Average Error: 5.7 → 0
Time: 4.6s
Precision: 64
Internal Precision: 128
\[e^{\log a + \log b}\]
↓
\[a \cdot b\]

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.7

    \[e^{\log a + \log b}\]

  2. Simplified0

    \[\leadsto \color{blue}{a \cdot b}\]

  3. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

  (exp (+ (log a) (log b))))

Details

Time bar (total: 4.4s)Debug log

sample125.0ms

Algorithm
intervals
Results
1211×(pre true 80)
906×(body nan 80)
305×(body real 80)

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(exp (+ (log a) (log b)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune7.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.2s

Algorithm
intervals
Results
36593×(pre true 80)
27471×(body nan 80)
9122×(body real 80)