Average Error: 0.4 → 0.4
Time: 1.1m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot y - 1}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - 1}\]
↓
\[e^{-\log \left(1 + y \cdot x\right)} \cdot 1\]

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.4

    \[\frac{x \cdot y - 1}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - 1}\]

  2. Applied simplify0.3

    \[\leadsto \color{blue}{\frac{1}{1 + y \cdot x} \cdot 1}\]
  3. Using strategy rm

  4. Applied add-exp-log0.4

    \[\leadsto \frac{1}{\color{blue}{e^{\log \left(1 + y \cdot x\right)}}} \cdot 1\]

  5. Applied rec-exp0.4

    \[\leadsto \color{blue}{e^{-\log \left(1 + y \cdot x\right)}} \cdot 1\]

Runtime

Time bar (total: 1.1m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (x y)
  :name "sec4-example"
  :pre (and (<= 1.001 x 2) (<= 1.001 y 2))
  (/ (- (* x y) 1) (- (* (* x y) (* x y)) 1)))