
62×expm1-log1p-u
60×add-cube-cbrt
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
114420
2234320
Stop Event
unsound

end0.0ms (0%)

preprocess43.0ms (1.5%)

Compiler

Compiled 152 to 126 computations (17.1% saved)

Profiling

Loading profile data...