Average Error: 14.4 → 0.4
Time: 12.7s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{y} = -\infty:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{z}{y} \le -4.947837546529902 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{z}{y} \le 1.0525424528083991 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{z}{y} \le 6.072183029885763 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 2 regimes

  2. if (/ z y) or -4.947837546529902e-208 < (/ z y) < 1.0525424528083991e-297 or 6.072183029885763e+171 < (/ z y)

    1. Initial program 24.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Applied simplify18.2

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

    4. Applied associate-/r/0.9

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y}\]

    if (/ z y) < -4.947837546529902e-208 or 1.0525424528083991e-297 < (/ z y) < 6.072183029885763e+171

    1. Initial program 9.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Applied simplify0.2

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 12.7s)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))