Average Error: 13.9 → 0.5
Time: 13.3s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{z} = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{x}{z} \le -6.144498705814999 \cdot 10^{-237}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{x}{z} \le 1.0319684037201142 \cdot 10^{-244}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\frac{x}{z} \le 3.2325387953513304 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 3 regimes

  2. if (/ x z)

    1. Initial program 5.9

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

    2. Applied simplify0.3

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

    4. Applied div-inv0.4

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}}\]

    5. Applied simplify0.3

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

    if (/ x z) < -6.144498705814999e-237 or 1.0319684037201142e-244 < (/ x z) < 3.2325387953513304e+150

    1. Initial program 17.9

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

    2. Applied simplify8.2

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

    4. Applied associate-/r/0.2

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

    if -6.144498705814999e-237 < (/ x z) < 1.0319684037201142e-244 or 3.2325387953513304e+150 < (/ x z)

    1. Initial program 6.3

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

    2. Applied simplify0.7

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

    3. Taylor expanded around 0 1.0

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

Runtime

Time bar (total: 13.3s)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))