Average Error: 14.2 → 0.5
Time: 22.6s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{if}\;\frac{y}{z} \le -1.5451803528438197 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 8.078956323401247 \cdot 10^{+209}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 (/ y z) < -inf.0

    1. Initial program 60.1

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
    2. Applied simplify60.1

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm
    4. Applied associate-*r/0.3

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
    5. Using strategy rm
    6. Applied associate-/l*54.4

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
    7. Using strategy rm
    8. Applied div-inv54.4

      \[\leadsto \frac{x}{\color{blue}{z \cdot \frac{1}{y}}}\]
    9. Applied associate-/r*0.3

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

    if -inf.0 < (/ y z) < -1.5451803528438197e-197 or 0.0 < (/ y z) < 8.078956323401247e+209

    1. Initial program 9.4

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
    2. Applied simplify0.4

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm
    4. Applied associate-*r/8.2

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
    5. Using strategy rm
    6. Applied associate-/l*0.6

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

    if -1.5451803528438197e-197 < (/ y z) < 0.0 or 8.078956323401247e+209 < (/ y z)

    1. Initial program 23.4

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
    2. Applied simplify15.9

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm
    4. Applied associate-*r/0.4

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

Runtime

Time bar (total: 22.6s)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +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)))