Average Error: 30.0 → 27.5
Time: 10.3s
Precision: 64
Internal Precision: 1344
\[\mathsf{j0} x - \mathsf{j0} \left(x + 1\right)\]
\[\mathsf{j0} x - \sqrt[3]{\log \left(e^{\mathsf{j0} \left(x + 1\right)}\right) \cdot \left(\log \left(e^{\mathsf{j0} \left(x + 1\right)}\right) \cdot \log \left(e^{\mathsf{j0} \left(x + 1\right)}\right)\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 30.0

    \[\mathsf{j0} x - \mathsf{j0} \left(x + 1\right)\]
  2. Using strategy rm
  3. Applied add-log-exp28.0

    \[\leadsto \mathsf{j0} x - \color{blue}{\log \left(e^{\mathsf{j0} \left(x + 1\right)}\right)}\]
  4. Using strategy rm
  5. Applied add-cbrt-cube27.5

    \[\leadsto \mathsf{j0} x - \color{blue}{\sqrt[3]{\left(\log \left(e^{\mathsf{j0} \left(x + 1\right)}\right) \cdot \log \left(e^{\mathsf{j0} \left(x + 1\right)}\right)\right) \cdot \log \left(e^{\mathsf{j0} \left(x + 1\right)}\right)}}\]
  6. Final simplification27.5

    \[\leadsto \mathsf{j0} x - \sqrt[3]{\log \left(e^{\mathsf{j0} \left(x + 1\right)}\right) \cdot \left(\log \left(e^{\mathsf{j0} \left(x + 1\right)}\right) \cdot \log \left(e^{\mathsf{j0} \left(x + 1\right)}\right)\right)}\]

Runtime

Time bar (total: 10.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "j0(x)-j0(x+1)"
  (- (j0 x) (j0 (+ x 1))))