Average Error: 2.4 → 0.1
Time: 1.4m
Precision: 64
Internal Precision: 320
\[\frac{\log \left(e^{23 \cdot x + y} \cdot 2\right)}{\log 14}\]
\[\frac{\left(x \cdot 23 + y\right) \cdot \left(x \cdot 23 + y\right) - \log 2 \cdot \log 2}{\log 14 \cdot \left(\left(x \cdot 23 + y\right) - \log 2\right)}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 2.4

    \[\frac{\log \left(e^{23 \cdot x + y} \cdot 2\right)}{\log 14}\]
  2. Applied simplify0.1

    \[\leadsto \color{blue}{\frac{\left(x \cdot 23 + y\right) + \log 2}{\log 14}}\]
  3. Using strategy rm
  4. Applied flip-+0.1

    \[\leadsto \frac{\color{blue}{\frac{\left(x \cdot 23 + y\right) \cdot \left(x \cdot 23 + y\right) - \log 2 \cdot \log 2}{\left(x \cdot 23 + y\right) - \log 2}}}{\log 14}\]
  5. Applied associate-/l/0.1

    \[\leadsto \color{blue}{\frac{\left(x \cdot 23 + y\right) \cdot \left(x \cdot 23 + y\right) - \log 2 \cdot \log 2}{\log 14 \cdot \left(\left(x \cdot 23 + y\right) - \log 2\right)}}\]

Runtime

Time bar (total: 1.4m)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name "log(exp(23 * x + y) * 2) / log(14)"
  (/ (log (* (exp (+ (* 23 x) y)) 2)) (log 14)))