Average Error: 1.5 → 0.5
Time: 50.6s
Precision: 64
Internal Precision: 384
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \cdot z \le -1.6745187988148798 \cdot 10^{+98}:\\ \;\;\;\;\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{if}\;\frac{x}{y} \cdot z \le 1.339208402867 \cdot 10^{+105}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Split input into 2 regimes

  2. if (* (/ x y) z) < -1.6745187988148798e+98 or 1.339208402867e+105 < (* (/ x y) z)

    1. Initial program 0.2

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

    3. Applied div-inv0.2

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

    if -1.6745187988148798e+98 < (* (/ x y) z) < 1.339208402867e+105

    1. Initial program 1.9

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

    3. Applied div-inv1.9

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

    4. Applied associate-*l*0.6

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

    5. Applied simplify0.5

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

Runtime

Time bar (total: 50.6s)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))