Average Error: 30.6 → 0
Time: 1.4s
Precision: 64
Internal Precision: 128
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{re^2 + im^2}^*\right)\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.6

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right)}\]

  3. Final simplification0

    \[\leadsto \log \left(\sqrt{re^2 + im^2}^*\right)\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))

Details

Time bar (total: 1.1s)Debug log

sample23.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

4.0ms
(log (sqrt (+ (* re re) (* im im))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune3.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.1s

Algorithm
intervals