Numeric.Log:$clog1p from log-domain-0.10.2.1, A

Details

Time bar (total: 1.8s)

analyze0.0ms (0%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (59.8%)

Results
643.0ms4620×body256valid
402.0ms3636×body256infinite
Bogosity

preprocess14.0ms (0.8%)

Algorithm
egg-herbie
Rules
52×fma-def
22×+-commutative
12×associate-+r+
12×associate-+l+
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01350
13042
26442
37842
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
(+.f64 (+.f64 (*.f64 y 2) (*.f64 y y)) (*.f64 x x))
Outputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))
(+.f64 (+.f64 (*.f64 y 2) (*.f64 y y)) (*.f64 x x))
(+.f64 (*.f64 x x) (*.f64 y (+.f64 2 y)))
(fma.f64 y (+.f64 2 y) (*.f64 x x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify56.0ms (3.2%)

Algorithm
egg-herbie
Rules
28×fma-def
12×+-commutative
associate-+r+
associate-+l+
*-commutative
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01025
11921
23621
34421
Stop Event
saturated
Counts
1 → 3
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
Outputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))

eval1.0ms (0%)

Compiler

Compiled 30 to 15 computations (50% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New123
Fresh011
Picked000
Done000
Total134
Accurracy
100.0%
Counts
4 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
100.0%
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
100.0%
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
100.0%
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
Compiler

Compiled 48 to 30 computations (37.5% saved)

localize85.0ms (4.8%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
100.0%
(*.f64 x (+.f64 2 x))
Compiler

Compiled 56 to 25 computations (55.4% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(*.f64 x (+.f64 2 x))
0.0ms
x
@inf
(*.f64 x (+.f64 2 x))
0.0ms
x
@0
(*.f64 x (+.f64 2 x))

rewrite84.0ms (4.7%)

Algorithm
batch-egg-rewrite
Rules
1398×pow1
1306×add-exp-log
1304×log1p-expm1-u
1304×expm1-log1p-u
1286×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
113413
2174313
Stop Event
node limit
Counts
1 → 22
Calls
Call 1
Inputs
(*.f64 x (+.f64 2 x))
Outputs
(+.f64 (*.f64 x x) (*.f64 x 2))
(+.f64 (*.f64 x 2) (*.f64 x x))
(+.f64 (*.f64 (*.f64 x 2) 1) (*.f64 (*.f64 x x) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 2) 3) (pow.f64 (*.f64 x x) 3)) (+.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x 2) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 x 2) (*.f64 x x)))
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (*.f64 x (-.f64 x 2))))
(/.f64 (*.f64 x (-.f64 4 (*.f64 x x))) (-.f64 2 x))
(/.f64 (*.f64 (+.f64 (pow.f64 x 3) 8) x) (+.f64 4 (*.f64 x (-.f64 x 2))))
(/.f64 (*.f64 (-.f64 4 (*.f64 x x)) x) (-.f64 2 x))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))

simplify67.0ms (3.8%)

Algorithm
egg-herbie
Rules
1148×associate-*r/
766×associate-*l/
698×times-frac
552×fma-def
540×associate-+r+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
073556
1213516
2786508
33545508
Stop Event
node limit
Counts
34 → 32
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 x x) (*.f64 x 2))
(+.f64 (*.f64 x 2) (*.f64 x x))
(+.f64 (*.f64 (*.f64 x 2) 1) (*.f64 (*.f64 x x) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (+.f64 (pow.f64 (*.f64 x 2) 3) (pow.f64 (*.f64 x x) 3)) (+.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x 2) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 x 2) (*.f64 x x)))
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (*.f64 x (-.f64 x 2))))
(/.f64 (*.f64 x (-.f64 4 (*.f64 x x))) (-.f64 2 x))
(/.f64 (*.f64 (+.f64 (pow.f64 x 3) 8) x) (+.f64 4 (*.f64 x (-.f64 x 2))))
(/.f64 (*.f64 (-.f64 4 (*.f64 x x)) x) (-.f64 2 x))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))
Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 x x) (*.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 x 2) (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 (*.f64 x 2) 1) (*.f64 (*.f64 x x) 1))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (+.f64 (pow.f64 (*.f64 x 2) 3) (pow.f64 (*.f64 x x) 3)) (+.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x 2) (*.f64 x x)))))
(/.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 (*.f64 x x) 3)) (+.f64 (*.f64 (*.f64 x x) 4) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 2 x)))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (*.f64 (*.f64 x x) (fma.f64 x (+.f64 x -2) 4)))
(/.f64 (-.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 x 2) (*.f64 x x)))
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (*.f64 x (-.f64 x 2))))
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (*.f64 x (+.f64 x -2))))
(/.f64 (+.f64 (pow.f64 x 4) (*.f64 x 8)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 x (-.f64 4 (*.f64 x x))) (-.f64 2 x))
(*.f64 x (+.f64 2 x))
(/.f64 (*.f64 (+.f64 (pow.f64 x 3) 8) x) (+.f64 4 (*.f64 x (-.f64 x 2))))
(/.f64 (*.f64 x (+.f64 (pow.f64 x 3) 8)) (+.f64 4 (*.f64 x (+.f64 x -2))))
(/.f64 (+.f64 (pow.f64 x 4) (*.f64 x 8)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 (-.f64 4 (*.f64 x x)) x) (-.f64 2 x))
(*.f64 x (+.f64 2 x))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(*.f64 x (+.f64 2 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(*.f64 x (+.f64 2 x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(*.f64 x (+.f64 2 x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(*.f64 x (+.f64 2 x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(fma.f64 x 2 (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

eval7.0ms (0.4%)

Compiler

Compiled 473 to 248 computations (47.6% saved)

prune6.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New30232
Fresh000
Picked022
Done000
Total30434
Accurracy
100.0%
Counts
34 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
100.0%
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
80.4%
(+.f64 (*.f64 x x) (*.f64 y y))
60.3%
(+.f64 (*.f64 2 x) (*.f64 y y))
100.0%
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
100.0%
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
80.4%
(+.f64 (*.f64 x x) (*.f64 y y))
60.3%
(+.f64 (*.f64 2 x) (*.f64 y y))
Compiler

Compiled 84 to 52 computations (38.1% saved)

localize34.0ms (1.9%)

Compiler

Compiled 34 to 12 computations (64.7% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New000
Fresh000
Picked022
Done022
Total044
Accurracy
100.0%
Counts
4 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
100.0%
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
80.4%
(+.f64 (*.f64 x x) (*.f64 y y))
60.3%
(+.f64 (*.f64 2 x) (*.f64 y y))
Compiler

Compiled 78 to 42 computations (46.2% saved)

regimes17.0ms (1%)

Counts
4 → 1
Calls
Call 1
Inputs
(+.f64 (*.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 y y))
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
Outputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
Calls

5 calls:

3.0ms
y
3.0ms
x
3.0ms
(+.f64 (*.f64 x 2) (*.f64 x x))
3.0ms
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
3.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
100.0%1(+.f64 (*.f64 x 2) (*.f64 x x))
100.0%1(*.f64 y y)
Compiler

Compiled 69 to 37 computations (46.4% saved)

regimes14.0ms (0.8%)

Counts
3 → 1
Calls
Call 1
Inputs
(+.f64 (*.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 y y))
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
Outputs
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
Calls

3 calls:

7.0ms
(*.f64 y y)
3.0ms
y
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(*.f64 y y)
Compiler

Compiled 36 to 19 computations (47.2% saved)

regimes34.0ms (1.9%)

Counts
2 → 3
Calls
Call 1
Inputs
(+.f64 (*.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 y y))
Outputs
(+.f64 (*.f64 x x) (*.f64 y y))
(+.f64 (*.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 x x) (*.f64 y y))
Calls

3 calls:

14.0ms
y
11.0ms
(*.f64 y y)
8.0ms
x
Results
AccuracySegmentsBranch
98.9%3x
84.0%5y
83.7%3(*.f64 y y)
Compiler

Compiled 27 to 15 computations (44.4% saved)

regimes56.0ms (3.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(+.f64 (*.f64 2 x) (*.f64 y y))
Outputs
(+.f64 (*.f64 2 x) (*.f64 y y))
Calls

3 calls:

51.0ms
x
2.0ms
y
2.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
60.3%1y
60.3%1(*.f64 y y)
60.3%1x
Compiler

Compiled 20 to 13 computations (35% saved)

bsearch30.0ms (1.7%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
13.0ms
0.18856910404413843
14.426936015121045
17.0ms
-4008537484.6315513
-0.026629370372996623
Results
22.0ms209×body256valid
6.0ms63×body256infinite
Compiler

Compiled 358 to 233 computations (34.9% saved)

simplify6.0ms (0.3%)

Algorithm
egg-herbie
Rules
12×+-commutative
*-commutative
if-if-or-not
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024138
138138
Stop Event
done
saturated
Calls
Call 1
Inputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
(if (<=.f64 x -2) (+.f64 (*.f64 x x) (*.f64 y y)) (if (<=.f64 x 2) (+.f64 (*.f64 2 x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))))
(+.f64 (*.f64 2 x) (*.f64 y y))
Outputs
(+.f64 (+.f64 (*.f64 x 2) (*.f64 x x)) (*.f64 y y))
(+.f64 (+.f64 (*.f64 x x) (*.f64 x 2)) (*.f64 y y))
(+.f64 (*.f64 x (+.f64 2 x)) (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))
(if (<=.f64 x -2) (+.f64 (*.f64 x x) (*.f64 y y)) (if (<=.f64 x 2) (+.f64 (*.f64 2 x) (*.f64 y y)) (+.f64 (*.f64 x x) (*.f64 y y))))
(if (or (<=.f64 x -2) (not (<=.f64 x 2))) (+.f64 (*.f64 x x) (*.f64 y y)) (+.f64 (*.f64 y y) (*.f64 x 2)))
(+.f64 (*.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 y y) (*.f64 x 2))
Compiler

Compiled 58 to 36 computations (37.9% saved)

soundness83.0ms (4.7%)

Rules
1148×associate-*r/
766×associate-*l/
698×times-frac
552×fma-def
540×associate-+r+
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01025
11921
23621
34421
073556
1213516
2786508
33545508
Stop Event
node limit
saturated
Compiler

Compiled 38 to 20 computations (47.4% saved)

end111.0ms (6.3%)

Compiler

Compiled 156 to 84 computations (46.2% saved)

Profiling

Loading profile data...