math.log/2 on complex, real part

Average Error: 32.1 → 17.8

Time: 7.8s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus re

Bits error versus im

Bits error versus base

Derivation

1. Split input into 3 regimes

2. if re < -1.33764999557969208e66

   1. Initial program 46.4

      \[\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 46.4

      \[\leadsto \]

   4. Applied log-prod 46.4

      \[\leadsto \]

   5. Applied distribute-lft-in 46.4

      \[\leadsto \]

   6. Simplified 46.4

      \[\leadsto \]

   7. Taylor expanded around -inf 9.9

      \[\leadsto \]

   8. Simplified 9.9

      \[\leadsto \]

   if -1.33764999557969208e66 < re < 3.53919578709125943e32

   1. Initial program 22.7

      \[\]
   2. Using strategy rm

   3. Applied clear-num 22.8

      \[\leadsto \]

   4. Simplified 22.8

      \[\leadsto \]

   if 3.53919578709125943e32 < re

   1. Initial program 43.5

      \[\]
   2. Using strategy rm

   3. Applied clear-num 43.5

      \[\leadsto \]

   4. Simplified 43.5

      \[\leadsto \]

   5. Taylor expanded around inf 12.1

      \[\leadsto \]

   6. Simplified 12.0

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 17.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (re im base)
  :name "math.log/2 on complex, real part"
  :precision binary64
  (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0))))