Average Error: 14.1 → 0.8
Time: 17.9s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.448330001222229 \cdot 10^{+248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le -3.0631198141689857 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 2.0561240807536962 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{y}{z} \le 5.206301519867918 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -4.448330001222229e+248 or 5.206301519867918e+229 < (/ y z)

    1. Initial program 43.6

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

    2. Applied simplify31.4

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

    4. Applied associate-*r/0.8

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

    if -4.448330001222229e+248 < (/ y z) < -3.0631198141689857e-91 or 2.0561240807536962e-191 < (/ y z) < 5.206301519867918e+229

    1. Initial program 8.3

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

    2. Applied simplify0.2

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

    if -3.0631198141689857e-91 < (/ y z) < 2.0561240807536962e-191

    1. Initial program 15.4

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

    2. Applied simplify7.7

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

    4. Applied associate-*r/1.7

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

    6. Applied associate-/l*8.3

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

    8. Applied associate-/r/1.7

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

Runtime

Time bar (total: 17.9s)Debug logProfile

herbie shell --seed 2018178 +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)))