Exp of sum of logs

Time bar (total: 2.1s)

analyze1.0ms (0%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
100%25%0%0.1%0%74.9%0%3
Compiler

Compiled 8 to 8 computations (0% saved)

sample1.2s (57%)

Samples
996.0ms8 255×0valid
0.0ms1valid
Precisions
Click to see histograms. Total time spent on operations: 574.0ms
ival-log: 399.0ms (69.5% of total)
ival-exp: 104.0ms (18.1% of total)
ival-add: 60.0ms (10.5% of total)
ival-true: 6.0ms (1% of total)
ival-assert: 4.0ms (0.7% of total)
adjust: 0.0ms (0% of total)
Bogosity

preprocess304.0ms (14.4%)

Algorithm
egg-herbie
Rules
23×fma-define
16×fmm-def
14×distribute-lft-neg-in
neg-sub0
neg-mul-1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
024183
14499
27799
311899
419199
521999
Stop Event
saturated
Calls
Call 1
Inputs
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(exp.f64 (+.f64 (log.f64 (neg.f64 a)) (log.f64 b)))
(exp.f64 (+.f64 (log.f64 a) (log.f64 (neg.f64 b))))
(neg.f64 (exp.f64 (+.f64 (log.f64 (neg.f64 a)) (log.f64 b))))
(neg.f64 (exp.f64 (+.f64 (log.f64 a) (log.f64 (neg.f64 b)))))
(exp.f64 (+.f64 (log.f64 b) (log.f64 a)))
Outputs
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(*.f64 b a)
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(*.f64 b a)
(exp.f64 (+.f64 (log.f64 (neg.f64 a)) (log.f64 b)))
(exp.f64 (+.f64 (log.f64 b) (log.f64 (neg.f64 a))))
(*.f64 b (neg.f64 a))
(exp.f64 (+.f64 (log.f64 a) (log.f64 (neg.f64 b))))
(exp.f64 (+.f64 (log.f64 b) (log.f64 (neg.f64 a))))
(*.f64 b (neg.f64 a))
(neg.f64 (exp.f64 (+.f64 (log.f64 (neg.f64 a)) (log.f64 b))))
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(*.f64 b a)
(neg.f64 (exp.f64 (+.f64 (log.f64 a) (log.f64 (neg.f64 b)))))
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(*.f64 b a)
(exp.f64 (+.f64 (log.f64 b) (log.f64 a)))
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
(*.f64 b a)
Symmetry

(negabs a)

(negabs b)

(sort a b)

explain99.0ms (4.7%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
14921(4.0286143637876665e-286 1.8145939759731626e+79)5(1.2333290479118994e-194 2.4592272073431147e+229)(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
21(4.990530167808975e-114 2.616440858362026e+114)1(5.300301647840877e-165 2.339067631076664e+159)(+.f64 (log.f64 a) (log.f64 b))
00-0-a
00-0-b
00-0-(log.f64 a)
00-0-(log.f64 b)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
exp.f64(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))sensitivity16520
+.f64(+.f64 (log.f64 a) (log.f64 b))cancellation21
Confusion
Predicted +Predicted -
+15020
-1769
Precision
0.8982035928143712
Recall
0.8823529411764706
Confusion?
Predicted +Predicted MaybePredicted -
+150191
-17267
Precision?
0.898936170212766
Recall?
0.9941176470588236
Freqs
test
numberfreq
089
1167
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
34.0ms512×0valid
Compiler

Compiled 54 to 28 computations (48.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-log: 12.0ms (56.7% of total)
ival-exp: 5.0ms (23.6% of total)
ival-add: 3.0ms (14.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 5 to 3 computations (40% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 b a)
Compiler

Compiled 5 to 3 computations (40% saved)

simplify6.0ms (0.3%)

Algorithm
egg-herbie
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 b a)
Rules
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
1921
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 b a)
b
a
Outputs
(*.f64 b a)
b
a

localize10.0ms (0.5%)

Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 b a)
Samples
7.0ms256×0valid
Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-mult: 2.0ms (91.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series14.0ms (0.7%)

Counts
1 → 24
Calls
Call 1
Inputs
#<alt (*.f64 b a)>
Outputs
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
#<alt (*.f64 a b)>
Calls

6 calls:

TimeVariablePointExpression
12.0ms
b
@-inf
(* b a)
1.0ms
a
@-inf
(* b a)
0.0ms
b
@0
(* b a)
0.0ms
b
@inf
(* b a)
0.0ms
a
@0
(* b a)

rewrite285.0ms (13.5%)

Algorithm
batch-egg-rewrite
Rules
502×associate-*r*
437×associate-*l*
251×log1p-expm1-u
251×expm1-log1p-u
247×unpow-prod-down
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
16513
270613
Stop Event
node limit
Counts
1 → 25
Calls
Call 1
Inputs
(*.f64 b a)
Outputs
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 b a))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) (*.f64 #s(literal 2 binary64) a)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) a))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) (+.f64 #s(literal 1 binary64) (*.f64 b a))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) (+.f64 #s(literal 1 binary64) (*.f64 b a))) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64)))
(pow.f64 (*.f64 b a) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 b a)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 b a) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 b a)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 b a)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 b a))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 b a))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 b a)))) (sqrt.f64 (log.f64 (*.f64 b a))))
(sqrt.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))
(fabs.f64 (*.f64 b a))
(log.f64 (pow.f64 (exp.f64 b) a))
(cbrt.f64 (pow.f64 (*.f64 b a) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 b a)))
(log1p.f64 (expm1.f64 (*.f64 b a)))
(exp.f64 (log.f64 (*.f64 b a)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 b a))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (*.f64 b a))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 b a))) #s(literal 2 binary64)))

simplify68.0ms (3.2%)

Algorithm
egg-herbie
Rules
662×cancel-sign-sub-inv
430×sub-neg
429×times-frac
381×prod-exp
306×div-sub
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
080877
1160859
2460845
32198845
44680845
Stop Event
node limit
Counts
49 → 35
Calls
Call 1
Inputs
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 b a))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) (*.f64 #s(literal 2 binary64) a)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) a))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) (+.f64 #s(literal 1 binary64) (*.f64 b a))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) (+.f64 #s(literal 1 binary64) (*.f64 b a))) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64)))
(pow.f64 (*.f64 b a) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 b a)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 b a) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 b a)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 b a)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 b a))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 b a))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 b a)))) (sqrt.f64 (log.f64 (*.f64 b a))))
(sqrt.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))
(fabs.f64 (*.f64 b a))
(log.f64 (pow.f64 (exp.f64 b) a))
(cbrt.f64 (pow.f64 (*.f64 b a) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 b a)))
(log1p.f64 (expm1.f64 (*.f64 b a)))
(exp.f64 (log.f64 (*.f64 b a)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 b a))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (*.f64 b a))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 b a))) #s(literal 2 binary64)))
Outputs
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(*.f64 a b)
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal -1 binary64))
(*.f64 a b)
(+.f64 #s(literal 0 binary64) (*.f64 b a))
(*.f64 a b)
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) (*.f64 #s(literal 2 binary64) a)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) a))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) (*.f64 a #s(literal 2 binary64))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) a))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 b) (*.f64 a #s(literal 2 binary64))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 a) b))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))))
(*.f64 #s(literal 2 binary64) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 b) a))))
(*.f64 #s(literal 2 binary64) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a) b))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64))
(*.f64 a b)
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) (+.f64 #s(literal 1 binary64) (*.f64 b a))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64)))))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 a b)) #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 a b)) (+.f64 #s(literal 1 binary64) (*.f64 a b)) (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 a b)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 a b #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (fma.f64 a b #s(literal 1 binary64)) (fma.f64 a b #s(literal 1 binary64)) (+.f64 (*.f64 a b) #s(literal 2 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 a b #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 a b #s(literal 1 binary64)) (fma.f64 a b #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) (+.f64 #s(literal 1 binary64) (*.f64 b a))) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 b a)) #s(literal 1 binary64)))
(*.f64 a b)
(pow.f64 (*.f64 b a) #s(literal 1 binary64))
(*.f64 a b)
(pow.f64 (cbrt.f64 (*.f64 b a)) #s(literal 3 binary64))
(*.f64 a b)
(pow.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 a b)
(pow.f64 (pow.f64 (*.f64 b a) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 a b)
(pow.f64 (sqrt.f64 (*.f64 b a)) #s(literal 2 binary64))
(*.f64 a b)
(pow.f64 (E.f64) (log.f64 (*.f64 b a)))
(*.f64 a b)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 b a))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 b a))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 a b))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 a b))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 b a)))) (sqrt.f64 (log.f64 (*.f64 b a))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 a b)))) (sqrt.f64 (log.f64 (*.f64 a b))))
(sqrt.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))
(*.f64 a b)
(fabs.f64 (*.f64 b a))
(*.f64 a b)
(log.f64 (pow.f64 (exp.f64 b) a))
(*.f64 a b)
(cbrt.f64 (pow.f64 (*.f64 b a) #s(literal 3 binary64)))
(*.f64 a b)
(expm1.f64 (log1p.f64 (*.f64 b a)))
(*.f64 a b)
(log1p.f64 (expm1.f64 (*.f64 b a)))
(*.f64 a b)
(exp.f64 (log.f64 (*.f64 b a)))
(*.f64 a b)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 b a))) #s(literal 3 binary64)))
(*.f64 a b)
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (*.f64 b a))) #s(literal 1/3 binary64)))
(*.f64 a b)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 b a))) #s(literal 2 binary64)))
(*.f64 a b)

eval4.0ms (0.2%)

Compiler

Compiled 371 to 112 computations (69.8% saved)

prune5.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New35035
Fresh000
Picked011
Done000
Total35136
Accuracy
100.0%
Counts
36 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 b a)
Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes39.0ms (1.8%)

Accuracy

Total -4.9b remaining (-∞%)

Threshold costs -4.9b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 b a)
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
Outputs
(*.f64 b a)
Calls

6 calls:

31.0ms
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
2.0ms
(+.f64 (log.f64 a) (log.f64 b))
1.0ms
(log.f64 b)
1.0ms
b
1.0ms
(log.f64 a)
Results
AccuracySegmentsBranch
100.0%1a
100.0%1b
100.0%1(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
100.0%1(+.f64 (log.f64 a) (log.f64 b))
100.0%1(log.f64 a)
100.0%1(log.f64 b)
Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
1913
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 b a)
Outputs
(*.f64 b a)

soundness15.0ms (0.7%)

Rules
23×fma-define
16×fmm-def
14×distribute-lft-neg-in
neg-sub0
neg-mul-1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
024183
14499
27799
311899
419199
521999
Stop Event
done
saturated
Compiler

Compiled 34 to 16 computations (52.9% saved)

preprocess54.0ms (2.6%)

Remove

(sort a b)

(negabs b)

(negabs a)

Compiler

Compiled 96 to 60 computations (37.5% saved)

end0.0ms (0%)

Profiling

Loading profile data...