Average Error: 13.5 → 0.3
Time: 37.7s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{y} = -\infty:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{z}{y} \le -8.798247200565599 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{z}{y} \le 2.8879472012504446 \cdot 10^{-253}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{z}{y} \le 1.3145792709569102 \cdot 10^{+294}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 (/ z y) < -inf.0 or -8.798247200565599e-169 < (/ z y) < 2.8879472012504446e-253 or 1.3145792709569102e+294 < (/ z y)

    1. Initial program 27.2

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

    2. Applied simplify21.4

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

    4. Applied associate-*r/0.5

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

    if -inf.0 < (/ z y) < -8.798247200565599e-169

    1. Initial program 7.5

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

    2. Applied simplify0.2

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

    if 2.8879472012504446e-253 < (/ z y) < 1.3145792709569102e+294

    1. Initial program 9.4

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

    2. Applied simplify0.2

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

    4. Applied associate-*r/7.8

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

    6. Applied associate-/l*0.2

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

Runtime

Time bar (total: 37.7s)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' +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)))