Error

Try it out

Derivation

1. Split input into 2 regimes

2. if x < -5.762898133811914e-43 or 1.556736452891557e-58 < x

   1. Initial program 0.3

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
   2. Using strategy rm

   3. Applied div-inv0.4

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]

   4. Applied associate-*l*0.4

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]

   5. Applied simplify0.3

      \[\leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\frac{z}{y}}\right|\]

   if -5.762898133811914e-43 < x < 1.556736452891557e-58

   1. Initial program 2.9

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
   2. Using strategy rm

   3. Applied associate-*l/0.1

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
3. Recombined 2 regimes into one program.

4. Applied simplify0.2

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;x \le -5.762898133811914 \cdot 10^{-43} \lor \neg \left(x \le 1.556736452891557 \cdot 10^{-58}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z \cdot x}{y}\right|\\ \end{array}}\]

Runtime

Time bar (total: 31.5s)Debug logProfile

herbie shell --seed 2018170 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))