Exp of sum of logs

Time bar (total: 2.0s)

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 9 to 7 computations (22.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-log: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-exp: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.3s (63.9%)

Results
984.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 750.0ms
ival-log: 415.0ms (55.4% of total)
ival-add: 216.0ms (28.8% of total)
ival-exp: 108.0ms (14.4% of total)
const: 8.0ms (1.1% of total)
backward-pass: 3.0ms (0.4% of total)
Bogosity

preprocess61.0ms (3%)

Algorithm
egg-herbie
Rules
23×fma-define
16×fma-neg
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)

explain95.0ms (4.7%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
15324(1.0785869546126283e-236 6.14436490564131e+183)11(1.2953074160150896e-32 1.604297037046556e-10)(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
30-1(3.285357478194726e-247 3.1402601320466296e+242)(+.f64 (log.f64 a) (log.f64 b))
00-0-(log.f64 b)
00-0-(log.f64 a)
00-0-b
00-0-a
Results
58.0ms512×0valid
Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-log: 19.0ms (70% of total)
ival-exp: 5.0ms (18.4% of total)
ival-add: 3.0ms (11.1% of total)
const: 1.0ms (3.7% of total)
backward-pass: 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)

localize46.0ms (2.3%)

Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 b a)
accuracy100.0%
(*.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
Results
36.0ms256×0valid
Compiler

Compiled 8 to 4 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 2.0ms (78% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series3.0ms (0.2%)

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

rewrite326.0ms (16.1%)

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)))

simplify85.0ms (4.2%)

Algorithm
egg-herbie
Rules
663×cancel-sign-sub-inv
433×sub-neg
429×times-frac
381×prod-exp
310×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)

regimes21.0ms (1%)

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:

13.0ms
(exp.f64 (+.f64 (log.f64 a) (log.f64 b)))
2.0ms
(log.f64 a)
2.0ms
(+.f64 (log.f64 a) (log.f64 b))
1.0ms
(log.f64 b)
1.0ms
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×fma-neg
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)

preprocess69.0ms (3.4%)

Remove

(sort a b)

(negabs b)

(negabs a)

Compiler

Compiled 96 to 60 computations (37.5% saved)

end0.0ms (0%)

Profiling

Loading profile data...